{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"2.3.PCA_applications.ipynb","provenance":[],"collapsed_sections":[]},"kernelspec":{"name":"python3","display_name":"Python 3"}},"cells":[{"cell_type":"markdown","metadata":{"id":"_jz4bCWSk_za"},"source":["# Principal Component Analysis"]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"u4pJqFwZk_zb"},"source":["Ένας από τους ευρύτερα χρησιμοποιούμενους αλγόριθμους μη επιβλεπόμενης μάθησης, είναι η Ανάλυση Κύριων Συνιστωσών (PCA -Principal Component Analysis). \n","Το PCA είναι ένας αλγόριθμος μείωσης διαστάσεων, μια γρήγορη και ευέλικτη μέθοδος χωρίς επίβλεψη για μείωση της διαστατικότητας στα δεδομένα, αλλά μπορεί επίσης να είναι χρήσιμος ως εργαλείο οπτικοποίησης, φιλτραρίσματος θορύβου, εξαγωγής χαρακτηριστικών και πολλά άλλα. \n","\n","Σίγουρα το PCA δεν είναι χρήσιμο για κάθε σύνολο δεδομένων υψηλών διαστάσεων, αλλά προσφέρει μια απλή και αποτελεσματική διαδρομή για την απόκτηση πληροφοριών σχετικά με τα δεδομένα υψηλής διάστασης. \n","\n","Η κύρια αδυναμία του PCA είναι ότι τείνει να επηρεάζεται ιδιαίτερα από τα ακραία σημεία στα δεδομένα. \n","\n","Για αυτόν τον λόγο, έχουν αναπτυχθεί πολλές ισχυρές παραλλαγές του PCA, πολλές από τις οποίες ενεργούν για να απορρίψουν επαναληπτικά σημεία δεδομένων που δεν περιγράφονται καλά από τα αρχικά στοιχεία. \n","\n","Το Scikit-Learn περιέχει μερικές ενδιαφέρουσες παραλλαγές στο PCA, συμπεριλαμβανομένων των \"RandomizedPCA\" και \"SparsePCA\", και οι δύο στο υποσύστημα \"sklearn.decomposition\". \n","Το \"RandomizedPCA\" χρησιμοποιεί μια μη ντετερμινιστική μέθοδο για να προσεγγίσει γρήγορα τα πρώτα βασικά συστατικά σε δεδομένα πολύ υψηλής διαστάσης, ενώ το \"SparsePCA\" εισάγει έναν όρο κανονικοποίησης που χρησιμεύει για την ενίσχυση του sparsity των συστατικών.\n"]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"8sEFKznJk_zc"},"source":["%matplotlib inline\n","import numpy as np\n","import matplotlib.pyplot as plt\n","import seaborn as sns; sns.set()"],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"SjbhI2VRk_zf"},"source":["## Ένα απλό παράδειγμα \n","\n","Έστω ότι έχουμε ένα τυχαίο σύνολο με 200 σημεία:"]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"weGq1MsOk_zg","colab":{"base_uri":"https://localhost:8080/","height":268},"executionInfo":{"status":"ok","timestamp":1604327007015,"user_tz":-120,"elapsed":899,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"6fab3e79-78d4-4352-a58f-5228ad227f0d"},"source":["rng = np.random.RandomState(1)\n","X = np.dot(rng.rand(2, 2), rng.randn(2, 200)).T\n","plt.scatter(X[:, 0], X[:, 1])\n","plt.axis('equal');"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"YkRVzYrJk_zj"},"source":["Με μια πρώτη ματιά φαίνεται ότι υπάρχει σχεδόν γραμμική σχέση μεταξύ των μεταβλητών x και y. Εδώ, αντί να προσπαθούμε να προβλέψουμε τις τιμές y από τις τιμές x, το μη επιτηρούμενης μάθησης πρόβλημα προσπαθεί να μάθει για τη σχέση μεταξύ τις τιμές x και y. \n","\n","Στο PCA αυτή η σχέση ποσοτικοποιείται με την εύρεση μιας λίστας των κύριων αξόνων στα δεδομένα και χρησιμοποιώντας αυτούς τους άξονες περιγράφει το σύνολο δεδομένων. \n","\n","Χρησιμοποιώντας τον εκτιμητή PCA του Scikit-Learn, μπορούμε να το υπολογίσουμε ως εξής:"]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"kMQy8PNDk_zk","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1604327112449,"user_tz":-120,"elapsed":1149,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"b2d6b5d0-bd16-4fb6-c153-19f7da455cf9"},"source":["from sklearn.decomposition import PCA\n","pca = PCA(n_components=2)\n","pca.fit(X)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,\n"," svd_solver='auto', tol=0.0, whiten=False)"]},"metadata":{"tags":[]},"execution_count":3}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"Zg-Ktfesk_zn"},"source":["Κατά την εφαρμογή μαθαίνει κάποιες ποσότητες από τα δεδομένα, το πιο σημαντικό είναι τα \"components\" και η \"explained variance\""]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"pUbsZQwkk_zn","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1604327118142,"user_tz":-120,"elapsed":826,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"2eae9578-c287-4cfa-a718-ee02d10a59b7"},"source":["print(pca.components_)"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[[-0.94446029 -0.32862557]\n"," [-0.32862557 0.94446029]]\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"yNGAgX1Wk_zq","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1604327121247,"user_tz":-120,"elapsed":766,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"802e07b7-bd1b-4f49-adfa-cda7ec5fdb51"},"source":["print(pca.explained_variance_)"],"execution_count":null,"outputs":[{"output_type":"stream","text":["[0.7625315 0.0184779]\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"_c9EoTtok_zt"},"source":["Για να δούμε τι σημαίνουν αυτοί οι αριθμοί, ας τους απεικονίσουμε ως διανύσματα πάνω από τα δεδομένα εισόδου, χρησιμοποιώντας τα \"components\" για να καθορίσουμε την κατεύθυνση του διανύσματος και την \"explained variance\" για να καθορίσουμε το τετράγωνο του μήκους του διανύσματος."]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"AdjCpXyNk_zu","colab":{"base_uri":"https://localhost:8080/","height":268},"executionInfo":{"status":"ok","timestamp":1604327127815,"user_tz":-120,"elapsed":835,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"86990838-719b-4b36-8f44-e39fcefa22f8"},"source":["def draw_vector(v0, v1, ax=None):\n"," ax = ax or plt.gca()\n"," arrowprops=dict(arrowstyle='->',\n"," linewidth=2,\n"," shrinkA=0, shrinkB=0)\n"," ax.annotate('', v1, v0, arrowprops=arrowprops)\n","\n","# plot data\n","plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n","for length, vector in zip(pca.explained_variance_, pca.components_):\n"," v = vector * 3 * np.sqrt(length)\n"," draw_vector(pca.mean_, pca.mean_ + v)\n","plt.axis('equal');"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"SdpDY6zRk_zz"},"source":["Αυτά τα διανύσματα αντιπροσωπεύουν τους *κύριους άξονες* των δεδομένων και το μήκος του διανύσματος είναι μια ένδειξη του πόσο «σημαντικός» είναι αυτός ο άξονας στην περιγραφή της κατανομής των δεδομένων.\n","Η προβολή κάθε σημείου δεδομένων στους κύριους άξονες είναι οι «κύριες συνιστώσες» των δεδομένων.\n"," Εάν σχεδιάσουμε αυτές τις κύριες συνιστώσες εκτός από τα αρχικά δεδομένα, βλέπουμε τις γραφικές παραστάσεις που εμφανίζονται εδώ:"]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"5eu-p-1iMKYo"},"source":["from sklearn.decomposition import PCA"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"a8Aop-nhMKYq"},"source":["def draw_vector(v0, v1, ax=None):\n"," ax = ax or plt.gca()\n"," arrowprops=dict(arrowstyle='->',\n"," linewidth=2,\n"," shrinkA=0, shrinkB=0)\n"," ax.annotate('', v1, v0, arrowprops=arrowprops)"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"7nVbdFIBMKYt","colab":{"base_uri":"https://localhost:8080/","height":502},"executionInfo":{"status":"ok","timestamp":1604327193777,"user_tz":-120,"elapsed":1420,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"156581a4-8114-435b-83ca-8dd0048ec2a1"},"source":["rng = np.random.RandomState(1)\n","X = np.dot(rng.rand(2, 2), rng.randn(2, 200)).T\n","pca = PCA(n_components=2, whiten=True)\n","pca.fit(X)\n","\n","fig, ax = plt.subplots(1, 2, figsize=(16, 6))\n","fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)\n","\n","# plot data\n","ax[0].scatter(X[:, 0], X[:, 1], alpha=0.2)\n","for length, vector in zip(pca.explained_variance_, pca.components_):\n"," v = vector * 3 * np.sqrt(length)\n"," draw_vector(pca.mean_, pca.mean_ + v, ax=ax[0])\n","ax[0].axis('equal');\n","ax[0].set(xlabel='x', ylabel='y', title='input')\n","\n","# plot principal components\n","X_pca = pca.transform(X)\n","ax[1].scatter(X_pca[:, 0], X_pca[:, 1], alpha=0.2)\n","draw_vector([0, 0], [0, 3], ax=ax[1])\n","draw_vector([0, 