{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"Clustering 1.2 Hierarchical - Density - Fuzzy.ipynb","provenance":[],"collapsed_sections":[]},"kernelspec":{"name":"python3","display_name":"Python 3"}},"cells":[{"cell_type":"markdown","metadata":{"id":"6kwtzEtzwdef"},"source":["\n","# Ιεραρχική συσταδοποίηση\n","\n","Η [ιεραρχική συσταδοποίηση](https://scikit-learn.org/stable/modules/clustering.html#hierarchical-clustering) δημιουργεί μια ολόκληρη ιεραρχία απο συστάδες. Με αυτόν τον τρόπο, κάθε παράδειγμα μπορεί να ανήκει σε πολλαπλές συστάδες, διαφορετικών ιεραρχιών.\n","\n","![](http://quantdare.com/wp-content/uploads/2016/06/AggloDivHierarClustering-800x389.png)\n","\n","\n","Η ιεραρχική συσταδοποίηση μπορεί να γίνει με δύο τρόπους: \n","* Top-down: διαιρετική συσταδοποίηση (divisive clustering). Από ένα cluster που\n","περιλαμβάνει όλα τα σημεία φτάνουμε σέ ένα cluster ανά σημείο. Παράδειγμα divisive αλγόριθμου: DIANA (DIvisive ANAlysis).\n","\n","* Bottom-up: συσσωρευτική συσταδοποίηση (agglomerative clustering). Ξεκινάμε από ένα cluster ανά σημείο και συσσωρεύουμε (ενώνουμε) clusters μέχρι να καταλήξουμε σε ένα cluster που περιλαμβάνει όλα τα σημεία. Παράδειγμα αλγόριθμου: AGNES (AGglomerative NESting), ή αλλιώς HAC (Hierarchical Aglomerative Clustering).\n"]},{"cell_type":"markdown","metadata":{"id":"gUasK4r7hD5e"},"source":["## DIANA\n","\n"]},{"cell_type":"markdown","metadata":{"id":"dyPsQmBpib9G"},"source":["Θα ορίσουμε ένα toy - dataset και έναν πίνακα απόστασης-ανομοιομορφίας (dissimilarity_matrix) μεταξύ των σημείων του."]},{"cell_type":"code","metadata":{"id":"Lk-qBtD3hoPV","colab":{"base_uri":"https://localhost:8080/","height":286},"executionInfo":{"status":"ok","timestamp":1637654693973,"user_tz":-120,"elapsed":919,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"7abd3b74-2011-482e-92d8-e2d2bacddc16"},"source":["import numpy as np;\n","import pandas as pd\n","import seaborn as sns\n","%matplotlib inline\n","\n","num_clusters = 0\n","mat = np.array([[0,2,6,10,9],[2,0,5,9,8],[6,5,0,4,5],[10,9,4,0,3],[9,8,5,3,0]])\n","all_elements = ['a','b','c','d','e']\n","dissimilarity_matrix = pd.DataFrame(mat,index=all_elements, columns=all_elements)\n","\n","sns.heatmap(dissimilarity_matrix)"],"execution_count":1,"outputs":[{"output_type":"execute_result","data":{"text/plain":[""]},"metadata":{},"execution_count":1},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"1E9IWGn4jmSH"},"source":["Βήμα 1. Ας υποθέσουμε ότι η συστάδα Cl πρόκειται να χωριστεί σε συστάδες Ci και Cj .\n","\n","Βήμα 2. Έστω Ci = Cl και Cj = Ø.\n","\n","Βήμα 3. Για κάθε αντικείμενο x > Ci:\n","1. Για την πρώτη επανάληψη, υπολογίστε τη μέση απόσταση του x από όλα τα άλλα\n","αντικείμενα.\n","2. Για τις υπόλοιπες επαναλήψεις, υπολογίστε Dx = μέσος όρος {d(x; y) ∈ y > Ci} - μέσος όρος{d(x; y) ∈ y > Cj}: \n","\n","![](https://educatech.in/wp-content/uploads/2020/12/ml7.png)\n","\n","*Σχήμα : Dx= (μέσος όρος των διακεκομμένων γραμμών) - (μέσος όρος των συμπαγών γραμμών)*\n","\n","Βήμα 4.\n","1. Για την πρώτη επανάληψη, μετακινήστε το αντικείμενο με τη μέγιστη μέση απόσταση στο Cj .\n","2. Για τις υπόλοιπες επαναλήψεις, βρείτε ένα αντικείμενο x στο Ci για το οποίο το Dx είναι το μεγαλύτερο. Εάν Dx > 0, τότε μετακινήστε το x στο Cj .\n","\n","Βήμα 5. Επαναλάβετε τα βήματα 3.2 και 4.2 έως ότου όλες οι διαφορές Dx είναι αρνητικές. Τότε το Cl χωρίζεται σε Ci και Cj .\n","\n","Βήμα 6. Επιλέξτε τη μικρότερη συστάδα με τη μεγαλύτερη διάμετρο. (Η διάμετρος μιας συστάδας είναι η μεγαλύτερη ανομοιότητα μεταξύ δύο οποιωνδήποτε αντικειμένων της). Στη συνέχεια, διαιρέστε αυτή τη συστάδα, ακολουθώντας τα βήματα 1-5.\n","\n","Βήμα 7. Επαναλάβετε το Βήμα 6 έως ότου όλες οι συστάδες να περιέχουν μόνο ένα αντικείμενο.