{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### K Means\n", "\n", " \n", "\n", "K means is the easiest form of unsupervised learning. Unsupervised learning is a type of self-organized learning that helps find previously unknown patterns in data set without pre-existing labels. Supervised learning is trying to find a boundary to separate data with different properties. Unsupervised learning is trying to aggregate data with similar properties. Think of unsupervised learning as a bottom-up approach and supervised learning is a top-down approach. Unsupervised learning is mostly used in cluster problems to sort data into different categories.\n", "\n", "The way K means works is very intuitive. Basically, we assign K centroids with different labels to random positions. Then the iteration begins. We compute the distance from each data point to K centroids. The label of the data point is determined by the centroid with the shortest distance. Each centroid is recalibrated to the mean of all the data points of the same label. We repeat the previous three steps until centroids do not move any more. Unsupervised learning done!\n", "\n", "For more technical details, feel free to read the following link (even though it is in R)\n", "\n", "https://towardsdatascience.com/k-means-a-complete-introduction-1702af9cd8c" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import imageio\n", "import random as rd" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import sklearn.cluster\n", "import sklearn.decomposition" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import os\n", "os.chdir('K:/ecole/github')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "#euclidean distance is the measure of the distance between two points in geometry\n", "#other measures include manhattan distance\n", "#actually u can use np.linalg.norm to save u time\n", "def euclidean_distance(p1,p2):\n", " \n", " assert len(p1)==len(p2),\"p1 and p2 should be the same dimension\"\n", " \n", " dist=sum([i**2 for i in np.subtract(p1,p2)])\n", " \n", " return dist**0.5" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "#for unsupervised learning, clf.score doesnt return the accuracy\n", "#there is no cross validation, no known labels\n", "#the only way to detect the accuracy is vote of the majority\n", "#for each label given\n", "#we check which iris type is the majority\n", "#we consider the majority as the correct classification\n", "#all we need to do is to count the minority\n", "def get_accuracy(data,class_,checked):\n", " \n", " df=data.copy()\n", " \n", " #use dictionary to keep track of everything\n", " d={}\n", " \n", " #counting\n", " for i in df['label'][df['y']==class_].unique():\n", " if i not in checked and i!=-1:\n", " d[i]=df['label'][df['y']==class_].tolist().count(i)\n", "\n", " #comparison\n", " maxval=-1\n", " lbl=None\n", " for i in d:\n", " if d[i]>maxval:\n", " lbl=i\n", " maxval=d[i]\n", "\n", " return len(df['label'][df['y']==class_][df['label']!=lbl])" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "#create random centroids\n", "#centroids are bounded by the extreme value of our data points\n", "def random_centroid(data):\n", " \n", " x=data.copy()\n", " \n", " centroid=[]\n", " \n", " #the dimension of centroid should align to training dataset\n", " #*100 then /100 to get decimal numbers\n", " for i in x:\n", " rdnum=rd.randint(int(min(x[i])*100),\n", " int(max(x[i])*100))/100\n", " centroid.append(rdnum)\n", " \n", " return centroid" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": true }, "outputs": [], "source": [ "#the logic of kmeans is very intuitive\n", "#assuming we are using 3 centroids (the selection of k is another topic)\n", "#we insert 3 random centroids into the data\n", "#we calculate the euclidean distance from each data point to each centroid\n", "#each data point is mapped to the closest centroid\n", "#once classification is done, we move the centroids to the centre of the cluster\n", "#we keep repeating three steps above until the centroids dont move any move\n", "#or the iteration has reached the limit set by us, which is 50 by default\n", "#k