0], [3, 0], ax=ax[1])\n","ax[1].axis('equal')\n","ax[1].set(xlabel='component 1', ylabel='component 2',\n"," title='principal components',\n"," xlim=(-5, 5), ylim=(-3, 3.1))\n","\n"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["[(-3.0, 3.1),\n"," Text(0, 0.5, 'component 2'),\n"," (-5.0, 5.0),\n"," Text(0.5, 0, 'component 1'),\n"," Text(0.5, 1.0, 'principal components')]"]},"metadata":{"tags":[]},"execution_count":9},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"dHTN9NVkk_z1"},"source":["Αυτός ο μετασχηματισμός από τους άξονες των δεδομένων στους κύριους άξονες είναι ένας *αφινικός μετασχηματισμού *, που ουσιαστικά σημαίνει ότι αποτελείται από μια μετακίνηση, περιστροφή και ομοιόμορφη κλιμάκωση. \n","\n"]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"aNXVt2-Tk_z2"},"source":["### Χρήση PCA για μείωση διαστάσεων\n","\n","Η χρήση PCA για μείωση διαστάσεων συνεπάγεται μηδενισμό ενός ή περισσοτέρων από τις μικρότερες κύριες συνιστώσες, με αποτέλεσμα την προβολή σε λιγότερες διαστάσεων των δεδομένων η οποία διατηρεί τη μέγιστη διακύμανση δεδομένων. \n"," "]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"8aw8vnfFk_z3","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1604327365381,"user_tz":-120,"elapsed":875,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"9936a32b-3d4f-4679-a2c3-3918b31217d3"},"source":["pca = PCA(n_components=1)\n","pca.fit(X)\n","X_pca = pca.transform(X)\n","print(\"original shape: \", X.shape)\n","print(\"transformed shape:\", X_pca.shape)"],"execution_count":null,"outputs":[{"output_type":"stream","text":["original shape: (200, 2)\n","transformed shape: (200, 1)\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"imj3FWOsk_z8"},"source":["Τα μετασχηματισμένα δεδομένα έχουν μειωθεί σε μία μόνο διάσταση. Για να κατανοήσουμε το αποτέλεσμα αυτής της μείωσης διαστάσεων, μπορούμε να πραγματοποιήσουμε τον αντίστροφο μετασχηματισμό αυτών των μειωμένων δεδομένων και να το σχεδιάσουμε μαζί με τα αρχικά δεδομένα:"]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"XoU5FKlSk_z8","colab":{"base_uri":"https://localhost:8080/","height":268},"executionInfo":{"status":"ok","timestamp":1604327367495,"user_tz":-120,"elapsed":857,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"3caa2bea-3b6c-478f-b5c8-4d1f4d1eec15"},"source":["X_new = pca.inverse_transform(X_pca)\n","plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n","plt.scatter(X_new[:, 0], X_new[:, 1], alpha=0.8)\n","plt.axis('equal');"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"bubVxlWCk_z_"},"source":["Τα αρχικά δεδομένα είναι τα μπλε ενώ τα μειωμένα είναι τα πορτοκαλί\n","\n","Βλέπουμε ότι με τo PCA oι πληροφορίες κατά μήκος του λιγότερο σημαντικού κύριου άξονα αφαιρούνται, αφήνοντας μόνο τις κύριες συνιστώσες των δεδομένων με την υψηλότερη διακύμανση.\n","\n","Το κλάσμα διακύμανσης που αποκόπτεται (ανάλογο με την εξάπλωση σημείων σχετικά με τη γραμμή που σχηματίζεται σε αυτό το σχήμα) είναι περίπου ένα μέτρο του πόσο απορρίπτονται οι \"πληροφορίες\" σε αυτή τη μείωση της διαστατικότητας.\n","\n","Αυτό το σύνολο δεδομένων μειωμένης διάστασης είναι κατά κάποιο τρόπο «αρκετά καλό» για να κωδικοποιήσει τις πιο σημαντικές σχέσεις μεταξύ των σημείων: παρά τη μείωση της διάστασης των δεδομένων κατά 50%, η συνολική σχέση μεταξύ των σημείων δεδομένων διατηρείται ως επί το πλείστον.\n"]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"RfTCMvCXk_0A"},"source":["## PCA για οπτικοποίηση: Χειρόγραφα ψηφία\n","\n","Η χρησιμότητα της μείωσης διαστάσεων δεν μπορεί να είναι απολύτως εμφανής μόνο σε δύο διαστάσεις, αλλά γίνεται πολύ πιο ξεκάθαρη όταν εξετάζουμε δεδομένα υψηλών διαστάσεων. \n","\n","Θα δούμε λοιπόν μία εφαρμογή του PCA σε ένα σύνολο από χειρόγραφα ψηφία. "]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"spB3hP8wk_0B","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1604327563475,"user_tz":-120,"elapsed":839,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"3093666e-10e1-45b6-cfb7-12b7ec2d0d90"},"source":["from sklearn.datasets import load_digits\n","digits = load_digits()\n","digits.data.shape"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["(1797, 64)"]},"metadata":{"tags":[]},"execution_count":12}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"PQIpIj8Yk_0E"},"source":["Τα δεδομένα μας είναι 8 × 8 pixel, που σημαίνει ότι είναι 64-διαστάσεων. Για να αποκτήσουμε κάποια διαίσθηση στις σχέσεις μεταξύ αυτών των σημείων, μπορούμε να χρησιμοποιήσουμε το PCA για να τα προβάλουμε σε έναν πιο διαχειρίσιμο αριθμό διαστάσεων, π.χ. 2:"]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"d2Wj1q_fk_0E","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1604327617146,"user_tz":-120,"elapsed":773,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"3742dbcd-06d6-4b2c-a935-ad7e74bea665"},"source":["pca = PCA(2) # project from 64 to 2 dimensions\n","projected = pca.fit_transform(digits.data)\n","print(digits.data.shape)\n","print(projected.shape)"],"execution_count":null,"outputs":[{"output_type":"stream","text":["(1797, 64)\n","(1797, 2)\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"YgVVfJpgk_0H"},"source":["Μπορούμε τώρα να σχεδιάσουμε τις πρώτες δύο κύριες συνιστώσες (principal components) κάθε σημείου για να μάθουμε για τα δεδομένα:"]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"RG6wk0KRk_0I","colab":{"base_uri":"https://localhost:8080/","height":289},"executionInfo":{"status":"ok","timestamp":1604327624759,"user_tz":-120,"elapsed":1891,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"1c0f7303-750e-438c-ffe3-2f199c7d22fb"},"source":["plt.scatter(projected[:, 0], projected[:, 1], c=digits.target, alpha=0.5)\n","plt.xlabel('component 1')\n","plt.ylabel('component 2')\n","plt.colorbar();"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"wQRfJcp0k_0L"},"source":["Τα πλήρη δεδομένα είναι σημεία 64-διαστάσεων και αυτά τα σημεία που βλέπουμε τώρα είναι η προβολή του κάθε σημείου δεδομένων κατά τις κατευθύνσεις με τη μεγαλύτερη διακύμανση. \n","\n","Ουσιαστικά, βρήκαμε τη βέλτιστη έκταση και περιστροφή σε 64-διαστατικό χώρο που μας επιτρέπει να βλέπουμε τη διάταξη των ψηφίων σε δύο διαστάσεις και το έχουμε κάνει με έναν μη επιβλεπόμενο τρόπο - δηλαδή, χωρίς αναφορά στις ετικέτες."]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"W_5VWpZzk_0L"},"source":["**Τι σημαίνουν οι συνιστώσες; Τι σημαίνουν οι μειωμένες διαστάσεις;**\n","\n","Αυτό μπορεί να γίνει κατανοητό μέσω των συνδυασμών διανυσμάτων βάσης.\n","\n","Για παράδειγμα, κάθε εικόνα στο σύνολο εκπαίδευσης καθορίζεται από μια συλλογή τιμών 64 pixel, τις οποίες θα ονομάσουμε διάνυσμα $x$: \n","\n","$$\n","x = [x_1, x_2, x_3 \\cdots x_{64}]\n","$$\n","\n","Ένας τρόπος για να το σκεφτούμε αυτό είναι από την άποψη των pixel. Δηλαδή, για την κατασκευή της εικόνας, πολλαπλασιάζουμε κάθε συνιστώσα του διανύσματος με το pixel που περιγράφει και στη συνέχεια, προσθέτουμε τα αποτελέσματα μαζί για να δημιουργήσουμε την εικόνα:\n","\n","$${\\rm image}(x) = x_1 \\cdot{\\rm (pixel~1)} + x_2 \\cdot{\\rm (pixel~2)} + x_3 \\cdot{\\rm (pixel~3)} \\cdots x_{64} \\cdot{\\rm (pixel~64)}$$\n","\n","Ένας τρόπος που θα μπορούσαμε να φανταστούμε τη μείωση της διάστασης αυτών των δεδομένων είναι να μηδενιστoύν όλα εκτός από μερικά από αυτά τα διανύσματα βάσης. \n","\n","Για παράδειγμα, εάν χρησιμοποιούμε μόνο τα πρώτα οκτώ pixel, έχουμε μια οκταδιάστατη προβολή των δεδομένων,αλλά δεν αντανακλά σε ολόκληρη την εικόνα: έχουμε πετάξει σχεδόν το 90% των pixel!"]