\n","\n","\n","Ακολουθεί ο κώδικας υλοποίησης καθώς και έξοδός που τυπώνει όλα τα επίπεδα clustering για το συγκεκριμένο παράδειγμα, από το ένα ενιαίο cluster σε πέντε μεμονωμένα:\n"]},{"cell_type":"code","metadata":{"id":"tgLOq3rPdepV","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1637654694309,"user_tz":-120,"elapsed":3,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"5436db87-8ff3-4271-dce4-776aa87801e3"},"source":["def avg_dissim_within_group_element(ele, element_list):\n"," max_diameter = -np.inf\n"," sum_dissm = 0\n"," for i in element_list:\n"," sum_dissm += dissimilarity_matrix[ele][i] \n"," if( dissimilarity_matrix[ele][i] > max_diameter):\n"," max_diameter = dissimilarity_matrix[ele][i]\n"," if(len(element_list)>1):\n"," avg = sum_dissm/(len(element_list)-1)\n"," else: \n"," avg = 0\n"," return avg\n","\n","def avg_dissim_across_group_element(ele, main_list, splinter_list):\n"," if len(splinter_list) == 0:\n"," return 0\n"," sum_dissm = 0\n"," for j in splinter_list:\n"," sum_dissm = sum_dissm + dissimilarity_matrix[ele][j]\n"," avg = sum_dissm/(len(splinter_list))\n"," return avg\n"," \n"," \n","def splinter(main_list, splinter_group):\n"," most_dissm_object_value = -np.inf\n"," most_dissm_object_index = None\n"," for ele in main_list:\n"," x = avg_dissim_within_group_element(ele, main_list)\n"," y = avg_dissim_across_group_element(ele, main_list, splinter_group)\n"," diff= x -y\n"," if diff > most_dissm_object_value:\n"," most_dissm_object_value = diff\n"," most_dissm_object_index = ele\n"," if(most_dissm_object_value>0):\n"," return (most_dissm_object_index, 1)\n"," else:\n"," return (-1, -1)\n"," \n","def split(element_list):\n"," main_list = element_list\n"," splinter_group = [] \n"," (most_dissm_object_index,flag) = splinter(main_list, splinter_group)\n"," while(flag > 0):\n"," main_list.remove(most_dissm_object_index)\n"," splinter_group.append(most_dissm_object_index)\n"," (most_dissm_object_index,flag) = splinter(element_list, splinter_group)\n"," \n"," return (main_list, splinter_group)\n","\n","def max_diameter(cluster_list):\n"," max_diameter_cluster_index = None\n"," max_diameter_cluster_value = -np.inf\n"," index = 0\n"," for element_list in cluster_list:\n"," for i in element_list:\n"," for j in element_list:\n"," if dissimilarity_matrix[i][j] > max_diameter_cluster_value:\n"," max_diameter_cluster_value = dissimilarity_matrix[i][j]\n"," max_diameter_cluster_index = index\n"," \n"," index +=1\n"," \n"," if(max_diameter_cluster_value <= 0):\n"," return -1\n"," \n"," return max_diameter_cluster_index\n"," \n","\n","current_clusters = ([all_elements])\n","level = 1\n","index = 0\n","while(index!=-1):\n"," print(level, current_clusters)\n"," (a_clstr, b_clstr) = split(current_clusters[index])\n"," del current_clusters[index]\n"," current_clusters.append(a_clstr)\n"," current_clusters.append(b_clstr)\n"," index = max_diameter(current_clusters)\n"," level +=1\n","\n","\n","print(level, current_clusters)"],"execution_count":2,"outputs":[{"output_type":"stream","name":"stdout","text":["1 [['a', 'b', 'c', 'd', 'e']]\n","2 [['c', 'd', 'e'], ['a', 'b']]\n","3 [['a', 'b'], ['d', 'e'], ['c']]\n","4 [['a', 'b'], ['c'], ['e'], ['d']]\n","5 [['c'], ['e'], ['d'], ['b'], ['a']]\n"]}]},{"cell_type":"markdown","metadata":{"id":"2-KV2SM9lw3K"},"source":["## Ιεραρχική συσσωρευτική συσταδοποίηση\n","\n","Υπάρχουν γενικά αρκετά περισσότεροι συσσωρευτικοί αλγόριθμοι συσταδοποίησης από διαιρετικούς. Ένας ευρέως χρησιμοποιούμενος είναι η Ιεραρχική συσσωρευτική συσταδοποίηση (Hieararchical Agglomerative Clustering - HAC).\n","\n","\n","### Τύποι συνδέσμων (linkage)\n","\n","Μια σημαντική υπερπαράμετρος των συσσωρευτικών αλγορίθμων είναι ο τύπος των συνδέσμων μεταξύ συστάδων. Μπορούμε να έχουμε τους εξής συνδέσμους (ή αλλιώς αποστάσεις μεταξύ clusters):\n","\n","- Ward: ελαχιστοποίηση της διακύμανσης των cluster που θα ενωθούν. Η σύνδεση Ward έχει πολλά κοινά με την ανάλυση διακύμανσης (ANOVA). Η συνάρτηση σύνδεσης που προσδιορίζει την απόσταση μεταξύ δύο συστάδων υπολογίζεται ως η αύξηση του \"αθροίσματος τετραγώνων σφάλματος\" (ESS) μετά τη συνένωση δύο συστάδων σε μία ενιαία συστάδα. Η μέθοδος Ward επιδιώκει να επιλέξει τα διαδοχικά βήματα συσταδοποίησης έτσι ώστε να ελαχιστοποιείται η αύξηση του ESS σε κάθε βήμα. To ESS για ένα cluster με $n$ δείγματα $x_1, x_2, ..., x_n$ υπολογίζεται από τη σχέση: $$\n","\\mathrm{ESS}=\\sum_{i=1}^{n} x_{i}^{2}-\\frac{1}{n}\\left(\\sum_{i=1}^{n} x_{i}\\right)^{2}.\n","$$ Μπορούμε να δείξουμε ότι: $$\n","\\begin{aligned}\n","\\operatorname{Var}(\\vec{x}) \\propto \\sum_{i=1}^{n}\\left(x_{i}-\\bar{x}\\right)^{2} &=\\sum_{i} x_{i}^{2}-2 \\bar{x} \\sum_{i} x_{i}+n \\bar{x}^{2} \\\\\n","&=\\sum_{i} x_{i}^{2}-n \\bar{x}^{2}=\\sum_{i} x_{i}^{2}-\\frac{1}{n}\\left(\\sum_{i} x_{i}\\right)^{2}=\\mathrm{ESS} .