means is simple but it has some shortcomings\n", "#it does not always converge to the local optima\n", "#if you run a few iterations you will see different results\n", "#and its boundary is always linear\n", "def kmeans(data1,data2,knum=3,itrlimit=50,fixed_pos=True,\n", " show_acc=False,show_viz=False,genr_gif=False):\n", " \n", " x=data1.copy()\n", " df=data2.copy()\n", " \n", " if fixed_pos==True:\n", " centroids=[]\n", " var=locals()\n", " \n", " #using fixed position of centroids\n", " #centroids will be scattered on the diagonal hyperspace\n", " for i in x:\n", " var[i.replace(' ','_')]=(max(x[i])-min(x[i]))/(knum+2)\n", " \n", " for j in range(1,knum+1):\n", " centroids.append([min(x[i])+var[i.replace(' ','_')]*(j) for i in x])\n", "\n", " else:\n", " #create random centroids\n", " centroids=[]\n", " for j in range(knum):\n", "\n", " centroid=random_centroid(x)\n", "\n", " #no duplicates\n", " while centroid in centroids:\n", " centroid=random_centroid(x)\n", "\n", " centroids.append(centroid)\n", "\n", " #converge is used to stop the loop when centroids dont move any more\n", " #counter is to stop the infinite iteration\n", " #on a very rare occasion, centroids would swing between 2 clusters\n", " #in that sense, we stop the iteration\n", " converge=False\n", " counter=0\n", " \n", " \n", " while not converge:\n", " \n", " #calculate distance\n", " labels=[]\n", " for i in range(len(x)):\n", " point=x.loc[i].tolist()\n", "\n", " distance=[]\n", "\n", " for j in centroids:\n", "\n", " distance.append(euclidean_distance(point,j))\n", " \n", " #set label of each data point as the closest centroid\n", " labels.append(distance.index(min(distance)))\n", " \n", " x['label']=labels\n", " df['label']=labels\n", " \n", " #visualization\n", " if show_viz==True or genr_gif==True: \n", " \n", " ax=plt.figure().add_subplot(111)\n", " ax.spines['top'].set_visible(False)\n", " ax.spines['right'].set_visible(False)\n", " plt.scatter(x['dimension 1'],x['dimension 2'],\n", " c=labels,alpha=0.2,s=50,label='clusters')\n", "\n", " plt.scatter([i[0] for i in centroids],\n", " [i[1] for i in centroids],\n", " c=range(knum),\n", " s=200,marker='*',\n", " edgecolors='k',\n", " label='centroids')\n", "\n", " plt.ylabel('Dimension 2')\n", " plt.xlabel('Dimension 1')\n", " plt.title('K Means')\n", " plt.legend(loc='lower right')\n", " \n", " if genr_gif==True:\n", " #this line is used to create gif animation\n", " plt.savefig('kmeans%d.png'%(counter))\n", " plt.show()\n", " elif show_viz==True:\n", " plt.show()\n", " else:\n", " pass\n", " \n", " #check if converged\n", " centroids_prev=[i for i in centroids]\n", " centroids=[]\n", "\n", " for i in range(knum):\n", " \n", " #sometimes one of the centroids is too far from any data point\n", " #we have to reset the centroid\n", " if x[x['label']==i].empty:\n", "\n", " centroid=random_centroid(x)\n", " while centroid in centroids:\n", " centroid=random_centroid(x)\n", " centroids.append(centroid)\n", " \n", " #otherwise we update the centroids\n", " #we move them to the centre of the cluster\n", " else:\n", " centroids.append(np.mean(x[x['label']==i]).tolist()) \n", " \n", " #two conditions to stop the iteration\n", " #either converged or reaching iteration limit\n", " counter+=1\n", " if centroids==centroids_prev or counter>=itrlimit:\n", " converge=True\n", " \n", " #print accuracy\n", " if show_acc==True: \n", " \n", " erreur=0\n", " checked=[]\n", " for i in range(len(df['label'].unique())):\n", " erreur+=get_accuracy(df,i,checked)\n", " checked.append(i)\n", " accuracy=1-erreur/len(df)\n", "\n", " print('accuracy: %s'%(accuracy))\n", " \n", " #create gif\n", " if genr_gif==True:\n", " \n", " filenames=['kmeans%d.png'%(i) for i in range(counter)] \n", " images=list(map(lambda filename:imageio.imread(filename),\n", " filenames))\n", " imageio.mimsave('kmeans.gif',images,duration=0.8)\n", " \n", " return labels" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "scrolled": true }, "outputs": [], "source": [ "#kmeans implemented by sklearn\n", "def