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"TdQCSNf4MKYv"},"source":["def plot_pca_components(x, coefficients=None, mean=0, components=None,\n"," imshape=(8, 8), n_components=8, fontsize=12,\n"," show_mean=True):\n"," if coefficients is None:\n"," coefficients = x\n"," \n"," if components is None:\n"," components = np.eye(len(coefficients), len(x))\n"," \n"," mean = np.zeros_like(x) + mean\n"," \n","\n"," fig = plt.figure(figsize=(1.2 * (5 + n_components), 1.2 * 2))\n"," g = plt.GridSpec(2, 4 + bool(show_mean) + n_components, hspace=0.3)\n","\n"," def show(i, j, x, title=None):\n"," ax = fig.add_subplot(g[i, j], xticks=[], yticks=[])\n"," ax.imshow(x.reshape(imshape), interpolation='nearest')\n"," if title:\n"," ax.set_title(title, fontsize=fontsize)\n","\n"," show(slice(2), slice(2), x, \"True\")\n"," \n"," approx = mean.copy()\n"," \n"," counter = 2\n"," if show_mean:\n"," show(0, 2, np.zeros_like(x) + mean, r'$\\mu$')\n"," show(1, 2, approx, r'$1 \\cdot \\mu$')\n"," counter += 1\n","\n"," for i in range(n_components):\n"," approx = approx + coefficients[i] * components[i]\n"," show(0, i + counter, components[i], r'$c_{0}$'.format(i + 1))\n"," show(1, i + counter, approx,\n"," r\"${0:.2f} \\cdot c_{1}$\".format(coefficients[i], i + 1))\n"," if show_mean or i > 0:\n"," plt.gca().text(0, 1.05, '$+$', ha='right', va='bottom',\n"," transform=plt.gca().transAxes, fontsize=fontsize)\n","\n"," show(slice(2), slice(-2, None), approx, \"Approx\")\n"," return fig"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"jFq8mGXJMKYz","colab":{"base_uri":"https://localhost:8080/","height":177},"executionInfo":{"status":"ok","timestamp":1604327903841,"user_tz":-120,"elapsed":2170,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"d7898887-131d-4e19-be38-686f11452ae1"},"source":["from sklearn.datasets import load_digits\n","\n","digits = load_digits()\n","sns.set_style('white')\n","\n","fig = plot_pca_components(digits.data[10],\n"," show_mean=False)\n"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA3AAAACgCAYAAABNPI5lAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAd7ElEQVR4nO3de3QU9R338U+urIBi0ERuVXxaI9FUTJoCAfVUGjCotZiWW0gUKRrxUg4ikKr1UhQEoVZQ8I6RhJ4jApGCYCrPKXJRNAhF+iQKthRBhRgQDZJssv6ePzikRLKXZHYzO5v36xzPSXbmN3zn4283892ZnY0yxhgBAAAAAMJetN0FAAAAAAACQwMHAAAAAA5BAwcAAAAADkEDBwAAAAAOQQMHAAAAAA5BAwcAAAAADkEDBwAAAAAOEWt3AW0tLS2t8efjx48rPj5eMTExkqRHHnlEN9xwg12lAQAAAI6Vn5+vyspKbd68WfHx8XaXE7Ha3Rm47du3N/7Xo0cPPfvss42/n9q8NTQ02FglWmP16tW67rrr1LdvX2VlZWnr1q12lxSWyMk/MgoMOflHRoEhp8CQk39kZJ/9+/ervLxcUVFRWr9+fUj+DY7PT2h3Z+C82bp1q6ZOnaq8vDwVFRVp4MCByszM1LJly/TXv/61cb2LL75YZWVluuCCC+R2u/Xkk09q7dq1crvdysrK0n333SeXy2XjnrRPL7/8spYvX645c+YoJSVFu3fvVqdOnewuK+yQk39kFBhy8o+MAkNOgSEn/8jIXqWlperbt6/69u2r0tJSDRs2TJJUWFio+Ph4ffbZZ9qxY4cuvfRSzZ49Wz179pR04tj6/vvvV1FRkWpqapSTk6OpU6cqOjpaK1as0GuvvabLLrtMb7zxhkaPHq0JEyZoxowZeuedd3TGGWdoxIgRuv322/XNN9/ohhtu0MMPP6zBgwfr2LFjGj58uO68804NHz7czmiCz7RjV199tdm8ebMxxpj33nvPpKSkmDlz5pi6ujpz/Phxs3z5cjN69OgmY5KTk83evXuNMcY89thjpqCgwBw5csR8++23pqCgwMydO7fN96O9q66uNmlpaaaioqLJ49988435zW9+Yy6//HLz8ccf21Rd+PCW0z//+U8zcuRIk5ubayZPnmzcbrdNFdrPW0ZVVVVm1KhRZuzYsSY/P98cPHjQpgrDg7ecTvrb3/5m+vfv38ZVhRdvGX322Wemf//+Ji8vz+Tl5Znq6mqbKgwPvubSe++9Z2666SaTl5dnysrKbKgufHjL6cMPP2ycS0OHDjWPPfaYTRXaz1tGHo/HTJ8+3YwZM8aMHj3a7Nmzx6YKI19WVpYpLi42H330kbnkkktMVVWVMcaY6dOnm8svv9y8//77pq6uzsyYMaPJ8XVycrLJy8szR44cMQcOHDBDhw41r732mjHGmOXLl5uUlBTz6quvmvr6enP8+HEzdepUc/vtt5tvv/3WfPbZZ03W37hxoxk4cKD56quvzP3332/uvvvutg+iDbS7Syh9iY6O1u9//3vFx8f7PYtmjNFrr72m++67T2effbY6d+6sgoICrVmzpo2qxUlbtmxRcnKy+vTp0+Rxl8ul559/Xtdcc41NlYUXbzl169ZNRUVFKikpUc+ePUN22YMTeMsoISFBS5cuVXFxsYYPH67XX3/dpgrDg7ecJMnj8WjdunXq3r27DZWFD18Z9evXT0uWLNGSJUvUtWtXG6oLH95yqq2t1eLFi/XCCy9oyZIlGjJkiE0VhgdvOaWlpTXOpbS0NGVlZdlUof28ZVRRUSG3262lS5dqypQpeuWVV+wpMMKVl5fr888/17Bhw5Samqof/ehHWr16dePyX/ziF/r5z3+u+Ph4TZ48WTt27NAXX3zRuPzWW2/V2WefrR49euimm25qMjYpKUn5+fmKjY1VXFyc3nzzTU2ZMkWdO3dWr169dMstt2jVqlWSpCuuuELZ2dkaN26cNmzYoEceeaTtQmhDNHCnSEhIUIcOHQJa9/Dhwzp+/LhycnKUkZGhjIwMTZgwQUeOHAlxlfiho0eP6qyzzjrt8bi4uHZ/cHQqbzklJSU1vmERFxen6Oj2+7LgLaOYmJjGXI4dO6aLLrqorUsLK95ykk58/iQ7O1tRUVFtXFV48ZXRhx9+qNzcXP35z3+WMaaNKwsv3nLavn27OnTooIkTJ+rOO+9UVVWVDdWFD1/zSZLcbrd27typjIyMNqwqvHjLqFu3bjLGyBijo0ePKiEhwYbqIl9paakGDRrUeNx1/fXXa+XKlY3Lu3Xr1vhzp06d1KVLFx06dKjxsVPf9OvZs2eTZaeOPXLkiOrr69WjR4/Gx3r06KGDBw82/j5y5Eh98sknysnJidj/3+33SK0ZPzzgOOOMM1RbW9v4+6l/QBISEuRyubRmzRqVl5ervLxc27Zt0/bt29usXpyQkpKibdu2qbKyUsYY7d27V59++qndZYUdfzkdOHBAmzdv1tVXX21jlfbylVFFRYVGjBih4uJiXXLJJTZXai9vOXk8Hq1du1bXXnut3SXazltGSUlJKisrU0lJiaqrq1VWVmZ3qbbyllN1dbX27dunRYsWaeTIkVqwYIHdpdrK3+v3u+++q8zMzHb9Bpy3jBISEhQbG6vs7Gw9+uijys3NtbvUiFNbW6u1a9fqgw8+0KBBgzRo0CAVFRWpsrJSlZWVkqQvv/yycf1jx47p6NGjSkpKanzs1LNxn3/+eZNlpx6fJyQkKC4uTp9//nmTseedd56kE1eBPPjggxo+fLiWLl2q//73v8Hf4TDQfp/pAejTp492796tiooK1dXVNfkDEh0drREjRmjmzJmqrq6WJB08eFAbN260q9x2Kz09XRMnTlRBQYHS09N11113NWm8cYKvnGpqajRt2jTNmjVLcXFxNldqH18ZpaSkaNmyZZo0aZKee+45myu1l7ecVq1apWHDhrXrg8iTvGUUHx+vjh07KioqSkOHDm08uGmvvOV05plnKj09XfHx8crMzNSePXvsLtVW/v7OrVu3TtnZ2TZWaD9vGW3atEmxsbF66623NH/+fD3++ON2lxpx3n77bcXExGjNmjUqLS1VaWmp3nzzTWVkZKi0tFSStGHDBpWXl8vtduupp55S3759m5x1e+mll3T06FF98cUXevXVV72+ERgTE6Ps7Gw9+eSTqqmp0YEDB7R48eLGO8k/++yzioqK0syZM/W73/1O06dPl8fjCX0Ibc2ej96Fhx/exOTKK688bZ2FCxeafv36mauuusqUlpY2uYlJbW2tmTdvnhk8eLBJS0sz2dnZpqioqE33Af5Nnz6dm5j4UF9fbyZMmGC2bNlidylhq66urvHnd955x8ycOdPGasLXnDlzzC233GLGjx9v0tPTzYwZM+wuKex8++23jT/PnTvXrFy50sZqwld1dbW5+eabzffff2927Nhhpk2bZndJYcvtdpvrrrvOeDweu0sJS//4xz/M448/bow5cROh8ePH21xR5Bk/fryZNWvWaY+vWbPGDBw40EyZMsX88Y9/NOPGjTOXX365yc3NNfv27WtcLzk52RQVFZnBgwebfv36mVmzZpmGhgZjjGn2hoJff/21mTJliunfv7+56qqrzIIFC4zH4zEfffSRycjIaDxOb2hoMKNGjTILFy4M4d7bI8qYdn4BPiLarbfeqoqKCvXs2VOjRo1STk6O3SWFndLSUs2aNUvJycmSpDFjxnAJ3A/s3LlTs2fPVnR0tDp06KCZM2c2ubwDp8vJydGKFSvsLiPsbNiwQU899ZRcLpd69eqlmTNnKjaWb/RpTklJid58883Gd9PPP/98u0sKSxs2bNDGjRv1wAMP2F1KWGpoaNC9996rr776Sm63W4WFhUpPT7e7rHalsLBQ5513niZPntzs8lO/oguBoYEDAAAAEBI0cMHHBxUAAAAAwCE4AwcAAAAADuH1wvva2lrt2rVLiYmJiomJacuaEGY8Ho+qqqqUmprq9wvOm9Me5pLVjCRyClSk50RGgSEn/8goMOQUGI4F/GMuIVj8zSWvDdyuXbs0duzYkBYHZykpKWnVl4S2p7nU2owkcgpUe8mJjAJDTv6RUWDIKTAcC/jHXEKweJtLXhu4xMRESdL+A8fU4LHvKstzzjjL0vgVvc6zND7xqYmWxktSQ/GLlsZftvT/Wa7BitiYKPXq2alxTrTUyXFFzzyhbknnnrb84v4jLNUXDqxmJPl/zn28dZnXsU7JsC1y8sUJGdqdkS/hlF845+SLrwyl4Obo1Iz8CfY8jNScfGlNhsE6FnBKRr54y+/LQ1/p5junRsRcOrdjF0vjV/dJsDQ+YdETlsZLkvvVuZbG//SZrZZraC1/zzevDdzJ07YNHqOGBvsmkPk+yv9KPnSLtnZ75m5J51gaL0n1Z1j7YmQ78z9Va0/lnxzXLelc9ex+ekMdLvsXDFYud/D3nGsuu5OclmEoc/LFSRnalZEv4ZhfOObki68MpdDk6LSM/AnVPIy0nHyxkqHVYwGnZOSLv+dxJMwlq8ff3S1+Pco5fjIORF3nDpbGh8M89TaXuAslAAAAADgEDRwAAAAAOAQNHAAAAAA4BA0cAAAAADiEtU8YAi1wcf8RYfGBUKdy9bjS7hIcjwytIT/ryNA6MrSODK3xll9sbJR6n9+5jatBe8QZOAAAAABwCBo4AAAAAHAIGjgAAAAAcAgaOAAAAABwCBo4AAAAAHAIGjgAAAAAcAgaOAAAAABwCBo4AAAAAHCIsP8i70/yelsa73pogaXx/7x8iqXxknTpq8MtjX+6tKvlGu46+H8tbwMAAACR72DNEUvje26xNl582bxPnIEDAAAAAIeggQMAAAAAh6CBAwAAAACHoIEDAAAAAIeggQMAAAAAh6CBAwAAAACHoIEDAAAAAIeggQMAAAAAh6CBAwAAAACHoIEDAAAAAIeggQMAAAAAh6CBAwAAAACHoIEDAAAAAIeggQMAAAAAh6CBAwAAAACHoIEDAAAAAIeIDeXGf3pOb8vbcD20wNL4b8bfYml8/0N7LI2XpE+n1FgaP+xcyyVIB4OwDQAAAAC24gwcAAAAADgEDRwAAAAAOAQNHAAAAAA4BA0cAAAAADgEDRwAAAAAOAQNHAAAAAA4BA0cAAAAADgEDRwAAAAAOAQNHAAAAAA4BA0cAAAAADgEDRwAAAAAOAQNHAAAAAA4BA0cAAAAADgEDRwAAAAAOAQNHAAAAAA4RGwoN36w9utQbj4gU3cmWtzCHss1fFXV2fI2AAAAAIAzcAAAAADgEDRwAAAAAOAQNHAAAAAA4BA0cAAAAADgEDRwAAAAAOAQNHAAAAAA4BAh/RoBQJI8Ho8kKTYmyuZKQufkvp3c19Ygp8BEek5kFBhy8o+MAkNOgbGaExkBwUMDh5CrqqqSJPXq2cnmSkKvqqpKF1xwQavHSuQUyFgp8nMio8CQk39kFBhyCkxrcyIjIHho4BByqampKikpUWJiomJiYuwuJyQ8Ho+qqqqUmpra6m2QU2AiPScyCgw5+UdGgSGnwFjNiYyA4KGBQ8i5XC5lZGR4Xf7111/r/vvv1+bNm5WQkKB77rlHv/rVr1q1bku2FWxW323zlVOkZCSFNqfi4mKtWLFCn3zyia6//no9/vjjXrcTzjmFMqNPP/1UjzzyiP71r3+pa9eumjZtmoYMGdLsuuGckRTcnHzNnfz8fO3YsUOxsSf+ZCYlJemtt97yul1fubR1Zm2VUUuee1J4ZSTx+h0oKzmRERA8NHCw3Z/+9CfFxcVp8+bNqqioUEFBgfr06aOLLrqoxeu2ZFtOQkaBSUpK0h133KGNGzeqrq7O57rtMaeGhgbdcccdGj16tBYvXqz3339fEydO1MqVK3XhhReetn57ysjf3HnwwQc1YsSIgLblKxcnZ+Yro5Y896TIzag5vH77R0ZAy3AXStjqu+++U1lZmSZNmqROnTopIyNDgwcP1htvvNHidVuyLV9Wr16t6667Tn379lVWVpa2bt0alH091YIFC7RgwYKA1m2vGUkty0mShg4dqqysLJ199tk+14uknFqS0b///W8dOnRI48aNU0xMjDIzM5Wens5cUuBzxx9fuYR7ZlYyakl+Ts5I4vU7UIHm1J4zAlqLM3Cw1d69exUTE9Pk3f8+ffrogw8+aPG6LdmWNy+//LKWL1+uOXPmKCUlRbt371anTvZ+4JqMgo+c/scYo927d5/2OBk1NW/ePM2dO1cXXnihJk+erP79+ze7nq9c2ltm3rSnjHj99