\n","\\end{aligned}\n","$$ Ορίζουμε τελικά την απόσταση δύο clusters $Χ$ και $Y$ ως $$\n","D(X, Y)=\\operatorname{ESS}(X Y)-[E S S(X)+\\operatorname{ESS}(Y)],\n","$$ όπου\n"," - $ΧY$ είναι το ενοποιημένο cluster των $Χ$ και $Y$ και\n"," - $ESS(\\cdot)$ είναι το άθροισμα τετραγώνων σφάλματος που ορίστηκε προηγουμένως.\n","\n","- Μέσος όρος (average): χρησιμοποιεί το μέσο όρο των αποστάσεων κάθε παρατήρησης των δύο συνόλων.\n","- Πλήρης (complete) ή μέγιστη (maximum) σύνδεση: χρησιμοποιεί τις μέγιστες αποστάσεις μεταξύ όλων των παρατηρήσεων των δύο συνόλων.\n","- Μονή (single) σύνδεση: χρησιμοποιεί τις ελάχιστες αποστάσεις μεταξύ όλων των παρατηρήσεων των δύο συνόλων.\n","\n","Η επιλογή του τύπου συνδέσμου οδηγεί σε διαφορετικά clustering του ίδιου dataset όπως φαίνεται στο ακόλουθο σχήμα:\n","\n","![](https://slideplayer.com/slide/5116404/16/images/53/Hierarchical+Clustering%3A+Comparison.jpg)"]},{"cell_type":"markdown","metadata":{"id":"KbVavfWtfX8J"},"source":["\n","\n","\n","\n","\n","\n","\n","\n","\n","#### Παράδειγμα: HAC στο Iris\n","\n","\n","Θα χρησιμοποιήσουμε τη συνάρτηση HAC του scikit με μέθοδο Ward.\n","\n","\n"]},{"cell_type":"code","metadata":{"id":"vcCdIrTy1K7V","executionInfo":{"status":"ok","timestamp":1637654694901,"user_tz":-120,"elapsed":593,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}}},"source":["from sklearn import datasets\n","\n","# εισαγωγή του iris dataset από το scikit-learn\n","iris = datasets.load_iris()\n","feat = iris.feature_names\n","X = iris.data[:, :2] # Για εποπτικούς λόγους, λαμβάνουμε υπόψη μας μόνο τα δύο \n"," # πρώτα χαρακτηριστικά\n","y = iris.target\n","y_name = ['Setosa', 'Versicolour', 'Virginica']"],"execution_count":3,"outputs":[]},{"cell_type":"code","metadata":{"id":"0cXJsQHX4qDI","executionInfo":{"status":"ok","timestamp":1637654694901,"user_tz":-120,"elapsed":2,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}}},"source":["# Φορτώνουμε τον αλγόριθμο (κλάση) HAG, ο οποίος υπάρχει υλοποιημένος στο\n","# scikit-learn\n","\n","from sklearn.cluster import AgglomerativeClustering\n","clustering = AgglomerativeClustering(linkage=\"ward\", n_clusters=3)\n","clustering.fit(X);"],"execution_count":4,"outputs":[]},{"cell_type":"code","metadata":{"id":"Gp4rGINK46RH","colab":{"base_uri":"https://localhost:8080/","height":257},"executionInfo":{"status":"ok","timestamp":1637654695797,"user_tz":-120,"elapsed":3,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"40cc62a5-ad91-4e4e-a5cd-38252014f8c0"},"source":["import numpy as np\n","import matplotlib.pyplot as plt\n","%matplotlib inline\n","# Γραμμική κλιμάκωση των δεδομένων, έτσι ώστε να εμφανίζονται καλύτερα στους \n","# άξονες του διαγράμματος\n","from sklearn import preprocessing\n","X_plot = preprocessing.MinMaxScaler().fit_transform(X)\n","\n","colours = 'rbg'\n","for i in range(X.shape[0]):\n"," plt.text(X_plot[i, 0], X_plot[i, 1], str(clustering.labels_[i]),\n"," color=colours[y[i]],\n"," fontdict={'weight': 'bold', 'size': 9}\n"," )\n","\n","plt.xticks([])\n","plt.yticks([])\n","plt.axis('off')\n","plt.show()"],"execution_count":5,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{}}]},{"cell_type":"markdown","metadata":{"id":"PkznuNRa4-Hi"},"source":["## Δενδρογράμματα\n","\n","Τα δενδρογράμματα είναι μια ιεραρχική απεικόνιση των συστάδων όπου: \n","\n","- ο οριζόντιος άξονας αντιπροσωπεύει συστάδες.\n","- το ύψος των κατακόρυφων ακμών είναι ανάλογο με την απόσταση μεταξύ των κέντρων των συστάδων"]},{"cell_type":"code","metadata":{"id":"5EkBpCn-8wXH","colab":{"base_uri":"https://localhost:8080/","height":369},"executionInfo":{"status":"ok","timestamp":1637654700328,"user_tz":-120,"elapsed":4533,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"0ab4310b-9265-490c-abaf-869d1f271a35"},"source":["from scipy.cluster.hierarchy import dendrogram, linkage\n","\n","linkage_matrix = linkage(X, 'ward')\n","figure = plt.figure(figsize=(7.5, 5))\n","dendrogram(\n"," linkage_matrix,\n"," color_threshold=0,\n",")\n","plt.title('Hierarchical Clustering Dendrogram (Ward)')\n","plt.xlabel('sample