skl_kmeans(data1,data2,n=3):\n", " \n", " x=data1.copy()\n", " df=data2.copy()\n", " \n", " clf=sklearn.cluster.KMeans(n_clusters=n)\n", " df['label']=clf.fit_predict(x)\n", " \n", " #compute accuracy\n", " erreur=0\n", " checked=[]\n", " for i in range(len(df['label'].unique())):\n", " erreur+=get_accuracy(df,i,checked)\n", " checked.append(i)\n", " accuracy=1-erreur/len(df)\n", " print('accuracy: %s'%(accuracy))" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "df=pd.read_csv('iris.csv')" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "x=pd.concat([df['sepal length'], \\\n", " df['sepal width'], \\\n", " df['petal length'],\\\n", " df['petal width']],axis=1)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "#convert text to discrete number\n", "df['y']=np.unique(df['type'],return_inverse=True)[1]" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "scrolled": true }, "outputs": [], "source": [ "#for the purpose of visualization\n", "#we reduce 4 dimensions to 2\n", "#more details of pca can be found in the link below\n", "# https://github.com/je-suis-tm/machine-learning/blob/master/principal%20component%20analysis.ipynb\n", "dims=2\n", "x=sklearn.decomposition.PCA(n_components=dims).fit_transform(x)\n", "x=pd.DataFrame(x,columns=[f'dimension {i}' for i in range(1,dims+1)])" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "accuracy: 0.86\n" ] } ], "source": [ "df['label']=kmeans(x,df,show_acc=True,\n", " show_viz=True,fixed_pos=False,\n", " genr_gif=True)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "accuracy: 0.8866666666666667\n" ] } ], "source": [ "skl_kmeans(x,df)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " \n", "\n", "### Selection of K\n", "\n", " \n", "\n", "The key part of K Means is the selection of K. There are many metrics used in unsupervised learning. Here we only talk about 3 of the most common ones for K Means. All of them are brute force calculation. We have a fancy word for that, grid search. Run an iteration of different amounts of centroids and use some metrics to evaluate the effect." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Elbow Method\n", "\n", " \n", "\n", "It is called inertia in scikit-learn. It is the computation of within-cluster sum of squared error (WSSE). WSSE refers to the sum of the euclidean distance from each data point to its underlying centroid. It is quite intuitive that the overall distance gets smaller as we increase the amount of centroids. Think of it as more variables lead to the increase of R squared in OLS. \n", "\n", "The idea of elbow method is to find the optimal spot where you have a reasonable amount of centroid and smaller overall distance. It is where inertia curve takes a sharp decline. We call the critical point 'The Elbow'. To identify the sweet spot, we create a new line by connecting the start of inertia curve to the end. The G spot exists at the largest perpendicular distance from the newly formed line to inertia curve." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "#plot two curves on separate axis\n", "def dual_axis_plot(xaxis,data1,data2,fst_color='r',\n", " sec_color='b',fig_size=(10,5),x_label='',\n", " y_label1='',y_label2='',grid=False,title='',\n", " legend1='',legend2=''):\n", " \n", " fig=plt.figure(figsize=fig_size)\n", " ax=fig.add_subplot(111) \n", "\n", " ax.set_xlabel(x_label)\n", " \n", " #differentiate two y axis by different colors\n", " ax.set_ylabel(y_label1, color=fst_color)\n", " ax.plot(xaxis, data1, color=fst_color,label=legend1)\n", " ax.tick_params(axis='y',labelcolor=fst_color)\n", " ax.yaxis.labelpad=15\n", " \n", " #legend of y1 goes to the left\n", " plt.legend(loc=3)\n", " \n", " #the crucial part of dual axis plot\n", " ax2 = ax.twinx()\n", "\n", " ax2.set_ylabel(y_label2, color=sec_color,rotation=270)\n", " ax2.plot(xaxis, data2, color=sec_color,label=legend2)\n", " ax2.plot(xaxis[data2.index(max(data2))],max(data2),\n", " marker='*',markersize=25,lw=0,color='#b23850',\n", " alpha=0.7,label='optimal')\n", " ax2.tick_params(axis='y',labelcolor=sec_color)\n", " ax2.yaxis.labelpad=15\n", "\n", " fig.tight_layout()\n", " plt.legend(loc=4)\n", " plt.grid(grid)\n", " plt.title(title)\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "#using