o+MgJbjDBxs9d1336lz585NHjvzzDN17NixFq/bkm2NGzfutHcGDx8+rKefflrz5s3TpZdequjoaF188cXq0qWLfvvb3yotLU2ffPJJq/bTCidkdPjwYY0aNUpjx47VPffco/r6+lbta1uxKyeXy6XRo0crLy9PN910kw4dOhTkPfPtwgsvVNeuXfXiiy+qvr5emzZt0gcffKDa2trT1rUro169ekk68Q74gAEDLO1vsNx77716++23tXHjRo0aNUq333679u3b1+y6vnIJZWb79+/XgAEDlJ+fr/z8fB0+fNjiXoeOXRlJ0tatW3XzzTcrPz9ff//734O8Z6dzwut3VVVV47y55pprNHPmzFbta2s5IaMePXqosLBQubm5GjNmjD799NNW7SsQLJyBg606duyompqaJo/V1NQ0+26Xv3Vbsq2cnBx17969yWNbtmxRcnKy+vTp0+Rxl8ul559/XnPmzAl8x4LICRl169ZNRUVFcrlcmjdvntavX6/s7OzAd7KN2ZVTQkKCli5dqujoaK1YsUKvv/667rjjjmDsUkDi4uL0zDPP6NFHH9WLL76o1NRUZWdnKz4+/rR17cpIOnEnt3Xr1p02xi59+/Zt/PnGG2/U6tWrtWHDBuXn55+2rq9cQpmZJPXr10/z588PeL/sYldGtbW1Wrx4sV544YVm53woOOH1Oy0tTUuWLJEkFRYWKisrK8C9Cw4nZFRRUSG3262lS5eqvLxcr7zyimbMmBH4TgJBFtIGbliXlFBuHhGgd+/e8ng82rt3r3r37i1Jqqys1E9+8pMWr9uSbd1www2nPXb06FGdddZZpz0eFxenrl27tnIP/6egoEDbtm2TpMYP+RcVFUmSfvazn+m5555rdpwTMkpKSmr8OS4uTtHRrT+539qcWsKunE69dfaxY8da/aF6Kxn16dNHxcXFjb+PHj1aw4cPP209uzKSTpx9y87O1ssvv+x1PwIRqrkUFRUlY0yzy3zlEsrMJOnDDz9Ubm6uMjIyNHnyZEVF+f/C5LZ4vv2QXRlt375dHTp00MSJE+VyufTwww8rMTExoJoj+fX7JLfbrZ07d1o6A9eanJyQUbdu3WSMkTFGR48eVUJCgp8kgNDiEkrYqmPHjhoyZIjmz5+v7777Ttu2bdP69ev161//usXrtmRbzUlJSdG2bdtUWVkpY4z27t0b1MsknnvuOZWXl6u8vFy33XabbrvttsbffR0kOSmjAwcOaPPmzbr66qtbmM7/tDYn6cRdFuvq6vT999/L4/Gorq5ODQ0Np61nZ04VFRUaMWKEiouLdckll7QwnROsZFRZWam6ujodP35cL730kg4dOqScnJzT1rMrI4/Ho7Vr1+raa69teTA/0JKcvM2db775pvHOig0NDVq1apXKy8t15ZVXNvtv+sollPMqKSlJZWVlKikpUXV1tcrKytosI3/LwiWj6upq7du3T4sWLdLIkSNbdIOk9vD6/e677yozM9PSG3CtyckJGSUkJCg2NlbZ2dl69NFHlZub2+qMgGCggYPtHnroIdXW1mrgwIGaMmWKHn744cYzExMmTNCzzz4b0LqBLPclPT1dEydOVEFBgdLT03XXXXc1+9kgOzgho5qaGk2bNk2zZs1SXFxcEPc+cIsWLdJll12m559/XqtWrdJll12mRYsWSQqfnFJSUrRs2TJNmjQpJGc3/HnjjTd0xRVXaODAgXr33Xe1ePHixsvJwiGjVatWadiwYZYOIlvD29xpaGjQX/7yFw0YMEADBgxQcXGxnnnmmSY3SWhJbqGaV/Hx8erYsaOioqI0dOhQVVZWBjGdE3w9v3wtk8IjozPPPFPp6emKj49XZmam9uzZE6xofHLC67ckrVu3zrZL38M9o02bNik2NlZvvfWW5s+f7/d7DoFQizJergPZv3+/fvnLX2rvvho1NDR/qYg/N/fItFScJD1Xbu1zRwUZ0yyNL/r8XUvjJWlrUj/L27Cq/6H3Wz02NjZKvc/vrPXr1zd+ELw9Kiws1Pjx45WcnGx5Wyff+b377rstbyscNDQ0aOLEiRo/frwyM60/70+KtJzcbndjs7Rx40Zt2rRJf/jDHyxtM9IyeuKJJ1RRUaGoqCjt2LFDN954ox544AHL2420nH6opqam8eYN8+bN049//ONmL431JdIzOnz4sO655x4tXrxYO3fu1NKlSzV79uwWbycSc6qvr9eNN96oVatWBe3Nk0jKacOGDXrvvfc0ffp07d+/Xw899JBeeumlkPxbwTj+hvP5O/bmJiZAAG699VZVVFToP//5j0aNGtXsJWctEQl/0E61evVq7dy5UwsXLtTChQs1ZsyYoFwCF2k5VVZWavbs2YqOjlaHDh2Ccre3SMto6tSpjT/n5OQEpXmTIi+nH9q2bZueeuopuVwu9erVS5MmTWrxNiI9o65du2rIkCHKy8tTVFRUq59/kZjTli1bNGDAgKCe+Y6knAYNGqSVK1cqLy9PbrdbhYWFdpeEdo4zcH5wBo4zcAAAAG2BM3CQ/B978xk4AAAAAHAIGjgAAAAAcAg+A4eQq62t1a5du5SYmNjke7AiicfjUVVVlVJTU+VyuVq1DXIKTKTnREaBISf/yCgw5BQYqzmRERA8NHAIuV27dmns2LF2l9EmSkpKlJGR0aqx5BSY9pITGQWGnPwjo8CQU2BamxMZAcFDA4eQS0xMlCTtP3BMDZ7I/EBubEyUevXs1LivrUFOgbGS08dbl3lddnH/Ea2uKZjszuj/dOnuddnasvlel7V1fnbndG7HLl6Xre6T4HVZwqInfG43mDlGakbuV+d6XfbTZ7b6L+wHyCkwVnMiIyB4aOAQcicvlWjwmIi/o5KVy0LIqWVjW5NTz+7neV0WbpnblVHU994/Gh2O+dmVk/k+yuuy7rHe/7Se4yNDKTQ5RlpGdZ07eF1mJT9yCkxrcyIjIHi4iQkAAAAAOAQNHAAAAAA4BA0cAAAAADgEDRwAAAAAOAQ3MQHQbrh6XGl3CWHv4yP7vS4jv/85WHPE67KeW7wvUzvKkIwCQ07+kRHQVEgbuLVHK0K5+YB0k/c7DAUiqdPZlmu4+Ea3pfEj3givu+MBAAAAsAeXUAIAAACAQ9DAAQAAAIBD0MABAAAAgEPQwAEAAACAQ9DAAQAAAIBD0MABAAAAgEPQwAEAAACAQ9DAAQAAAIBD0MABAAAAgEPQwAEAAACAQ9DAAQAAAIBD0MABAAAAgEPQwAEAAACAQ9DAAQAAAIBD0MABAAAAgEPEhnLjh459bXkb7pdmWBp//8R4S+OnbD7X0nhJcv+3xtL4v3+5x3INAAAAAJyPM3AAAAAA4BA0cAAAAADgEDRwAAAAAOAQNHAAAAAA4BA0cAAAAADgEDRwAAAAAOAQNHAAAAAA4BA0cAAAAADgEDRwAAAAAOAQNHAAAAAA4BA0cAAAAADgEDRwAAAAAOAQNHAAAAAA4BA0cAAAAADgEDRwAAAAAOAQNHAAAAAA4BCxdhfgz08ef9/S+F1Xnmtp/Bkjr7Q0XpJy7vvQ8jYAAAAAgDNwAAAAAOAQNHAAAAAA4BA0cAAAAADgEDRwAAAAAOAQNHAAAAAA4BA0cAAAAADgEDRwAAAAAOAQNHAAAAAA4BA0cAAAAADgEDRwAAAAAOAQNHAAAAAA4BA0cAAAAADgEDRwAAAAAOAQNHAAAAAA4BCx3hZ4PJ4TK8REtVkxzYmKNpbGf1HvsTTe9fUxS+MlqT6q3tL42Fh7/x+cnAMn50RLhctcCiWrGZ06lpx8i/ScyCgw5OQfGQWGnALDsYB/zCUEi7+55LWBq6qqkiT16tkpBGW1xPeWRv/mP19Z++efXmttvCSdYW147/M7W68hCKqqqnTBBRe0apwUDnMp9Fqb0cmxEjkFMlaK/JzIKDDk5B8ZBYacAsOxgH/MJQSLt7kUZYxp9hRXbW2tdu3apcTERMXExIS8QIQvj8ejqqoqpaamyuVytXh8e5hLVjOSyClQkZ4TGQWGnPwjo8CQU2A4FvCPuYRg8TeXvDZwAAAAAIDwwk1MAAAAAMAhaOAAAAAAwCFo4AAAAADAIWjgAAAAAMAh/j9eICs/FAdbmAAAAABJRU5ErkJggg==\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"o-TyPedqk_0M"},"source":["Η πάνω σειρά εικόνων δείχνει τα μεμονωμένα εικονοστοιχεία και η κάτω σειρά δείχνει τη συσσωρευτική συνεισφορά αυτών των εικονοστοιχείων στην κατασκευή της εικόνας. \n","\n","Χρησιμοποιώντας μόνο οκτώ στοιχεία βασισμένα σε pixel, μπορούμε να κατασκευάσουμε μόνο ένα μικρό τμήμα της εικόνας 64 pixel. Αν συνεχίσουμε αυτήν την ακολουθία και χρησιμοποιήσουμε και τα 64 pixel, θα ανακτήσουμε την αρχική εικόνα."]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"OHundEJwk_0N"},"source":["Αλλά η αναπαράσταση με pixel δεν είναι η μόνη επιλογή βάσης. \n","Μπορούμε επίσης να χρησιμοποιήσουμε άλλες βασικές συναρτήσεις, οι οποίες καθεμιά περιέχουν κάποια προκαθορισμένη συνεισφορά από κάθε pixel, και να γράψουμε κάτι παρόμοιο με το:\n","\n"," $$\n","image(x) = {\\rm mean} + x_1 \\cdot{\\rm (basis~1)} + x_2 \\cdot{\\rm (basis~2)} + x_3 \\cdot{\\rm (basis~3)} \\cdots\n","$$\n"," \n","Το PCA μπορεί να θεωρηθεί ως μια διαδικασία επιλογής βέλτιστων συναρτήσεων βάσης, έτσι ώστε η προσθήκη μόνο των πρώτων από αυτές είναι αρκετή για την κατάλληλη ανακατασκευή του όγκου του σύνολου των δεδομένων. \n"," \n","Οι κύριες συνιστώσες, οι οποίες λειτουργούν ως η χαμηλή διάστασης αναπαράσταση των δεδομένων μας, είναι απλά οι συντελεστές που πολλαπλασιάζουν κάθε ένα από τα στοιχεία αυτής της σειράς. \n","\n","Αυτό το σχήμα δείχνει μια παρόμοια απεικόνιση της ανακατασκευής αυτού του ψηφίου χρησιμοποιώντας τη μέση τιμή συν τις πρώτες οκτώ συναρτήσεις βάσης του PCA:"]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"DUc0PAC0UfDm","colab":{"base_uri":"https://localhost:8080/","height":176},"executionInfo":{"status":"ok","timestamp":1604328006386,"user_tz":-120,"elapsed":1691,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"b222271f-0c94-4149-8f92-58b157cc94eb"},"source":["pca = PCA(n_components=8)\n","Xproj = pca.fit_transform(digits.data)\n","sns.set_style('white')\n","fig = plot_pca_components(digits.data[10], Xproj[10],\n"," pca.mean_, pca.components_)\n","\n"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"Ah2tTeXXk_0O"},"source":["Σε αντίθεση με τη βάση με pixel, η βάση PCA μας επιτρέπει να ανακτήσουμε τα εμφανή χαρακτηριστικά της εικόνας εισόδου με ένα μέσο συν οκτώ συνιστώσες. \n","\n","Η ποσότητα κάθε εικονοστοιχείου σε κάθε συνιστώσα είναι το αποτέλεσμα του προσανατολισμού του διανύσματος στο δισδιάστατο μας παράδειγμα.\n","\n","Αυτή είναι η έννοια με την οποία το PCA παρέχει μια χαμηλής διάστασης αναπαράσταση των δεδομένων: ανακαλύπτει ένα σύνολο συναρτήσεων βάσης που είναι πιο αποτελεσματικές από τη φυσική βάση των pixel των δεδομένων εισόδου."]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"erf39LmTk_0O"},"source":["####Επιλογή του αριθμού των συνιστωσών\n","\n","Ένα ουσιαστικό μέρος της χρήσης του PCA στην πράξη είναι η ικανότητα εκτίμησης πόσων συνιστωσών απαιτούνται για την περιγραφή των δεδομένων. Αυτό μπορεί να καθοριστεί εξετάζοντας την αθροιστική *explained variance ratio* ως συνάρτηση του αριθμού των συνιστωσών:"]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"2DuJathMk_0P","colab":{"base_uri":"https://localhost:8080/","height":284},"executionInfo":{"status":"ok","timestamp":1604303546558,"user_tz":-120,"elapsed":931,"user":{"displayName":"Parask Tz","photoUrl":"","userId":"08609487936413149826"}},"outputId":"81b718b6-d91d-4d7f-9c9b-f20cf139f670"},"source":["pca = PCA().fit(digits.data)\n","plt.plot(np.cumsum(pca.explained_variance_ratio_))\n","plt.xlabel('number of components')\n","plt.ylabel('cumulative explained variance');"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"vMPX2Rf4k_0S"},"source":["Αυτή η καμπύλη ποσοτικοποιεί πόση από τη συνολική, 64-διαστατική διακύμανση περιέχεται στις πρώτες $Ν$ συνιστώσες. Για παράδειγμα, βλέπουμε ότι με τα ψηφία οι πρώτες 10 συνιστώσες περιέχουν περίπου το 75% της διακύμανσης, ενώ χρειάζετε περίπου 50 συνιστώσες για να περιγραφεί σχεδόν το 100% της διακύμανσης. \n","\n","Εδώ βλέπουμε ότι η δισδιάστατη προβολή μας, χάνει πολλές πληροφορίες (όπως μετράται από την explained variance) και ότι χρειαζόμαστε περίπου 20 συνιστώσες για να διατηρήσουμε το 90% της διακύμανσης. \n","\n","Κοιτάζοντας αυτό το διάγραμμα για ένα σύνολο δεδομένων υψηλής διάστασης μπορούμε να κατανοήσουμε το επίπεδο πλεονασμού που υπάρχει σε πολλές παρατηρήσεις."]