index')\n","plt.ylabel('Από')\n","plt.tight_layout()"],"execution_count":6,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"wx3bF_Zk9BA3"},"source":["Μπορούμε να απλοποιήσουμε το δενδρόγραμμα ως εξής:"]},{"cell_type":"code","metadata":{"id":"5g0oYGR99vj8","colab":{"base_uri":"https://localhost:8080/","height":381},"executionInfo":{"status":"ok","timestamp":1637654701546,"user_tz":-120,"elapsed":1221,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"ed2d4b01-8371-400c-e8b1-26b23b06d1c0"},"source":["figure = plt.figure(figsize=(7.5, 5))\n","dendrogram(\n"," linkage_matrix,\n"," truncate_mode='lastp', # εμφάνιση μόνο των τελευταίων p συγχωνευμεων \n"," # συστάδων\n"," p=24, \n"," leaf_rotation=90.,\n"," leaf_font_size=12.,\n"," color_threshold=0,\n"," show_contracted=True, \n",")\n","plt.title('Hierarchical Clustering Dendrogram (Ward, aggregated)')\n","plt.xlabel('sample index or (cluster size)')\n","plt.ylabel('distance')"],"execution_count":7,"outputs":[{"output_type":"execute_result","data":{"text/plain":["Text(0, 0.5, 'distance')"]},"metadata":{},"execution_count":7},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"aJY-sENOuf20"},"source":["# Συσταδοποίηση βασισμένη στην πυκνότητα\n"]},{"cell_type":"markdown","metadata":{"id":"9fcVoyxn0LMl"},"source":["\n","## Μη κυρτά σύνολα δεδομένων\n","\n","Ένα από τα προβλήματα του kMeans είναι ότι δεν μπορεί να διαχωρίσει μη κυρτές επιφάνειες:"]},{"cell_type":"code","metadata":{"id":"e8i0pH3wzNpG","colab":{"base_uri":"https://localhost:8080/","height":265},"executionInfo":{"status":"ok","timestamp":1637654701546,"user_tz":-120,"elapsed":4,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"ad4cd504-1586-4b2e-f120-d6430ab0d351"},"source":["from sklearn import datasets\n","from sklearn.cluster import KMeans\n","from sklearn.datasets import make_moons\n","from mpl_toolkits.mplot3d import Axes3D\n","\n","import itertools\n","\n","# irregular shaped data\n","X, y = make_moons(n_samples=1400, shuffle=True, \n","\tnoise=0.1, random_state=120)\n","y_pred = KMeans(n_clusters=2, random_state=0).fit_predict(X)\n","colors = [['r', 'g', 'b'][c] for c in y_pred]\n","\n","plt.scatter(X[:, 0], X[:, 1], \n","\tcolor=colors, edgecolor='k', alpha=0.5)\n","\n","plt.show()"],"execution_count":8,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"2BcrzyWPz_1j"},"source":["Σε τέτοιου είδους προβλήματα είναι καταλληλότεροι οι αλγόριθμοι που βασίζονται στην πυκνότητα όπως ο DBSCAN."]},{"cell_type":"markdown","metadata":{"id":"bVs7HmpRzJjE"},"source":["\n","\n","\n","## DBSCAN\n","\n","Η πιο διαδεδομένη συσταδοποίηση με βάση την πυκνότητα είναι η χωρική συσταδοποίηση βάσει πυκνότητας για εφαρμογές με θόρυβο (Density-based spatial clustering of applications with noise - DBSCAN).\n","\n","Η DBSCAN μπορεί να ανακαλύψει συστάδες διαφορετικών σχημάτων και μεγεθών από μεγάλο όγκο δεδομένων, τα οποία περιέχουν θόρυβο και ακραίες τιμές.\n","\n","Ο αλγόριθμος DBSCAN χρησιμοποιεί δύο παραμέτρους:\n","\n","- $minPts$: Ο ελάχιστος αριθμός σημείων (ένα κατώφλι) που συγκεντρώνονται σε συστάδες για να θεωρηθεί μια περιοχή πυκνή.\n","- $eps(ε)$: Ένα μέτρο απόστασης που θα χρησιμοποιηθεί για τον εντοπισμό των σημείων στη γειτονιά κάθε σημείου.\n","\n","Αυτές οι παράμετροι μπορούν να γίνουν κατανοητές αν εξερευνήσουμε δύο έννοιες που ονομάζονται Density Reachability (Προσπελασιμότητα πυκνότητας) και Density Connectivity (Συνδεσιμότητα πυκνότητας).\n","\n","Η προσπελασιμότητα από την άποψη της πυκνότητας ορίζει ότι ένα σημείο είναι προσπελάσιμο από ένα άλλο εάν βρίσκεται σε μια συγκεκριμένη απόσταση (eps) από αυτό.\n","\n","Η συνδεσιμότητα, από την άλλη πλευρά, περιλαμβάνει μια προσέγγιση αλυσίδας με βάση τη μεταβατικότητα για να καθοριστεί αν τα σημεία βρίσκονται σε μια συγκεκριμένη συστάδα. Για παράδειγμα, τα σημεία p και q μπορούν να συνδεθούν εάν p->r->s->t->q, όπου a->b σημαίνει ότι το b βρίσκεται στη γειτονιά του a.\n","\n","Με το πέρας της συσταδοποίησης DBSCAN προκύπτουν τρεις τύπου σημείων:\n","\n","![](https://miro.medium.com/max/627/1*yT96veo7Zb5QeswV7Vr7YQ.png)\n","\n","- Πυρήνας (Core) - Πρόκειται για ένα σημείο που έχει τουλάχιστον m σημεία σε απόσταση n από το ίδιο.\n","- Όριο (Border) - Είναι ένα σημείο που έχει τουλάχιστον ένα σημείο Core σε απόσταση n.