{"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":1636350432830,"user_tz":-120,"elapsed":1546,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"49a6f19b-ec61-47e0-f7d0-b066b9616606"},"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":1636350433375,"user_tz":-120,"elapsed":553,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"fa7d94d7-5541-47dc-8ab4-7915e056c34c"},"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":1636350433375,"user_tz":-120,"elapsed":4,"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":1636350433790,"user_tz":-120,"elapsed":419,"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":1636350434864,"user_tz":-120,"elapsed":1077,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"f9fa6ead-1b74-417b-cd4b-5664e7acbf75"},"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":1636350439920,"user_tz":-120,"elapsed":5071,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"8853612b-089f-457a-eb7a-feb837a4d1d9"},"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":1636350440503,"user_tz":-120,"elapsed":612,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"63a74a8e-0a33-4ae2-bd94-dfc49128d364"},"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":1636350441549,"user_tz":-120,"elapsed":1056,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"5148eae5-e334-414d-ece7-4e32b719255d"},"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":417},"executionInfo":{"status":"ok","timestamp":1636350442305,"user_tz":-120,"elapsed":779,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"c0a17cd4-5200-4a7c-9193-bcbeb07a0aa0"},"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=658b603c42cb410120bfc8d9b6e6e5b3601057f4cbb222bae05bba78e88854d2\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":1636350448793,"user_tz":-120,"elapsed":700,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"6771153f-6519-4227-fa0f-81c8e74dd612"},"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":738},"executionInfo":{"status":"ok","timestamp":1636350450116,"user_tz":-120,"elapsed":1348,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"448a26aa-5bdc-496c-abf7-c296afd434e7"},"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":1636350450875,"user_tz":-120,"elapsed":778,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"1c9640ee-f6ae-4dbb-fb0f-f1fd56db9af4"},"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":1636350450877,"user_tz":-120,"elapsed":26,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"d227fd8c-516d-4d10-b5e3-332e914d471e"},"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":1636353931376,"user_tz":-120,"elapsed":405,"user":{"displayName":"Parask Tz","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"08609487936413149826"}},"outputId":"2d5cf9b9-adb2-47ce-d2a3-bee3a5980ecf"},"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":16,"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"]}]}