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"ahfTDrD8k_0S"},"source":["## Φιλτράρισμα θορύβου με PCA\n","Το PCA μπορεί επίσης να χρησιμοποιηθεί ως φιλτραρίσμα για θορυβώδη δεδομένα.\n","\n","Οποιεσδήποτε συνιστώσες με διακύμανση πολύ μεγαλύτερες από την επίδραση του θορύβου θα πρέπει να μην επηρεάζονται σχετικά από τον θόρυβο.\n","\n","Έτσι, εάν ανακατασκευάσετε τα δεδομένα χρησιμοποιώντας μόνο το μεγαλύτερο υποσύνολο των κύριων συνιστωσών, θα πρέπει να διατηρείτε το σήμα και να εξαλείφεται ο θόρυβος."]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"iOUmRM5uk_0T","colab":{"base_uri":"https://localhost:8080/","height":248},"executionInfo":{"status":"ok","timestamp":1604328401476,"user_tz":-120,"elapsed":2590,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"594fba39-2f75-450d-dd79-0f31a63616c3"},"source":["def plot_digits(data):\n"," fig, axes = plt.subplots(4, 10, figsize=(10, 4),\n"," subplot_kw={'xticks':[], 'yticks':[]},\n"," gridspec_kw=dict(hspace=0.1, wspace=0.1))\n"," for i, ax in enumerate(axes.flat):\n"," ax.imshow(data[i].reshape(8, 8),\n"," cmap='binary', interpolation='nearest',\n"," clim=(0, 16))\n","plot_digits(digits.data)"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"nqVKdZM2k_0W"},"source":["Πρώτα θα σχεδιάσουμε πολλά από τα δεδομένα χωρίς θόρυβο εισόδου και έπειτα θα προσθέσουμε τυχαίο θόρυβο για να δημιουργήσουμε θορυβώδη σύνολο δεδομένων."]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"hdjqvLUDk_0W","colab":{"base_uri":"https://localhost:8080/","height":248},"executionInfo":{"status":"ok","timestamp":1604328412647,"user_tz":-120,"elapsed":2423,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"eda5bca7-77ff-48a7-bf43-123334d1757f"},"source":["np.random.seed(42)\n","noisy = np.random.normal(digits.data, 4)\n","plot_digits(noisy)"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"u4uSZyfKk_0Z"},"source":["Είναι ξεκάθαρο ότι οι εικόνες είναι θορυβώδεις και περιέχουν πλαστά pixel. Ας εκπαιδεύσουμε ένα PCA για τα θορυβώδη δεδομένα, ζητώντας από την προβολή να διατηρήσει το 50% της διακύμανσης:"]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"noTpJEd5k_0Z","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1604328421458,"user_tz":-120,"elapsed":912,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"6637025e-b008-4c7b-9ccd-1077c75ee16b"},"source":["pca = PCA(0.50).fit(noisy)\n","pca.n_components_"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["12"]},"metadata":{"tags":[]},"execution_count":20}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"tq8LtOdUk_0c"},"source":["Εδώ το 50% της διακύμανσης ανέρχεται σε 12 βασικά συστατικά. Τώρα υπολογίζουμε αυτά τα συστατικά και στη συνέχεια χρησιμοποιούμε το αντίστροφο του μετασχηματισμού για να ανακατασκευάσουμε τις εικόνες με τα φιλτραρισμένα ψηφία:"]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"pgonaAoVk_0c","colab":{"base_uri":"https://localhost:8080/","height":248},"executionInfo":{"status":"ok","timestamp":1604328426046,"user_tz":-120,"elapsed":2493,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"fc3c4c7e-3e32-4562-eca5-9fc6e4ccae9e"},"source":["components = pca.transform(noisy)\n","filtered = pca.inverse_transform(components)\n","plot_digits(filtered)"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"uBv7GzX-k_0f"},"source":["Αυτή η ιδιότητα διατήρησης σήματος/φιλτραρίσματος θορύβου καθιστά το PCA μια πολύ χρήσιμη συνάρτηση επιλογής χαρακτηριστικών.\n","\n","Για παράδειγμα, αντί να εκπαιδεύετε έναν ταξινομητή σε δεδομένα πολύ υψηλής διάστασης, μπορείτε να τον εκπαιδεύσετε στην αναπαράσταση χαμηλότερης διάστασης, η οποία αυτόματα θα φιλτράρει και τον τυχαίο θόρυβο στις εισόδους."]},{"cell_type":"markdown","metadata":{"id":"oii7e-oaeiD3"},"source":["## EigenFaces"]},{"cell_type":"markdown","metadata":{"id":"38oEDQUveoe-"},"source":["To Labeled Faces in the Wild (LFW) είναι μια βάση δεδομένων με φωτογραφίες προσώπου που έχουν σχεδιαστεί για τη μελέτη του προβλήματος της αναγνώρισης προσώπου. Είναι ένα προσημειωμένο σύνολο δεδομένων που περιέχει περισσότερες από 13.000 εικόνες προσώπων. 1680 από τα άτομα που απεικονίζονται έχουν δύο ή περισσότερες ξεχωριστές φωτογραφίες στο σύνολο δεδομένων. "]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"tMmLySaKk_0g","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1604328518945,"user_tz":-120,"elapsed":17209,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"c07bdded-3420-47fc-f308-88d7a09dd29d"},"source":["from sklearn.datasets import fetch_lfw_people\n","faces = fetch_lfw_people(min_faces_per_person=60)\n","print(faces.target_names)\n","print(faces.images.shape)"],"execution_count":null,"outputs":[{"output_type":"stream","text":["Downloading LFW metadata: https://ndownloader.figshare.com/files/5976012\n","Downloading LFW metadata: https://ndownloader.figshare.com/files/5976009\n","Downloading LFW metadata: https://ndownloader.figshare.com/files/5976006\n","Downloading LFW data (~200MB): https://ndownloader.figshare.com/files/5976015\n"],"name":"stderr"},{"output_type":"stream","text":["['Ariel Sharon' 'Colin Powell' 'Donald Rumsfeld' 'George W Bush'\n"," 'Gerhard Schroeder' 'Hugo Chavez' 'Junichiro Koizumi' 'Tony Blair']\n","(1348, 62, 47)\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"rflxuc3gfrjP"},"source":["Επειδή πρόκειται για ένα μεγάλο σύνολο δεδομένων, θα χρησιμοποιήσουμε το RandomizedPCA - περιέχει μια τυχαιοποιημένη μέθοδο για την προσέγγιση των πρώτων βασικών συστατικών $N$ πολύ πιο γρήγορα από τον τυπικό εκτιμητή PCA, και ως εκ τούτου είναι πολύ χρήσιμο για δεδομένα υψηλής διάστασης (εδώ, μια διάσταση σχεδόν 3.000). Θα ρίξουμε μια ματιά στα πρώτα 150 συστατικά:"]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"a2hnvPpuk_0j","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1604328569083,"user_tz":-120,"elapsed":1186,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"dc220126-5ecf-45de-b1df-17516f1a57ea"},"source":["from sklearn.decomposition import PCA as RandomizedPCA\n","\n","pca = RandomizedPCA(150)\n","pca.fit(faces.data)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["PCA(copy=True, iterated_power='auto', n_components=150, random_state=None,\n"," svd_solver='auto', tol=0.0, whiten=False)"]},"metadata":{"tags":[]},"execution_count":23}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"Z_CJbWmhk_0m"},"source":["Είναι ενδιαφέρον να οπτικοποιήσουμε τις εικόνες που σχετίζονται με τα πρώτες κύριες συνιστώσες(τα ιδιοδιανύσματα και έτσι αυτοί οι τύποι εικόνων ονομάζονται συχνά \"eigenfaces\")."]