\n","- Θόρυβος (Noise) - Αυτό είναι ένα σημείο που δεν είναι ούτε πυρήνας ούτε σύνορο και έχει λιγότερα από m σημεία σε απόσταση n από το ίδιο.\n","\n","\n","Τα αλγοριθμικά βήματα για την ομαδοποίηση DBSCAN είναι τα εξής:\n","\n","- Ο αλγόριθμος προχωράει επιλέγοντας αυθαίρετα ένα σημείο στο σύνολο δεδομένων (μέχρι να επισκεφθεί όλα τα σημεία).\n","- Εάν υπάρχουν τουλάχιστον 'minPoint' σημεία σε ακτίνα 'ε' από το σημείο, τότε θεωρούμε ότι όλα αυτά τα σημεία ανήκουν στην ίδια συστάδα.\n","- Οι συστάδες επεκτείνονται στη συνέχεια με την αναδρομική επανάληψη του υπολογισμού της γειτονιάς για κάθε γειτονικό σημείο.\n","\n","\n","![](https://ml-explained.com/_nuxt/img/dbscan.4e37192.gif)\n"]},{"cell_type":"code","metadata":{"id":"vlgcArSz0b9H","colab":{"base_uri":"https://localhost:8080/","height":415},"executionInfo":{"status":"ok","timestamp":1637654702603,"user_tz":-120,"elapsed":1060,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"d2908beb-6a20-4f57-d11b-1c2128c46ffb"},"source":["from sklearn.cluster import DBSCAN\n","from sklearn.preprocessing import StandardScaler\n","from sklearn.cluster import DBSCAN\n","from sklearn import metrics\n","\n","X, labels_true= make_moons(n_samples=750, shuffle=True, noise=0.11, random_state=42)\n","X = StandardScaler().fit_transform(X)\n","# Compute DBSCAN\n","db = DBSCAN(eps=0.3, min_samples=10).fit(X)\n","core_samples_mask = np.zeros_like(db.labels_, dtype=bool)\n","core_samples_mask[db.core_sample_indices_] = True\n","labels = db.labels_\n","# Number of clusters in labels, ignoring noise if present.\n","n_clusters_ = len(set(labels)) - (1 if -1 in labels else 0)\n","n_noise_ = list(labels).count(-1)\n","\n","print(\"Estimated number of clusters: %d\" % n_clusters_)\n","print(\"Estimated number of noise points: %d\" % n_noise_)\n","print(\"Homogeneity: %0.3f\" % metrics.homogeneity_score(labels_true, labels))\n","print(\"Completeness: %0.3f\" % metrics.completeness_score(labels_true, labels))\n","print(\"V-measure: %0.3f\" % metrics.v_measure_score(labels_true, labels))\n","print(\"Adjusted Rand Index: %0.3f\" % metrics.adjusted_rand_score(labels_true, labels))\n","print(\n"," \"Adjusted Mutual Information: %0.3f\"\n"," % metrics.adjusted_mutual_info_score(labels_true, labels)\n",")\n","print(\"Silhouette Coefficient: %0.3f\" % metrics.silhouette_score(X, labels))\n","\n","# #############################################################################\n","# Plot result\n","import matplotlib.pyplot as plt\n","\n","# Black removed and is used for noise instead.\n","unique_labels = set(labels)\n","colors = [plt.cm.Spectral(each) for each in np.linspace(0, 1, len(unique_labels))]\n","for k, col in zip(unique_labels, colors):\n"," if k == -1:\n"," # Black used for noise.\n"," col = [0, 0, 0, 1]\n","\n"," class_member_mask = labels == k\n","\n"," xy = X[class_member_mask & core_samples_mask]\n"," plt.plot(\n"," xy[:, 0],\n"," xy[:, 1],\n"," \"o\",\n"," markerfacecolor=tuple(col),\n"," markeredgecolor=\"k\",\n"," markersize=14,\n"," )\n","\n"," xy = X[class_member_mask & ~core_samples_mask]\n"," plt.plot(\n"," xy[:, 0],\n"," xy[:, 1],\n"," \"o\",\n"," markerfacecolor=tuple(col),\n"," markeredgecolor=\"k\",\n"," markersize=6,\n"," )\n","\n","plt.title(\"Estimated number of clusters: %d\" % n_clusters_)\n","plt.show()"],"execution_count":9,"outputs":[{"output_type":"stream","name":"stdout","text":["Estimated number of clusters: 2\n","Estimated number of noise points: 5\n","Homogeneity: 0.995\n","Completeness: 0.947\n","V-measure: 0.970\n","Adjusted Rand Index: 0.987\n","Adjusted Mutual Information: 0.970\n","Silhouette Coefficient: 0.225\n"]},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"cnxrRXSw1HPC"},"source":["### Μειονεκτήματα\n","\n","Όπως όλοι οι αλγόριθμοι συσταδοποίησης, ο DBSCAN συνοδεύεται από ορισμένα μειονεκτήματα\n","\n","- Ο DBSCAN δεν είναι εντελώς ντετερμινιστικός: τα σημεία ορίων που είναι προσβάσιμα από περισσότερες από μία συστάδες μπορεί να αποτελούν μέρος οποιασδήποτε συστάδας, ανάλογα με τη σειρά επεξεργασίας των δεδομένων. Για τα περισσότερα σύνολα δεδομένων και προβλήματα, αυτή η κατάσταση ευτυχώς δεν προκύπτει συχνά και έχει μικρή επίδραση στο αποτέλεσμα της συσταδοποίησης: τόσο στα σημεία πυρήνα όσο και στα σημεία θορύβου, η DBSCAN είναι ντετερμινιστική. \n","- Η ποιότητα του DBSCAN εξαρτάται από τη μετρική απόστασης που χρησιμοποιείται στη συνάρτηση $eps(ε)$. Το πιο συνηθισμένο μέτρο απόστασης που χρησιμοποιείται είναι η ευκλείδεια απόσταση. Ειδικά για δεδομένα υψηλής διάστασης, αυτή η μετρική μπορεί να καταστεί σχεδόν άχρηστη λόγω της λεγόμενης \"κατάρας της διάστατικότητας\", καθιστώντας δύσκολη την εύρεση μιας κατάλληλης τιμής για το ε. Αυτό το φαινόμενο, ωστόσο, υπάρχει και σε οποιονδήποτε άλλο αλγόριθμο που βασίζεται στην ευκλείδεια απόσταση.