geometry to calculate the perpendicular distance\n", "def get_distance(x,y,a,b):\n", " \n", " numerator=y-x*a-b\n", " denominator=(a**2+1)**0.5\n", " \n", " return np.abs(numerator/denominator)\n", "\n", "#simple solution to get coefficients of the equation\n", "def get_line_params(x1,y1,x2,y2):\n", " \n", " a=(y1-y2)/(x1-x2)\n", " b=y1-a*x1\n", " \n", " return a,b" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "#calculate intra-cluster sum of squared error\n", "#some people call it within-cluster sum of squared error\n", "#it is the sum of the euclidean distance from each point to its underlying centroid\n", "#in sklearn, it is an attribute called inertia\n", "def get_inertia(data):\n", " \n", " x=data.copy()[[i for i in data.columns if i!='label']]\n", " \n", " wsse=[]\n", " \n", " for i in data['label'].unique():\n", " \n", " #centroid is basically the mean of a cluster\n", " centroid=np.mean(x[data['label']==i]).tolist()\n", "\n", " for j in x.loc[data['label']==i].index:\n", " wsse.append(euclidean_distance(x.loc[j].tolist(),\n", " centroid))\n", " \n", " return sum(wsse) " ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "scrolled": true }, "outputs": [], "source": [ "#calculate wsse\n", "inertia=[]\n", "\n", "for i in range(2,8):\n", " x['label']=kmeans(x[[i for i in x.columns if i!='label']],\n", " df,knum=i)\n", " inertia.append(get_inertia(x))" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x360 with 2 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#connect the start of inertia curve to the end\n", "a,b=get_line_params(0,inertia[0],len(inertia)-1,inertia[-1])\n", "\n", "#calculate the perpendicular distance \n", "#from each point on inertia curve to the straight line\n", "distance=[]\n", "for i in range(len(inertia)): \n", " distance.append(get_distance(i,inertia[i],a,b))\n", "\n", "#use dual axis visualization\n", "dual_axis_plot(np.arange(2,8),inertia,distance,\n", " x_label='Numbers of Cluster',\n", " y_label1='Within-cluster Sum of Squared Error',\n", " y_label2='Perpendicular Distance',\n", " legend1='Inertia',legend2='Distance',\n", " title='Elbow Method',\n", " fst_color='#b39bc8',sec_color='#464866')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Silhouette Score\n", "\n", " \n", "\n", "Silhouette score or silhouette coefficient is a more scientific approach to determine the amount of the clusters. The numerator consists of similarity and dissimilarity. Similarity implies the density of inside the cluster. The smaller the better. Dissimilarity implies the distance among clusters. The larger the better (think of it as functional margin in svm). The overall silhouette score proposed by Kaufman represents the mean silhouette over the entire dataset. We select K to maximize the silhouette score.\n", "\n", "For the details of the computation, please refer to Wikipedia\n", "\n", "https://en.wikipedia.org/wiki/Silhouette_(clustering)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "#calculate mean distance from one point to a cluster\n", "#it is the mean of euclidean distance from one point to all the points in the cluster\n", "def mean_distance(point,dataset):\n", " \n", " distance_list=[]\n", " \n", " assert not dataset.empty,'empty dataset'\n", " \n", " for i in dataset.index:\n", " \n", " #make sure we dont include the point itself\n", " if dataset.loc[i].tolist()!=point:\n", " distance_list.append(\n", " euclidean_distance(point,\n", " dataset.loc[i].tolist()))\n", " \n", " #if one cluster has only one element which is the point itself\n", " #we will return zero\n", " if len(dataset)==1 and dataset.iloc[0].tolist()==point:\n", " return 0\n", " \n", " #we raise warning here\n", " #because np.mean([]) returns np.nan\n", " #it will cause a huge problem for silhouette computation\n", " import warnings\n", " warnings.simplefilter('error')\n", " \n", " return np.mean(distance_list)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "#silhouette coefficient is the maximum value of the mean silhouette for each label\n", "#in sklearn, it is sklearn.metrics.silhouette_score\n", "#to calculate silhouette for each data point in the dataset\n", "#we need to create multiple loops\n", "#so the time complexity of silhouette score is way higher than other metrics\n", "def silhouette_coefficient(data):\n", " \n", " x=data.copy()[[i for i in data.columns if i!