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"htMoEk1Fk_0n","colab":{"base_uri":"https://localhost:8080/","height":248},"executionInfo":{"status":"ok","timestamp":1604328580329,"user_tz":-120,"elapsed":2385,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"72d699dd-644d-4b80-a5dd-dd8250cdd370"},"source":["fig, axes = plt.subplots(3, 8, figsize=(9, 4),\n"," subplot_kw={'xticks':[], 'yticks':[]},\n"," gridspec_kw=dict(hspace=0.1, wspace=0.1))\n","for i, ax in enumerate(axes.flat):\n"," ax.imshow(pca.components_[i].reshape(62, 47), cmap='bone')"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"umvPRQe1k_0q"},"source":["Τα αποτελέσματα είναι πολύ ενδιαφέροντα και μας δίνουν πληροφορίες για το πώς ποικίλλουν οι εικόνες: για παράδειγμα, τα πρώτα λίγα πρόσωπα (πάνω αριστερά) φαίνεται να σχετίζονται με τη γωνία φωτισμού στο πρόσωπο και οι επόμενες κύριες συνιστώσες σχετίζονται με ορισμένα χαρακτηριστικά, όπως τα μάτια, οι μύτες και τα χείλη. Ας ρίξουμε μια ματιά στη συσσωρευτική διακύμανση αυτών των συνιστωσών για να δούμε πόσες από τις πληροφορίες δεδομένων διατηρεί η προβολή:"]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"iLajyp7wk_0q","colab":{"base_uri":"https://localhost:8080/","height":285},"executionInfo":{"status":"ok","timestamp":1604328740464,"user_tz":-120,"elapsed":839,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"eed5fca2-c5c8-41a2-c884-a393e65ce8fc"},"source":["plt.plot(np.cumsum(pca.explained_variance_ratio_))\n","plt.xlabel('number of components')\n","plt.ylabel('cumulative explained variance');"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAYkAAAEMCAYAAAAxoErWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nO3deVxU5f4H8A8My7AKjCwDiAsli+CSKJqY4oYpCLmk4frSyNTS6v68oXWBIlOya5ZhpqZds1teVxTNvNel0tzFXABXRJZhgBmQZRhme35/IKMjjh6QYQb4vl8vXgyHM/N8Z5g5H855znkeM8YYAyGEEPIY5sYugBBCiOmikCCEEKIXhQQhhBC9KCQIIYToRSFBCCFELwtjF9Bc5HI5rly5AldXV/B4PGOXQwghrYJarUZJSQmCgoLA5/Mb/L7NhMSVK1cwdepUY5dBCCGt0o8//oiQkJAGy9tMSLi6ugKoe6IeHh5GroYQQlqHoqIiTJ06VbsNfVSbCYn6Q0weHh7w9vY2cjWEENK66DtMTx3XhBBC9KKQIIQQoheFBCGEEL0oJAghhOhFIUEIIUQvCglCCGnlDDnjQ5s5BZYQQlojtVqDarkK1TVKVMuVkMmVqK5R1X1/+HaNEjK5SruOTK6CTK5CTa0KGsbwydwX4d/Fpdnro5AghJBnoNYwVNcoUSVToKpGiUqZApUyJarv/1wtf2Qj/3AYyFWoVaif2gbfigdbviXsbCxgy7eEvY0V3JxtYWNd97OjnRW83R0M8vwoJAgh7R5jDHKFGpUyBapkSlTV1G3oq2S6G/8qnTCoC4JqueqJj21lyYMd30JnI9/R2QZ2fEvY8i1gZ3P/O98SdjaWjyyvu23BM17PAIUEIaTNkStUqKxWoqK6FhXVike+dJdVyuq+K1UavY9nwTODva0V7G0s4WBrBWcHPnzcHWBvawUHG0vY2dYtr/+93UPfLS1ad9cvhQQhxOQplGqUV9WivLL2wffKWtyrqvv50SBQKB9/CMfMDLC3qTs842hnDXcXWzzfyQmOdlZwsLWCg92DDb29bd1hHXtbS/CteDAzM2vhZ20aKCQIIS2OMYaaWpV2g3/voQ1/2aPLqmoh03NIx8baAh3srdDBzhoujnx0ETreD4C6EHhwu+7L3tYKPPP2ubFvKgoJQkizYYxBJldBWiHXfpVVyCGpkKOsorZu2T05pJVyvR22DrZWcHKwgpM9H77eTnBysEYH+7qfnR2s7/9c993akuaOMTQKCUIIJ0qVGpJ7cpSU16C0vEa7sZfek6OsshbSe3Vh8LhDPXwrHlwc+XDpwMfzPk5wcXywwXey59eFwP2NvzE7aUlDFBKEEKjVGkgralF6PwBKymtQeu+h2+U1KK+sbXC/Rzf+oY78ugBw5ENwf7mzgzVs+ZZGeFakOXAKCcYYtm/fjvT0dJSVlWHfvn04e/YsSkpKMGbMGE4N5eTkID4+HuXl5XByckJKSgq6dOmis05JSQkSEhKQn58PlUqFN998E9HR0Y1+UoQQXXKFCsVSGcQPfdUHQml5DaSVtdBodK/atbG2QEcnG7g62aCbZ4f7t/no6GQDQQcbCDrwaePfDnAKiS+//BJ//vknZs6cicTERAB1k/ssX76cc0gkJiYiNjYW0dHRSEtLQ0JCArZs2aKzzooVKxAUFIRvvvkGUqkU48ePR//+/SEUChv5tAhpX5QqDUrKZRBLZCguux8EkgeBUF6luxdgZWEOwf0A6Pm8K1ydbNDx/lf9bTsbCgDCMSR2796N3bt3w8XFBUlJSQAAb29v5OXlcWpEIpEgMzMTmzdvBgBERkYiOTkZUqkULi4PLiPPzs7GzJkzAQAuLi7w9/fHL7/8gtmzZzfmORHSJsnkSohKq1FYWn3/exWK7geB9F4NHt4R4JmbwdXZBu4utujfwwPuLrZ1XwJbuDvbwsnBut2e0kkah1NIqNVq2NnZAYD2jVVdXQ1bW1tOjYhEIri7u2unx+PxeHBzc4NIJNIJiR49euDAgQMIDg5Gfn4+MjIyaCpS0q7U1Kq0AVBY8iAMCkurG/QJuDhaw0Ngh2BfAdxd7ODuYnP/uy0EHfjgUQcwaQacQmLIkCFYvnw5li5dCqCuj+LLL79EeHh4sxYTHx+PTz/9FNHR0fD09MTAgQP1zrtKSGvFGIPknhx54krkF1chr7gSBcVVyC+uhLSiYRAIO9qjX4A7hB3t4NnRHp6udvAQ2MHGms47IYbH6V22ZMkSvP/+++jbty9UKhX69OmDQYMGISUlhVMjQqEQYrEYarUaPB4ParUaxcXFDfoaXFxc8Pnnn2t/jouLw3PPPdeIp0OI6VCqNBCVVmmDIL+4CvniShSUVKGm9sFponY2lujkZo8+fm7wcrWnICAmhdM70N7eHqmpqZBIJCgoKIBQKISrqyvnRgQCAQICApCeno7o6Gikp6cjICBA51ATAJSVlcHBwQEWFhY4efIkrl+/jq+++qpxz4iQFsYYg1gqQ66oAneKKpArqsQdUQUKSqp0zhjq6GQDbzd7jOjfGZ3c7OHt5gBvd3s42VP/ADFdnELi+PHj8PLyQteuXSEQCAAAt2/fhkgkwqBBgzg1lJSUhPj4eKxduxaOjo7avZC4uDgsXLgQwcHBuHTpEpYtWwZzc3M4Oztj3bp1sLGxaeJTI6T5VckUuCOq0H7liiqQW1SJmtoHw0a4udiii4cjBgR5oJO7Azq5OcDLzZ72CkirZMY4TGk0atQobN26FW5ubtplYrEYM2bMwK+//mrQArnKz8/H8OHDcfjwYersJs+svt/gZn45buXfw838cuQU3oPknly7jr2NJToLHdFF6IjOQkd0FTrCx8OBrh0grcrTtp2c/rWRSCQ6AQEAbm5uKCkpaZ4qCTEixhiKy2ruB0JdKNwqKMe9KgUAwNwM8HJzQLBvR20gdBE6QtCBT4eJSJvHKSQ6deqEkydPYuDAgdplp0+fpv/YSatUWl6D7FwpbuaVa/cUqmqUAABzczP4uDugX4AHfL074DlvJ3QROoJPh4pIO8Xpnf/WW2/h7bffxsSJE9GpUyfk5eVh165d+PTTTw1dHyHPRKnS4HZBObJzy5B9R4rs3DKUltcAqJtIprPQEYN6ecLXqwN87weCFY0sSogWp5AYMWIENm3ahB07duC3336Dh4cHNm7ciJ49exq6PkIapaxCjuxcKbLu1IXCzfxy7Yxjrs42COjiAv/OzvDv4oKuno6wtKBAIORJOO9D9+zZk0KBmJyyCjmu3JLg8q1SXLpZioKSKgCABc8cvt4dMHZQV/h3doF/F2cIOtCZcoQ0FqeQUCgU2L17N7KysiCTyXR+99lnnxmkMEIep6zyQShcuVWKPHFdKNhYW6BHNwFGhfogsKsAvt4daC+BkGbAKSTi4+ORnZ2N8PBwdOzY0dA1EaIlkyvx141SXLxejMu3JMgTVwIAbKx5COwqwPAQHwQ/1xG+Xh1orCJCDIBTSPzxxx84fPgwHB0dDV0PaefUGoZb+eXIuFaMjOslyL4jhVrDwLfiIbCbAMNCOqEnhQIhLYZTSAiFQigUCkPXQtqpsgo5zmeLceFaCS5eL0GlrO699px3B4wPfw59/Nzg39kFlhYUCoS0NE4hERMTg/nz52PGjBnaYTnqPXztBCFcMMaQW1SJM1eLcOZqEa7dLQMAODtYo1+gO/r4uaFPd1d0sLc2cqWEEE4hsXXrVgDAqlWrdJabmZnh8OHDzV8VaXOUKg0yb0twOrMIp68WoVhadwLE852cMG20P/oFeqCrpyNdwUyIieEUEkeOHDF0HaQNUqk1yLhWjN8vFuDs1SJUy1WwsjBHr+6ueHX48+gX6AEXR76xyySEPAGNNUCalUbDcPW2BL9l5OPPS4WolClhb2OJF3t6IrSHB3p1dwXfit52hLQWnD6tVVVVWLNmDc6ePYuysjI8PHDssWPHDFUbaSUYY7iZX47fMwrwe0YBpBVyWFvxENrDA0P6eKOPnxt1OhPSSnEKiaSkJIjFYsyfPx+LFy/GypUr8d133yEiIsLQ9RETVlYpx9FzeTh0+i4KSqpgwTNDX393vNTHC/0DPWhQPELaAE6f4hMnTuDAgQNwdnYGj8fDiBEjEBwcjDfffBOzZs0ycInElKg1DBnXinHodC7OXC2CWsMQ0MUFrwztjUE9hbC3tTJ2iYSQZsQpJDQaDRwcHAAAtra2qKyshKurK3Jzcw1aHDEdYqkM/z2Ti8Nn7qL0nhyOdlaIGtwNo0I7o5O7g7HLI4QYCKeQ8Pf3x9mzZzFw4ECEhIQgKSkJdnZ26NKlC+eGcnJyEB8fj/Lycjg5OSElJaXB/SUSCZYsWQKRSASVSoXQ0FB8+OGHsLCgwxbGoNEwXLhWjH1/3EbG9WIAQB8/N7weE4z+gR7Uz0BIO8Bp6/vJJ59oO6s/+OADrFq1ChUVFY0a3C8xMRGxsbGIjo5GWloaEhISsGXLFp111q1bB19fX6xfvx5KpRKxsbE4dOgQxowZ04inRJ5VTa0KR87exb7jt1FQUg0XRz6mjPTDiP4+cHO2NXZ5hJAWxHlmunoCgQDLli1rVCMSiQSZmZnYvHkzACAyMhLJycmQSqVwcXHRrmdmZobq6mpoNBooFAoolUq4u7s3qi3SdMVSGdJP5ODQqTuolqvQ3ccJ/ze1Lwb18oQFjZNESLukNyT27NmDmJgYAMCOHTv0PsDEiROf2ohIJIK7uzt4vLqhm3k8Htzc3CASiXRCYv78+Xj77bcRFhaGmpoaTJ06FX379uX8ZEjT5IoqsOPIDfx+sQAAMKinJ8a91A3+nV2eck9CSFunNyT279+vDYm0tLTHrmNmZsYpJLg6ePAg/Pz88K9//QvV1dWIi4vDwYMHMXr06GZrgzyQfUeK/xy+jrOZYthY8zBucDeMG+wLV2eanIcQUkdvSGzYsAFA3YVSn376KYRCYZM7kIVCIcRiMdRqNXg8HtRqNYqLiyEUCnXW27p1Kz799FOYm5vDwcEBw4YNw+nTpykkmtntgnvYciAT57OL4WBrhamj/TF2UFc40OmrhJBHPPVAs5mZGaKiomBu3vRj0gKBAAEBAUhPTwcApKenIyAgQOdQEwB4e3vj999/B1A3G97Jkyfx/PPPN7ldoquwtAorfziHRauO4VpuGWaNDcSmD0diykg/CghCyGNx2jUICAhATk4OfH19m9xQUlIS4uPjsXbtWjg6OiIlJQUAEBcXh4ULFyI4OBhLly5FYmIioqKioFarERoaildffbXJbZI6MrkSPx26hn1/3IaFhTleHdEdrwx9DvY2lsYujRBi4jiFRP/+/REXF4dXXnkFHh4eOsM5c+2T8PX1xfbt2xssrz+sBQA+Pj7aM6DIs9NoGI5dyMPm9Ezcq6rFqNDOmBrhD2caeZUQwhGnkLhw4QK8vLxw5swZneXN3XFNmk+uqAKpO/5C1h0p/HyckTAnFM93cjZ2WYSQVoZTSPzwww+GroM0E6VKg+2Hr2P74euw5Vti0eTeGBbiA3NzmsyHENJ4jT5diTGmM1T4s3Rok+Z1/W4ZvtqWgdyiSgzp4424mCCaApQQ8kw4hYRYLMbHH3+Mc+fOoaKiQud3WVlZBimMcKdSa/DvX7Ox88gNODvy8Y85oegf6GHssgghbQCnkEhMTASfz8f333+PadOm4ccff8SaNWswZMgQQ9dHnqKgpAqf/3geN/PKMaKfD16PDoIdnbVECGkmnEIiIyMDR48eha2tLczMzODv749ly5ZhypQpdIqqkTDGcOh0LjakXYElzxzxM/thUE9PY5dFCGljOIWEubm59mprR0dHSKVS2NvbQywWG7Q48njyWhW++s9F/HGxAL2e74h3X3sBgg40lAYhpPlxColevXrht99+w8iRIxEWFoZ33nkHfD4fQUFBhq6PPKJIUo1lm88gt6gCM8YEYEL483TmEiHEYDiFxGeffQaNRgMAWLp0KTZt2oTq6mrMnDnToMURXReuFWPlD+cAAEmvD8QL/m5GrogQ0tZxCgmVSqUdZ4nP52P+/PkGLYroYowh7ffb2LzvCnw8HLF0Vn8IO9oZuyxCSDvAKSTCw8PRv39/REZGYuTIkbC1pdnJWopaw7Bp7xXs/eM2XuwpxLtTXgDfmqZzJYS0DE5Xwh09ehRDhw7Fzz//jEGDBuG9997DkSNHoFKpDF1fu6ZQqrHyh3PY+8dtjHupG96f3o8CghDSojiFhIuLC6ZOnYqffvoJ6enp8Pf3xxdffIGwsDBD19duVcoUSFh/EicuFWLOuCDERQdTBzUhpMU1+t9SiUSC0tJSlJWVwdHR0RA1tXvVNUp8+M2fuCuuxN+nh2Bwby9jl0QIaac4hcTNmzeRnp6O/fv3Qy6X4+WXX8batWvRs2dPQ9fX7sgVKiRvOo274gp8ODsUff3djV0SIaQd4xQSr732GkaNGoWPP/4YoaGhNKifgajUGqRsOYfMHAkWTwuhgCCEGB2nkDhx4gSsrGh6S0PSaBhW/5SBc1liLJjYiw4xEUJMAqeQaI6AyMnJQXx8PMrLy+Hk5ISUlBR06dJFZ52///3vuHbtmvbna9euITU1FcOHD3/m9k3dd3uv4LeMfMwYE4DRA7sYuxxCCAHQhI7rpkpMTERsbCyio6ORlpaGhIQEbNmyRWedzz77THs7OzsbM2fOxODBg1uqRKM58GeO9jTXicOeN3Y5hBCi1SKdCxKJBJmZmYiMjAQAREZGIjMzE1KpVO99duzYgaioqDZ/mOvi9WJ8u/sy+gW6Y3ZUkM784YQQYmwtEhIikQju7u7g8XgAAB6PBzc3N4hEoseur1AosG/fPkyYMKElyjOagpIqrNhyDp3c7PF/U/uCR9dBEEJMjN7DTV9++SWnB1i0aFGzFVPvf//7Hzw9PREQENDsj20qqmQKJH93CjxzM/xjzgDY8mmiIEKI6dEbEkVFRdrbtbW1OHToEIKCguDl5YXCwkJcvnwZo0aN4tSIUCiEWCyGWq0Gj8eDWq1GcXExhELhY9ffuXNnm96L0GgYPvvhHMRSGT55cxDcXWgsLEKIadIbEsuXL9fefvfdd/HPf/4TERER2mWHDh3CwYMHOTUiEAgQEBCA9PR0REdHIz09HQEBAdqRZR9WVFSE8+fPY9WqVY15Hq3KzqM3kHG9BAsm9kKPbgJjl0MIIXpx6pP4/fffMWLECJ1lw4YNw2+//ca5oaSkJGzduhURERHYunUrPvroIwBAXFwcLl++rF1v9+7dCA8PR4cOHTg/dmuSfUeKrQezMbi3FyIGdDZ2OYQQ8kScToHt3LkzfvzxR8yYMUO77KeffoKPjw/nhnx9fbF9+/YGyzds2KDz87x58zg/ZmtTVaPEyq3n4OpkgwUTe9GZTIQQk8cpJD755BO89dZb2LhxI9zd3SEWi2FhYYE1a9YYur42gzGGNf/JgOSeHClvhcHOhjqqCSGmj1NIBAYG4tdff8Vff/2F4uJiuLq6onfv3rC0pA0dVwdP5eLPSyLMGhsIv84N+2IIIcQUNek6iX79+kGpVEImkzV3PW2SqLQaG9OuoE93V7wy9Dljl0MIIZxx2pO4du0a5s2bBysrK4jFYowZMwZnz57F7t27sXr1akPX2KoxxvD19ouw4Jlh0ZQ+NHEQIaRV4bQnkZSUhIULF+LgwYOwsKjLlX79+uH8+fMGLa4t+O+Zu7h0sxSzIntA0MHG2OUQQkijcAqJmzdvIjo6GgC0Z+TY2tqitrbWcJW1AVUyBTbtu4oe3QSICKXTXQkhrQ+nkPDy8sKVK1d0ll26dKlRp8C2R7uO3UR1jRJzX6H5qQkhrROnPolFixZh7ty5mDJlCpRKJb799lv8/PPPSE5ONnR9rVZ5ZS32/XEbg3t7oatn27wwkBDS9nHakwgPD8fGjRshlUrRr18/FBQUYM2aNQgLCzN0fa3WzqM3oFCqERvhZ+xSCCGkyThPOhQYGIikpCQDltJ2SO7VYP+JHISHdIK3m4OxyyGEkCbjFBIKhQK7d+9GVlZWg2sjHp5NjtTZ9r/rYIxhykjaiyCEtG6cQiI+Ph7Z2dkIDw9Hx44dDV1Tq1YkqcZ/T+diZGhneAjsjF0OIYQ8E04h8ccff+Dw4cNwdHQ0dD2t3rb/XoeZmRkmj+hu7FIIIeSZceq4FgqFUCgUhq6l1SuWynDk3F28/GIXunCOENImcNqTiImJwfz58zFjxgwIBLqT5AwcONAghbVGB0/dAQBEv+Rr3EIIIaSZcAqJrVu3AkCD2eLMzMxw+PDh5q+qFVKq1Dh0Ohf9Aj3g5kzTkRJC2gZOIXHkyBFD19Hqnbgkwr0qBcYM6mrsUgghpNk0aajwpsjJycHkyZMRERGByZMn486dO49d78CBA4iKikJkZCSioqJQWlraUiU+kwMnciDsaIfez7sauxRCCGk2evckXn75Zfzyyy8AgCFDhuidavPYsWOcGkpMTERsbCyio6ORlpaGhIQEbNmyRWedy5cv4+uvv8a//vUvuLq6orKyElZWVhyfivHcEVUg644Us6N60BhNhJA2RW9IPDwu08qVK5+pEYlEgszMTGzevBkAEBkZieTkZEilUri4PJil7fvvv8fs2bPh6lr337iDQ+u4Wvm/p3NhwTPHsJBOxi6FEEKald6QCAkJ0d7u37//MzUiEong7u4OHo8HAODxeHBzc4NIJNIJiVu3bsHb2xtTp06FTCbDyJEjMW/ePL17MaZAoVTj6Pk8DAjyQAd7a2OXQwghzYrz2E1ZWVk4d+4cysrKwBjTLl+0aFGzFaNWq3Ht2jVs3rwZCoUCr7/+Ojw9PRETE9NsbTS3U1dEqJQpMYrmiyCEtEGcOq63bduG1157DadOncKGDRtw/fp1bN68GXfv3uXUiFAohFgshlqtBlAXBsXFxRAKhTrreXp6YvTo0bCysoK9vT2GDx+OS5cuNfIptaxDp3Ph5myDXtRhTQhpgziFxMaNG7Fx40akpqaCz+cjNTUVX375pXYq06cRCAQICAhAeno6ACA9PR0BAQE6h5qAur6K48ePgzEGpVKJU6dOwd/fv5FPqeUUSarx141SjAztTB3WhJA2iVNISCQSbR+Fubk5NBoNhgwZgqNHj3JuKCkpCVu3bkVERAS2bt2Kjz76CAAQFxeHy5cvAwDGjh0LgUCAMWPGICYmBs899xwmTpzY2OfUYv535i7MzYDhITRDHyGkbeK0K+Dh4YH8/Hx4e3ujS5cuOHz4MJydnWFpacm5IV9fX2zfvr3B8g0bNmhvm5ubY8mSJViyZAnnxzUWtVqD/529ixf83eHqTOM0EULaJk4h8frrr2vPPJo/fz4WLVoEpVKJDz74wND1mawL14ohuSfH3FeCjV0KIYQYDKeQGD9+vPb2kCFDcObMGSiVStjZtd/5Eg6dzoWTvTX6BXoYuxRCCDEYvSGh0Wj038nCAhYWFtBoNDA3b7GRPUxGWaUcZzPFiH7JFxa89vf8CSHth96QCAwMfOJFbIwxmJmZISsryyCFmbJTl0VQaxhdYU0IafP0hgQNAa7fycsieHa0g49H6xg2hBBCmkpvSHh5eTVYxhhDWVkZnJ2dTXqoDEOqkilw6WYpYob4ttvXgBDSfnA6oF5RUYHFixcjODgYL774Inr27InFixejvLzc0PWZnLNZYqg1DAOChU9fmRBCWjlOIbFkyRLU1tYiLS0NGRkZ2LNnDxQKBZYuXWro+kzOycsiuDjy0b2Ts7FLIYQQg+N0CuypU6dw4sQJ8Pl8AHUXxq1YsQKDBw82aHGmRq5Q4Xx2MUb060TDcBBC2gVOexLdunVDQUGBzrLCwkJ07dq+puq8dLMUCqUaA4LoUBMhpH3gtCcxcOBAzJ49G9HR0fDw8EBRURH27t2L6Oho7NixQ7ueKY+z1Bz+ul4CKwtz9OgmMHYphBDSIjiFREZGBnx8fJCRkaFd1qlTJ1y4cAEXLlwAAJiZmbX5kLh4owSB3QSwsuQZuxRCCGkRnELihx9+MHQdJk9yrwZ3iyoxnC6gI4S0I5z6JM6ePfvY5fXzQ7QHf90oBQCaXIgQ0q5wComFCxdi5cqVUCqVAOqum3jnnXewZs0agxZnSv66UQIHWyt09exg7FIIIaTFcAqJPXv2IDs7GxMnTsT27dsRFRUFR0dH7N6929D1mQTGGC5eL0Gv5zvSqa+EkHaFU0i4u7sjNTUVGo0GCQkJeOmll/Dxxx/D1tbW0PWZhDxxJaQVcvTu7mbsUgghpEVxComsrCxMnDgRnTp1wtq1a3Hq1Cn87W9/Q0VFBeeGcnJyMHnyZERERGDy5Mm4c+dOg3XWrFmDgQMHIjo6GtHR0dopTo3tZv49AEBgV5enrEkIIW0Lp5CYNWsWZs6cibVr1yI8PBxpaWmwtrZGVFQU54YSExMRGxuLX3/9FbGxsUhISHjsejExMUhLS0NaWhoSExM5P74h5RdXgmduBmHH9jvJEiGkfeIUEjt27MCkSZO0P9va2uLTTz/Vu6F/lEQiQWZmJiIjIwEAkZGRyMzMhFQqbULJLS+/uAoeAjuaYIgQ0u5w2up16tQJt27dQmpqqvYQ0O3btx87nPjjiEQiuLu7g8eruwiNx+PBzc0NIpGowbr79+9HVFQUZs+erXPxnjEVlFTB283e2GUQQkiL4xQSv/zyC6ZNmwaxWIy0tDQAQHV1NVasWNGsxUyZMgWHDx/Gvn37MGfOHMyfPx9lZWXN2kZjqdUaFJZUU0gQQtolTiHx1VdfYfPmzfj444+1ewP+/v7Izs7m1IhQKIRYLIZarQYAqNVqFBcXQyjUHSjP1dUVlpaWAIBBgwZBKBTixo0bnJ+MIYjLZFCpNRQShJB2iVNISKVS+Pn5AYB2NjYzMzPOM7MJBAIEBARor9BOT09HQEAAXFx0zxYSi8Xa21lZWSgoKDD6SLP5xVUAAG83mqqUENL+cBq7qUePHkhLS0NMTIx22f79+9GzZ0/ODSUlJSE+Ph5r166Fo6MjUlJSAABxcXFYuHAhgoODsWrVKly9ehXm5uawtLTEZ599BldX4w6DUXA/JLxoT4IQ0g5xCokPPvgAc+bMwY4dOyCTycwFUukAABsSSURBVDBnzhzk5ORg06ZNnBvy9fXF9u3bGyzfsGGD9nZ9cJiS/OIqdLC3goOtlbFLIYSQFscpJHx9ffHLL7/g6NGjGDp0KIRCIYYOHQo7u7Z/3UB+cSUdaiKEtFucQgIAbGxsMGbMGEPWYpLyi6swMJhmoiOEtE90ddgTVFQrUFGtoDObCCHtFoXEExTQmU2EkHaOQuIJCkrqQsKTxmwihLRTnENCqVTi3LlzOHDgAABAJpNBJpMZrDBTIJbKYGYGuDq3jyHRCSHkUZw6rq9du4Z58+bBysoKYrEYY8aMwdmzZ7F7926sXr3a0DUajVhaDUEHG1ha0A4XIaR94rT1S0pKwsKFC3Hw4EFYWNTlSr9+/XD+/HmDFmdsRRIZPAS0F0EIab84hcTNmzcRHR0N4MGwHLa2tqitrTVcZSZALJXB3YVCghDSfnEKCS8vL1y5ckVn2aVLl+Dj42OQokyBQqmGtEIOdxfqtCaEtF+c+iQWLVqEuXPnYsqUKVAqlfj222/x888/Izk52dD1GU1xWV2nPO1JEELaM057EuHh4di4cSOkUin69euHgoICrFmzBmFhYYauz2iKJHUhQX0ShJD2jNOehFQqRWBgIJKSkgxcjukQS2lPghBCOO9JxMXFYe/evW3+2oh6YqkMlhbmcHbgG7sUQggxGk4hUT/6608//YRBgwbhvffew5EjR6BSqQxdn9EUSarh5mwLc3NuEysRQkhbxCkkXFxcMHXqVPz0009IT0+Hv78/vvjiizbdJyGWyuBO/RGEkHau0ZcSSyQSlJaWoqysDI6OjoaoySSIpTJ4UH8EIaSd43wx3erVqzFy5EgsWLAAALB27VocOnSIc0M5OTmYPHkyIiIiMHnyZNy5c0fvurdv30avXr2MNlNdlUyB6holXSNBCGn3OJ3d9Nprr2HUqFH4+OOPERoaCnPzxo9llJiYiNjYWERHRyMtLQ0JCQnYsmVLg/XUajUSExMxYsSIRrfRXIrqz2yiw02EkHaOU0icOHECVlZNn+NZIpEgMzMTmzdvBgBERkYiOTkZUqkULi4uOuuuX78eQ4cONeoos3T6KyGE1NEbEnv27EFMTAwAYO/evXofYOLEiU9tRCQSwd3dHTweDwDA4/Hg5uYGkUikExLZ2dk4fvw4tmzZgrVr13J+Es2tpKwGAOBGQ4QTQto5vSGxf/9+bUikpaU9dh0zMzNOIcGFUqnEP/7xDyxfvlwbJsYiuVcDK0seHGwtjVoHIYQYm96Q2LBhg/b2Dz/88EyNCIVCiMViqNVq8Hg8qNVqFBcXQygUatcpKSnB3bt38cYbbwAAKioqwBhDVVVVi48RVVpeg44d+NoRbwkhpL3i1ANdv0fxqPHjx3NqRCAQICAgAOnp6QCA9PR0BAQE6Bxq8vT0xOnTp3HkyBEcOXIEM2fOxKuvvmqUQQQl9+To6GTT4u0SQoip4RQSubm5DZYxxpCfn8+5oaSkJGzduhURERHYunUrPvroIwBAXFwcLl++zPlxWkJJeQ2FBCGE4ClnN/39738HUNdfUH+7XkFBAZ577jnODfn6+mL79u0Nlj98WOthb7/9NufHbk5qDYO0Qg5BBxqziRBCnhgSD08q9OgEQy+88AJGjx5tmKqMqLxSDo2G0Z4EIYTgKSHx1ltvAQB69eqFwYMHt0hBxia5JwcAdOxAIUEIIZwuphs8eDAUCgVycnJQVlYGxpj2dwMHDjRYccZQWl53jQTtSRBCCMeQOHfuHN555x0oFApUVVXB3t4e1dXV8PDwwOHDhw1dY4uqDwnqkyCEEI5nNy1fvhyvv/46zpw5Azs7O5w5cwbz5s1DbGysoetrcaX35LCyMIejXdOHISGEkLaCU0jcuXMHM2bM0Fn2xhtv4PvvvzdETUYlKa+BwMmGLqQjhBBwDAkHBwdUVVUBAFxdXXHz5k1UVFS0yalMS+/VUKc1IYTcxykkRo4cid9++w0AMGHCBMyYMQPjx49HRESEQYszhtJ7cgicqD+CEEIAjh3XH3zwgfb2nDlz0KtXL1RXV7e502I1GgYp7UkQQogWp5B4VEhISHPXYRLuVdVCpaYL6QghpJ7ekIiNjeXUefvjjz82a0HGVHrv/jUSdPorIYQAeEJITJo0qSXrMAml5XVXWwtoT4IQQgA8ISReeeWVlqzDJEgr7oeEI+1JEEIIwLFPYseOHXp/11wz05kCmVwJALCnGekIIQQAx5B4dPrS0tJS5OXloU+fPm0sJFSw4JnD0sK406cSQoip4BQSj5u+dMeOHbh161azF2RMNbUq2Fg36YQvQghpkzhdTPc448ePx86dO5uzFqOTyZWw5VNIEEJIPU5bRI1Go/NzTU0N9u7dCwcHB84N5eTkID4+HuXl5XByckJKSgq6dOmis87OnTvx/fffw9zcHBqNBpMmTWowZpQhyeQqCglCCHkIpy1iYGBgg2sm3N3dkZyczLmhxMRExMbGIjo6GmlpaUhISMCWLVt01omIiMD48eNhZmaGqqoqREVFoX///vD39+fczrOoqVXBlk+d1oQQUo9TSDw6Z4SNjQ1cXFw4NyKRSJCZmYnNmzcDACIjI5GcnAypVKrzOPb29trbcrkcSqWyRUdjlcmVcHKg018JIaQep5Dw8vJ6pkZEIhHc3d3B49WdNcTj8eDm5gaRSNQgbA4fPoxVq1bh7t27+Nvf/gY/P79narsxampV8OxIh5sIIaQepy1iYWEhvv76a2RlZTUYHvzXX39t1oKGDx+O4cOHo7CwEAsWLMBLL72Ebt26NWsb+sjkKthQnwQhhGhx2iIuWrQI3bp1w8KFC8HnN/5wjFAohFgshlqtBo/Hg1qtRnFxMYRCod77eHp6Ijg4GMeOHWu5kKA+CUII0cEpJG7fvo1t27bB3LxpZ8wKBAIEBAQgPT0d0dHRSE9PR0BAQINDTbdu3YKvry8AQCqV4vTp0xg1alST2mwstVqDWoWarpMghJCHcNoihoeH48yZMxgwYECTG0pKSkJ8fDzWrl0LR0dHpKSkAADi4uKwcOFCBAcHY9u2bThx4gQsLCzAGMO0adMQFhbW5DYbo6ZWBQB0CiwhhDyE0xbxww8/xJQpU+Dj4wOBQKDzu+XLl3NqyNfXF9u3b2+wfMOGDdrbS5cu5fRYhiCrDwnakyCEEC1OW8QlS5aAx+PB19cX1tbWhq7JKGrk9XsS1CdBCCH1OIXEqVOn8Mcff+hcx9DWyO6HBPVJEELIA5x6ov38/FBeXm7oWoxKVls3TDj1SRBCyAOctogDBgzAnDlzMH78+AZ9Em1lqHDtngSFBCGEaHHaIp4/fx5ubm44fvy4znIzM7M2ExLas5usqU+CEELqNXk+ibaG9iQIIaShJg0V/rCmXmBnamruT11KHdeEEPJAk4cKr5eVldWsBRmLrFYFvhUPPPOWG3WWEEJMXZOGCi8pKcH69esRHh5ukKKMgSYcIoSQhpo0VLiXlxdSUlIwceJETJo0ySCFtbS6+a2p05oQQh7W5A6FqqoqSKXS5qzFqGRyJXVaE0LIIzhtFRcvXqzTJyGXy3H27FmMGzfOYIW1NJlcReM2EULIIzhtFTt37qzzs42NDaZMmYIXX3zRIEUZQ02tCh3sbY1dBiGEmBROIfHWW28Zug6jk8mVNLgfIYQ8glOfxCeffIILFy7oLLtw4QKWLVtmkKKMoa7jmg43EULIwziFRHp6OoKCgnSWBQUFIT093SBFtTTGGJ0CSwghj8EpJMzMzMAY01mmVqufeCV2a6JQaaDWMNqTIISQR3AKiZCQEKxevVobChqNBmvWrEFISIhBi2spMnn9MOHUJ0EIIQ/j9K/zBx98gLlz5yIsLAyenp4QiURwdXXFunXrODeUk5OD+Ph4lJeXw8nJCSkpKejSpYvOOqmpqThw4ADMzc1haWmJd999F4MHD27UE2qKGppwiBBCHovTVtHDwwO7d+/GpUuXIBKJIBQK0bNnz0YN7peYmIjY2FhER0cjLS0NCQkJ2LJli846PXv2xOzZs2FjY4Ps7GxMmzYNx48fB5/Pb9yzaiTt/NbUJ0EIITo4b+XNzc3Ru3dvvPzyy+jdu3ejAkIikSAzMxORkZEAgMjISGRmZja4Ynvw4MGwsbEBUDcbHmOsRWbEezC/NYUEIYQ8rEXG+RaJRHB3dwePxwMA8Hg8uLm5QSQS6b3Pnj174OPjAw8PD4PXp+2ToLGbCCFEh0n+63zmzBl8+eWX2LRpU4u0V3+4icZuIoQQXS2yJyEUCiEWi6FWqwHUnT5bXFwMoVDYYN2MjAwsXrwYqamp6NatW0uUp52VjsZuIoQQXS0SEgKBAAEBAdqL79LT0xEQEAAXFxed9S5duoR3330XX331FXr06NESpQEA7PgWcLC1hL0tHW4ihJCHtdi/zklJSYiPj8fatWvh6OiIlJQUAEBcXBwWLlyI4OBgfPTRR5DL5UhISNDe77PPPoOfn59Ba3upjzdCg4SwtOAZtB1CCGltWiwkfH19sX379gbLN2zYoL29c+fOlipHh7m5GV0jQQghj9Eih5sIIYS0ThQShBBC9KKQIIQQoheFBCGEEL0oJAghhOhFIUEIIUSvNnPeZ/3V3EVFRUauhBBCWo/6bWb9NvRRbSYkSkpKAABTp041ciWEENL6lJSUoHPnzg2Wm7FH5yVtpeRyOa5cuQJXV1ftaLOEEEKeTK1Wo6SkBEFBQY+du6fNhAQhhJDmRx3XhBBC9KKQIIQQoheFBCGEEL0oJAghhOhFIUEIIUQvCglCCCF6UUgQQgjRi0ICQE5ODiZPnoyIiAhMnjwZd+7cMWo9ZWVliIuLQ0REBKKiovDWW29BKpUCAC5evIhx48YhIiICs2fPhkQiMWqtAPD111/Dz88P169fB2BaNdbW1iIxMRGjRo1CVFQU/vGPfwAwnb/50aNHERMTg+joaIwbNw6HDh0yen0pKSkYNmyYzt/0aTW1dL2Pq/FJnxug5d+X+l7Heo9+boxRIyeMsOnTp7M9e/Ywxhjbs2cPmz59ulHrKSsrY6dOndL+vGLFCrZkyRKmVqvZiBEj2NmzZxljjKWmprL4+HhjlckYY+zKlStszpw5LDw8nF27ds3kakxOTmbLli1jGo2GMcZYSUkJY8w0/uYajYaFhISwa9euMcYYy8rKYr1792Zqtdqo9Z09e5YVFhZq/6b1nlRTS9f7uBr1fW4YY0Z5X+p7HRlr+LkxVo1ctPuQKC0tZX379mUqlYoxxphKpWJ9+/ZlEonEyJU9cPDgQTZz5kz2119/sbFjx2qXSyQS1rt3b6PVVVtby1599VWWl5enfbObUo1VVVWsb9++rKqqSme5qfzNNRoN69+/Pzt37hxjjLEzZ86wUaNGmUx9D2/AnlSTMet93Aa4Xv3nhjFm1PflozU+7nNj7BqfpM0M8NdUIpEI7u7u2vGeeDwe3NzcIBKJ4OLiYuTqAI1Gg59++gnDhg2DSCSCp6en9ncuLi7QaDQoLy+Hk5NTi9f25ZdfYty4cfD29tYuM6Ua8/Ly4OTkhK+//hqnT5+GnZ0dFi1aBD6fbxJ/czMzM6xevRrz58+Hra0tqqursX79epN8Tz6pJsaYydX78Oemvn5TeV8+7nNjajU+jPokTFxycjJsbW0xbdo0Y5eiIyMjA1euXEFsbKyxS9FLrVYjLy8PgYGB2LVrF/7v//4Pb7/9NmQymbFLAwCoVCp8++23WLt2LY4ePYpvvvkG77zzjsnU15rR56b5tPs9CaFQCLFYDLVaDR6PB7VajeLiYgiFQmOXhpSUFOTm5mLdunUwNzeHUChEYWGh9vdSqRTm5uZG+S/j7NmzuHXrFoYPHw6gbkz6OXPmYPr06SZTo1AohIWFBSIjIwEAvXr1grOzM/h8vkn8zbOyslBcXIy+ffsCAPr27QsbGxtYW1ubRH0Pe9LnhDFmUvU++rmpr98U3pf6PjfLly83mRof1e73JAQCAQICApCeng4ASE9PR0BAgNEPNa1atQpXrlxBamoqrKysAABBQUGQy+U4d+4cAODnn3/G6NGjjVLfG2+8gePHj+PIkSM4cuQIPDw88N133+H11183mRpdXFwQGhqKEydOAKg7A0cikaBLly4m8Tf38PBAUVERbt++DQC4desWJBIJOnfubBL1PexJnxNT+gw97nMDmM5nR9/nJiwszGRqfBQNFY66D2d8fDwqKirg6OiIlJQUdOvWzWj13LhxA5GRkejSpYt2fHdvb2+kpqbiwoULSExMRG1tLby8vLBy5Up07NjRaLXWGzZsGNatW4fu3bubVI15eXlYunQpysvLYWFhgXfeeQdDhgwxmb/53r17sWHDBpiZmQEAFi5ciBEjRhi1vk8++QSHDh1CaWkpnJ2d4eTkhP379z+xppau93E1rl69Wu/nBkCLvy/1vY4Pe/hzY4wauaCQIIQQole7P9xECCFEPwoJQgghelFIEEII0YtCghBCiF4UEoQQQvSikCCt2rBhw/Dnn38ape3S0lJMnToVffr0wYoVK4xSAyGG1u6vuCakqbZt2wZnZ2dcuHBBe50DqRMfHw93d3e8++67xi6FPCPakyAEdeMoNVZhYSF8fX0pIEibRiFBmt2wYcPw3XffISoqCn379sU777yD2tpaAMCuXbvw2muv6azv5+eH3NxcAHX/gSYlJeH1119Hnz59MGXKFJSUlGDZsmXo168fRo8ejczMTJ37X758GWPGjEG/fv2wZMkSbVtA3aQ+0dHRCAkJwZQpU5Cdna1T5/r16xEVFYXevXs/NiguXLiACRMmoG/fvpgwYQIuXLigrXPPnj347rvv0KdPn8ce8pLL5VixYgXCw8PRt29fvPbaa5DL5QCAw4cPY+zYsQgJCcH06dNx69Ytnbo2btyorWvp0qUoLS3VviazZs3CvXv3AAD5+fnw8/PDtm3bEBYWhrCwMHz33Xfax1IoFFi2bJn2d8uWLYNCoQAAnD59Gi+99BI2bdqEgQMHIiwsDDt37tS5b0pKCoYOHYoXX3wRCQkJ2vqfdN9t27Zh37592tfmzTffBACsX78egwcPRp8+fRAREYGTJ082eM2ICTLmOOWkbQoPD2cTJkxgRUVFrKysjI0ePZr9+9//ZowxtnPnTjZlyhSd9bt3787u3LnDGGPs/fffZ/3792eXL19mcrmcTZ8+nYWHh7Pdu3czlUrFVq1axaZNm6bT1tixY1lhYSErKytjkydPZqtWrWKMMXb16lU2YMAAdvHiRaZSqdiuXbtYeHg4q62t1d533LhxrLCwkNXU1DR4HmVlZSwkJITt3r2bKZVKtm/fPhYSEsKkUqm21vq2HicpKYlNmzaNFRUVMZVKxc6fP89qa2vZ7du3Wa9evdjx48eZQqFg69evZyNGjNCpa9KkSaykpIQVFRWxAQMGsJiYGHb16lXta7JmzRrGGGN5eXmse/fu7N1332XV1dUsOzubhYaGshMnTjDGGFu9ejWbNGkSKy0tZRKJhE2ePJl98cUXjDHGTp06xQICAtjq1auZQqFgx44dYz179mTl5eWMMcaWLVvG5s6dy8rKylhlZSWbO3cu+/zzzznd99HX5tatW+yll15iRUVF2rpzc3Of9DYiJoL2JIhBTJ8+He7u7nByckJ4eDiysrI433fkyJEICgqCtbU1Ro4cCWtra8TExIDH42HMmDENHmvq1KkQCoVwcnLCvHnztOPjbNu2DZMnT0avXr3A4/HwyiuvwNLSEhcvXtSpUygUasf6edixY8fQuXNnxMTEaEeT7datG44ePfrU56DRaLBz50588MEH2rkWXnjhBVhZWeHAgQMYMmQIBg0aBEtLS8yZMwdyuRwZGRna+0+bNg0dO3aEu7s7QkJC0LNnTwQGBmpfk0f3phYsWABbW1v4+flh/Pjx2sH29u3bhwULFkAgEMDFxQULFizA3r17tfezsLDAggULYGlpiSFDhsDW1hY5OTlgjOE///kPli5dCicnJ9jb22Pu3Lk6Yw/pu+/j8Hg8KBQK3Lp1C0qlEt7e3vDx8Xnq60iMjzquiUG4urpqb9vY2KC4uJjzfQUCgfY2n8/XGeCMz+c3mG/h4SGpPT09tW0VFhZiz5492Lp1q/b3SqVSp5YnDWddXFysMwlM/eOLxeKnPoeysjLU1taiU6dOT33c+mHgH37ch5+ztbV1o14DLy8v7bzJj7b18OsDAE5OTrCweLAZsLGxgUwmg1QqRU1NDcaPH6/9HWMMGo3mqfd9nM6dO2Pp0qVYs2YNbt68ibCwMG3nNjFtFBKkRdnY2GiPawNASUnJMz+mSCTS3i4sLISbmxuAug3nm2++iXnz5um975M6nd3c3HTG969va/DgwU+tydnZGdbW1sjLy4O/v3+Dx63fiAN1G9/6md+aSiQSwdfXF4Dua1D/HJ5//nntevW/e1r9fD4f+/fvb1Jdj3tdo6KiEBUVhaqqKiQkJODzzz/HypUrG/3YpGXR4SbSovz9/XHjxg1kZWWhtrYWa9aseebH/Pe//42ioiKUl5dj3bp1GDNmDABg0qRJ+Pnnn/HXX3+BMQaZTIZjx46hqqqK0+MOGTIEd+7cwb59+6BSqXDgwAHcvHkTQ4cOfep9zc3NMWHCBCxfvlw7IU9GRgYUCgVefvll/Pbbbzh58iSUSiU2bdoEKysr9OnTp8mvwdq1a1FTU4MbN25g165d2tdg7Nix+OabbyCVSiGVSpGamoqoqChO9U+aNAmffvopJBIJAEAsFuOPP/7gVI9AIEB+fr7259u3b+PkyZNQKBSwsrKCtbW1dkIgYtror0RaVNeuXbFgwQLMmjULo0aN0s7K9iwiIyMxe/ZsjBgxAj4+Pto9h+DgYCQnJ+Pjjz9Gv379MGrUKOzatYvz4zo7O2PdunXYvHkzQkNDsXHjRqxbt47zZDrvv/8+unfvjokTJ6J///74/PPPodFo0K1bN6xcuRLJyckYMGAAjh49inXr1ulMktNY/fv3x8iRIzFr1izMnj0bYWFhAID58+cjKCgI48aNw7hx49CjRw/Mnz+f02MuXrwYnTt3xquvvooXXngBs2bN0tvn8KiJEyfi5s2bCAkJwfz586FQKPDPf/4ToaGhCAsLg1QqxXvvvdfk50taDs0nQUgrlp+fj+HDh+Pq1as6/QOENBfakyCEEKIXhQQhhBC96HATIYQQvWhPghBCiF4UEoQQQvSikCCEEKIXhQQhhBC9KCQIIYToRSFBCCFEr/8H/ZPztavx1fsAAAAASUVORK5CYII=\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"Uv5g6ooZk_0t"},"source":["Βλέπουμε ότι αυτά τα 150 στοιχεία αντιπροσωπεύουν λίγο περισσότερο από το 90% της διακύμανσης. Αυτό θα μας έκανε να πιστεύουμε ότι χρησιμοποιώντας αυτά τα 150 στοιχεία, θα ανακτήσουμε τα περισσότερα από τα βασικά χαρακτηριστικά των δεδομένων. Για να το κάνουμε πιο συγκεκριμένο, μπορούμε να συγκρίνουμε τις εικόνες εισόδου με τις εικόνες που ανακατασκευάστηκαν από αυτά τα 150 στοιχεία:"]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"PTwWghb5k_0u"},"source":["# Compute the components and projected faces\n","pca = RandomizedPCA(150).fit(faces.data)\n","components = pca.transform(faces.data)\n","projected = pca.inverse_transform(components)"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"deletable":true,"editable":true,"id":"9zxlJlpdk_0w","colab":{"base_uri":"https://localhost:8080/","height":178},"executionInfo":{"status":"ok","timestamp":1604328751429,"user_tz":-120,"elapsed":2535,"user":{"displayName":"Katerina A","photoUrl":"","userId":"12077637925353215781"}},"outputId":"0b2ed3a8-72db-413a-86cc-51027f376ffe"},"source":["# Plot the results\n","fig, ax = plt.subplots(2, 10, figsize=(10, 2.5),\n"," subplot_kw={'xticks':[], 'yticks':[]},\n"," gridspec_kw=dict(hspace=0.1, wspace=0.1))\n","for i in range(10):\n"," ax[0, i].imshow(faces.data[i].reshape(62, 47), cmap='binary_r')\n"," ax[1, i].imshow(projected[i].reshape(62, 47), cmap='binary_r')\n"," \n","ax[0, 0].set_ylabel('full-dim\\ninput')\n","ax[1, 0].set_ylabel('150-dim\\nreconstruction');"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"deletable":true,"editable":true,"id":"aawJMH-tk_0z"},"source":["Η επάνω σειρά δείχνει τις εικόνες εισόδου, ενώ η κάτω σειρά δείχνει την ανακατασκευή των εικόνων από μόλις 150 από τα ~ 3.000 αρχικά χαρακτηριστικά. \n","\n","Αυτή η οπτικοποίηση καθιστά σαφές γιατί η επιλογή χαρακτηριστικών με PCA είναι τόσο επιτυχημένη: αν και μειώνει τη διάσταση των δεδομένων κατά σχεδόν έναν παράγοντα 20, οι προβαλλόμενες εικόνες περιέχουν αρκετές πληροφορίες ώστε να μπορούμε να αναγνωρίσουμε τα άτομα που εμφανίζονται σε αυτές. \n","\n","Αυτό σημαίνει ότι ο αλγόριθμος ταξινόμησης πρέπει να εκπαιδεύεται σε δεδομένα 150 διαστάσεων και όχι σε δεδομένα 3.000 διαστάσεων, τα οποία ανάλογα με τον συγκεκριμένο αλγόριθμο που επιλέγουμε, μπορούν να οδηγήσουν σε πολύ πιο αποτελεσματική ταξινόμηση."]}]}