\n","- Ο DBSCAN δεν μπορεί να ομαδοποιήσει καλά σύνολα δεδομένων με μεγάλες διαφορές στις πυκνότητες, καθώς ο συνδυασμός minPts- ακτίνα ε δεν μπορεί τότε να επιλεγεί βέλτιστα για όλες τις συστάδες.\n","- Aν τα δεδομένα και η κλίμακά τους δεν είναι καλά κατανοητά, η επιλογή ενός κατωφλίου απόστασης ε μπορεί να είναι δύσκολη."]},{"cell_type":"markdown","metadata":{"id":"ZrmO9jGadAQb"},"source":["# Ασαφής ομαδοποίηση (fuzzy clustering)\n","\n"]},{"cell_type":"markdown","metadata":{"id":"SNV4VmX82kMh"},"source":["## Σκληρή και μαλακή συσταδοποίηση\n","\n","Τα παραδείγματα αλγόριθμων συσταδοποίησης που είδαμε μέχρι τώρα ήταν όλα παραδείγματα σκληρής (hard) συσταδοποίησης. Στην σκληρή συσταδοποίηση ένα δείγμα ανήκει σε ένα και μόνο cluster. \n","\n","Υπάρχουν ωστόσο και αλγόριθμοι μαλακής (soft) συσταδοποίησης. Στους αλγόριθμους αυτούς ένα δείγμα μπορεί να ανήκει σε περισσότερες συστάδες από μια με κάποιο βαθμό συμμετοχής στην καθεμία. Στην περίπτωση αυτή, οι βαθμοί συμμετοχής του σημείου για το σύνολο των συστάδων αθροίζει στην μονάδα.\n","\n","![](https://miro.medium.com/max/1400/1*ghEzFd4sMX37OvH_U1xPZQ.png)"]},{"cell_type":"markdown","metadata":{"id":"0fjlgssk5blX"},"source":["### Ασαφής λογική (Fuzzy logic)\n","\n","\n","Ο $c$-means που ακολουθεί βασίζεται σε ιδέες από την ασαφή λογική. Συγκεκριμένα, σύμφωνα με την ασαφή συλλογιστική, αν έχουμε για παράδειγμα μια μεταβλητή όπως η θερμοκρασία του νερού και μια απόφαση (ισχυρισμό) όπως ότι το νερό είναι κρύο, ζεστό, ή καυτό μπορούμε για κάθε ισχυρισμό από τους τρεις να σχεδιάσουμε τη συνάρτηση του βαθμού συμμετοχής ως εξής:\n","\n","![](https://www.researchgate.net/profile/Anna-Foerster-2/publication/235930521/figure/fig8/AS:669552820097041@1536645240765/Fuzzy-logic-example-The-classification-of-some-variable-temperature-is-not-binary.png)\n","\n","Η συμμετοχή του κάθε σημείου του οριζόντιου άξονα (θερμοκρασία νερού) στις τρεις υποθέσεις αθροίζει κάθε φορά στη μονάδα."]},{"cell_type":"markdown","metadata":{"id":"50xd5adXuDP6"},"source":["\n","## Ασαφής αλγόριθμος $c$-μέσων (fuzzy $c$-means)\n","\n","Ένα παράδειγμα αλγόριθμου μαλακής συσταδοποίησης είναι ο fuzzy $c$-means. \n","\n","Ο αλγόριθμος προσπαθεί να ελαχιστοποιήσει τη συνάρτηση:\n","$$\\sum_{j=1}^k \\sum\\limits_{x_i \\in C_j} u_{ij}^m (x_i - c_j)^2 $$\n","όπου:\n","\n","* $u_{ij}$ είναι ο βαθμός συμμετοχής κατά τον οποίο το δείγμα $x_i$ ανήκει στη συστάδα $c_j$ (membership)\n","* $c_j$ είναι το κέντρο της συστάδας $j$\n","* $m$ είναι ο ασαφοποιητής (fuzzyfier)\n","\n","Μπορούμε να δούμε ότι ο $c$-means διαφέρει από τον $k$-means ως προς τον βαθμό συμμετοχής $u_{ij}$ και τον ασαφοποιητή $m$.\n","\n","Η μεταβλητή $u_{ij}^m$ υπολογίζεται από τη σχέση\n","$$u_{ij}^m = \\frac{1}{\\sum\\limits_{l=1}^k \\left( \\frac{| x_i - c_j |}{| x_i - c_k |}\\right)^{\\frac{2}{m-1}}}$$\n","\n","Ο βαθμός συμμετοχής είναι αντίστροφα ανάλογος από την απόσταση από το κέντρο της ομάδας.\n","\n","Στην ασαφή ομοδοποίηση το κέντρο κάθε ομάδας είναι ο μέση τιμή όλων των σημείων ζυγισμένο το καθένα με το βαθμό συμμετοχής του στην ομάδα:\n","\n","$$c_j = \\frac{\\sum\\limits_{x \\in C_j} u_{ij}^m x}{\\sum\\limits_{x \\in C_j} u_{ij}^m}$$\n","\n","Ο αλγόριθμος ασαφούς ομαδοποίησης λειτουργεί ως εξής:\n","\n","1. Ορίζουμε τον αριθμό των συστάδων $c$. (υπερπαράμετρος) \n","2. Αναθέτουμε σε κάθε δείγμα τυχαίους συντελεστές συμμετοχής στις συστάδες. Πρέπει να αθροίζουν στο 1 για κάθε δείγμα.\n","3. Για τον μέγιστο αριθμό επαναλήψεων ή μέχρις ότου ο αλγόριθμος \"συγκλίνει\" (δηλαδή οι συντελεστές αλλάζουν λίγοτερο από ένα κατώφλι $\\epsilon$ επαναλαμβάνουμε:\n","- Υπολογίζουμε το κέντρο κάθε συστάδας.\n","- Για κάθε δείγμα, υπολογίζουμε το βαθμό συμμετοχής του σε όλες τις συστάδες.\n","\n","Η παράμετρος $m$ είναι ένας πραγματικός αριθμός με τιμές μεγαλύτερες του 1 ($1.0=1.6.0 in /usr/local/lib/python3.7/dist-packages (from scikit-fuzzy) (1.19.5)\n","Requirement already satisfied: scipy>=0.9.0 in /usr/local/lib/python3.7/dist-packages (from scikit-fuzzy) (1.4.1)\n","Requirement already satisfied: networkx>=1.9.0 in /usr/local/lib/python3.7/dist-packages (from scikit-fuzzy) (2.6.3)\n","Building wheels for collected packages: scikit-fuzzy\n"," Building wheel for scikit-fuzzy (setup.py) ... \u001b[?25l\u001b[?25hdone\n"," Created wheel for scikit-fuzzy: filename=scikit_fuzzy-0.4.2-py3-none-any.whl size=894089 sha256=437084b535dc38e7df447ce66a99bc1d540aaaafb42bd64874a49f1b71b47bce\n"," Stored in directory: /root/.cache/pip/wheels/d5/74/fc/38588a3d2e3f34f74588e6daa3aa5b0a322bd6f9420a707131\n","Successfully built scikit-fuzzy\n","Installing collected packages: scikit-fuzzy\n","Successfully installed scikit-fuzzy-0.4.2\n"]}]},{"cell_type":"markdown","metadata":{"id":"u3qri1oSj3TB"},"source":["### Δημιουργία ψευδοτυχαίων δεδομένων\n","\n","Σημειώστε πως μπορούμε να ελέγχουμε την κατεύθυνση των Γκαουσιανών με τη διακύμανση που ορίζουμε στον κάθε άξονα (sigmas)"]},{"cell_type":"code","metadata":{"id":"LjgLHARFOb0R","colab":{"base_uri":"https://localhost:8080/","height":298},"executionInfo":{"status":"ok","timestamp":1637654708160,"user_tz":-120,"elapsed":460,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"99ae4b6c-e6bd-456e-cd25-e16e6378703e"},"source":["from __future__ import division, print_function\n","import numpy as np\n","import matplotlib.pyplot as plt\n","import skfuzzy as fuzz\n","\n","colors = ['b', 'orange', 'g', 'r', 'c', 'm', 'y', 'k', 'Brown', 'ForestGreen']\n","\n","# Ορισμός των κέντρων των 3 συστάδων\n","centers = [[4, 2],\n"," [1, 7],\n"," [5, 6]]\n","\n","# Ορισμός της διασποράς του κάθε κέντρου στις διαστάσεις x και y αντίστοιχα\n","sigmas = [[0.8, 0.3],\n"," [0.3, 0.5],\n"," [1.1, 0.7]]\n","\n","# Δημιουργία δοκιμαστικών δεδομένων\n","np.random.seed(42) # Σταθερή σπορά\n","xpts = np.zeros(1)\n","ypts = np.zeros(1)\n","labels = np.zeros(1)\n","for i, ((xmu, ymu), (xsigma, ysigma)) in enumerate(zip(centers, sigmas)):\n"," xpts = np.hstack((xpts, np.random.standard_normal(200) * xsigma + xmu))\n"," ypts = np.hstack((ypts, np.random.standard_normal(200) * ysigma + ymu))\n"," labels = np.hstack((labels, np.ones(200) * i))\n","\n","# Οπτικοποίηση των δοκιμαστικών δεδομένων\n","fig0, ax0 = plt.subplots()\n","for label in range(3):\n"," ax0.plot(xpts[labels == label], ypts[labels == label], '.',\n"," color=colors[label])\n","ax0.set_title('Test data: 200 points x3 clusters.')"],"execution_count":11,"outputs":[{"output_type":"execute_result","data":{"text/plain":["Text(0.5, 1.0, 'Test data: 200 points x3 clusters.')"]},"metadata":{},"execution_count":11},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"d1NSg69okgUo"},"source":["### Eύρεση του βέλτιστου αριθμού συστάδων $c$\n","Στο παράδειγμά μας έχουμε φτιάξει ελεγχόμενα 3 συστάδες. Σε ένα κανονικό πρόβλημα όμως δεν γνωρίζουμε από πριν τον ακριβή αριθμό τους. Σημειώστε επίσης ότι στα παραδείγματά μας έχουμε μόνο δυο διαστάσεις, ένα τυπικό πρόβλημα έχει πολύ περισσότερες.\n","\n","Θα τρέξουμε τον αλγόριθμο για $c$ από 2 μέχρι 10 συστάδες:"]},{"cell_type":"code","metadata":{"id":"vbdX8awbOd3P","colab":{"base_uri":"https://localhost:8080/","height":736},"executionInfo":{"status":"ok","timestamp":1637654709289,"user_tz":-120,"elapsed":1131,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"79603132-1f5f-4c8e-a080-ecf06cbeb35e"},"source":["fig1, axes1 = plt.subplots(3, 3, figsize=(8, 8))\n","alldata = np.vstack((xpts, ypts))\n","fpcs = []\n","\n","for ncenters, ax in enumerate(axes1.reshape(-1), 2):\n"," cntr, u, u0, d, jm, p, fpc = fuzz.cluster.cmeans(\n"," alldata, ncenters, 2, error=0.005, maxiter=1000, init=None)\n"," print(u.shape, cntr.shape)\n"," # Αποθήκευση των τιμών του συντελεστή ασάφειας διαμερισμού\n"," fpcs.append(fpc)\n","\n"," # Σχεδιασμός των ανατιθέμενων συστάδων, γιά κάθε δείγμα δεδομένων\n"," cluster_membership = np.argmax(u, axis=0)\n"," for j in range(ncenters):\n"," ax.plot(xpts[cluster_membership == j],\n"," ypts[cluster_membership == j], '.', color=colors[j])\n","\n"," # Σημείωση του κέντρου της κάθε ασαφούς συστάδας\n"," for pt in cntr:\n"," ax.plot(pt[0], pt[1], 'rs')\n","\n"," ax.set_title('Centers = {0}; FPC = {1:.2f}'.format(ncenters, fpc))\n"," ax.axis('off')\n","d\n","fig1.tight_layout()"],"execution_count":12,"outputs":[{"output_type":"stream","name":"stdout","text":["(2, 601) (2, 2)\n","(3, 601) (3, 2)\n","(4, 601) (4, 2)\n","(5, 601) (5, 2)\n","(6, 601) (6, 2)\n","(7, 601) (7, 2)\n","(8, 601) (8, 2)\n","(9, 601) (9, 2)\n","(10, 601) (10, 2)\n"]},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"0AZyyo6vnRo8"},"source":["Και θα χρησιμοποιήσουμε τον συντελεστή ασάφειας του διαμερισμού (fuzzy partition coefficient) ή συντελεστή Dunn\n","\n","$$ F(U) = \\frac{1}{n} \\sum\\limits_{i=1}^k\\sum\\limits_{j=1}^nu_{ij}^2$$\n","\n","που είναι το άθροισμα των τετραγώνων όλων των βαθμών συμμετοχής δια του πλήθους των σημείων. Ο συντελεστής Dunn παίρνει τιμές\n","\n","$$\\frac{1}{k} \\leq F(U) \\leq 1$$\n","\n","Το κάτω όριο επιτυγχάνεται όταν όλοι οι βαθμοί συμμετοχής είναι $\\frac{1}{k}$ (απόλυτη ασάφεια, όλα τα σημεία ανήκουν σε όλες τις συστάδες κατά τον ίδιο βαθμό) και το άνω ($1$) όταν έχουμε μόνο μία συστάδα (τετριμμένη περίπτωση)."]},{"cell_type":"code","metadata":{"id":"n7NwVUFGY-s3","colab":{"base_uri":"https://localhost:8080/","height":297},"executionInfo":{"status":"ok","timestamp":1637654709830,"user_tz":-120,"elapsed":545,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"c56d420a-95cb-430f-b29f-4f9c68128f84"},"source":["fig2, ax2 = plt.subplots()\n","ax2.plot(np.r_[2:11], fpcs)\n","ax2.set_xlabel(\"Πλήθος κέντρων\")\n","ax2.set_ylabel(\"Συντελεστής ασάφειας διαμερισμού\")"],"execution_count":13,"outputs":[{"output_type":"execute_result","data":{"text/plain":["Text(0, 0.5, 'Συντελεστής ασάφειας διαμερισμού')"]},"metadata":{},"execution_count":13},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"ExSyZko0qEx_"},"source":["Συνεπώς το βέλτιστο είναι c=3. Κάνουμε συσταδοποίηση με αυτή την τιμή"]},{"cell_type":"code","metadata":{"id":"ycGgf0L1Y_Wu","colab":{"base_uri":"https://localhost:8080/","height":298},"executionInfo":{"status":"ok","timestamp":1637654709831,"user_tz":-120,"elapsed":8,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"1eea35d9-4608-49d9-bcc4-1a98039536c0"},"source":["# Επανασυσταδοποίηση για 3 κέντρα συστάδων\n","cntr, u_orig, _, _, _, _, _ = fuzz.cluster.cmeans(\n"," alldata, 3, 2, error=0.005, maxiter=1000)\n","\n","# Εμφάνιση του αποτελέσματος\n","fig2, ax2 = plt.subplots()\n","ax2.set_title('Trained model')\n","for j in range(3):\n"," ax2.plot(alldata[0, u_orig.argmax(axis=0) == j],\n"," alldata[1, u_orig.argmax(axis=0) == j], 'o',\n"," label='series ' + str(j))\n","ax2.legend()"],"execution_count":14,"outputs":[{"output_type":"execute_result","data":{"text/plain":[""]},"metadata":{},"execution_count":14},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"oWAEQtMtaKkr"},"source":["### Βαθμοί συμμετοχής τυχαίου σημείου\n","Για να δούμε πόσο ανήκει σε κάθε συστάδα ένα σημείο θα χρησιμοποιήσουμε τον πίνακα $u$"]},{"cell_type":"code","metadata":{"id":"M59b0y4WZDlr","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1637654709831,"user_tz":-120,"elapsed":7,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"728c0fd6-5e78-49af-cbf0-3c2fe71b21e7"},"source":["randompoint=10\n","print(\"τυχαίο σημείο\")\n","print(alldata[:,randompoint])\n","print(\"1 συστάδα 2 συστάδα 3 συστάδα\")\n","print(u_orig[:,randompoint])"],"execution_count":15,"outputs":[{"output_type":"stream","name":"stdout","text":["τυχαίο σημείο\n","[4.43404803 3.15581945]\n","1 συστάδα 2 συστάδα 3 συστάδα\n","[0.83157629 0.04517197 0.12325175]\n"]}]},{"cell_type":"markdown","metadata":{"id":"wGgWvcx9tocr"},"source":["### Μειονεκτήματα\n","\n","Ο αλγόριθμος c-means ελαχιστοποιεί τη διακύμανση εντός των ομάδων (intra-cluster variance) και μας δίνει τους βαθμούς συμμετοχής, έχει όμως τα ίδια προβλήματα με τον k-means:\n","* η βελτιστοποίηση καταλήγει σε ένα τοπικό ελάχιστο\n","* διαφορετική αρχικοποίηση δίνει διαφορετικά αποτελέσματα\n","* οι ομάδες έχουν αναγκαστικά κεντροειδές σχήμα"]}]}