='label']]\n", " cols=x.columns.tolist()\n", " \n", " #if there is only one cluster, silhouette score is zero\n", " if len(data['label'].unique())==1:\n", " return 0\n", " \n", " silhouette=[]\n", " \n", " #calculate silhouette for each data point\n", " for i in range(len(x)):\n", " lbl=data['label'][i]\n", " \n", " #similarity is mean distance from one point to every other point within the same cluster\n", " similarity=mean_distance(x[cols].loc[i].tolist(),\n", " x[cols].loc[data['label']==lbl])\n", "\n", " arr=[]\n", " \n", " otherlbl=[i for i in set(data['label']) if i!=lbl]\n", " \n", "\n", " #dissimilarity is mean distance from one point to all the points in the other clusters\n", " for j in otherlbl:\n", " \n", " arr.append(mean_distance(x[cols].loc[i].tolist(),\n", " x[cols].loc[data['label']==j]))\n", "\n", " dissimilarity=min(arr)\n", "\n", " silhouette.append((dissimilarity-similarity)/max(similarity,dissimilarity))\n", " \n", " x['silhouette']=silhouette\n", "\n", " silhouette=[]\n", "\n", " for i in set(data['label']):\n", "\n", " silhouette.append(np.mean(x['silhouette'][data['label']==i].tolist()))\n", " \n", " return max(silhouette)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "scrolled": true }, "outputs": [], "source": [ "#calculate silhouette score\n", "silhouette_score=[]\n", "for i in range(2,8):\n", "\n", " #avoid using label as one of the features\n", " x['label']=kmeans(x[[i for i in x.columns if i!='label']],\n", " df,knum=i)\n", "\n", " silhouette_score.append(silhouette_coefficient(x))" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x360 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#visualize silhouette\n", "ax=plt.figure(figsize=(10,5)).add_subplot(111)\n", "ax.spines['top'].set_visible(False)\n", "ax.spines['right'].set_visible(False)\n", " \n", "plt.plot([i for i in range(2,8)],silhouette_score,c='#0294a5',)\n", "plt.plot(silhouette_score.index(max(silhouette_score))+2,\n", " max(silhouette_score),lw=0,c='#f79e02',alpha=0.8,\n", " marker='*',markersize=15,label='Optimal')\n", "\n", "plt.legend(loc=0)\n", "plt.ylabel('Silhouette Score')\n", "plt.xlabel('Numbers of Cluster')\n", "plt.title('Silhouette Analysis')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Gap Statistic\n", "\n", " \n", "\n", "Gap statistic is a relatively new metric compared to the others. It was invented 20 years ago by some scholars from Stanford University. Sklearn has not included gap statistic in its package. Gap statistic is the logarithm difference between mean WSSE of reference data and WSSE of real data. We select K to satisfy the gap statistic K plus standard deviation of reference data WSSE K+1 is larger than the gap statistic K+1. Similar to autocorrelation plot in time series analysis, we pick the smallest K.\n", "\n", "For coding reference, feel free to check anaconda notebook\n", "\n", "https://anaconda.org/milesgranger/gap-statistic/notebook\n", "\n", "For math reference, feel free to check the original paper\n", "\n", "https://statweb.stanford.edu/~gwalther/gap" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "scrolled": true }, "outputs": [], "source": [ "#there are two ways to generate the reference data\n", "#here we take the first approach from the paper\n", "#using uniform distribution for simplicity\n", "#the distribution is bounded by the extreme value of the original dataset\n", "def get_reference_data(x):\n", " \n", " montecarlo=[] \n", " for i in range(len(x)): \n", " arr=[]\n", " for j in x.columns:\n", " if j!='label':\n", " rdnum=rd.uniform(min(x[j]),\n", " max(x[j]))\n", " arr.append(rdnum)\n", " montecarlo.append(arr)\n", " \n", " output=pd.DataFrame()\n", " \n", " for i in x.columns:\n", " if i!='label':\n", " output[i]=[j[x.columns.tolist().index(i)] for j in montecarlo]\n", " \n", " return output" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "#use monte carlo simulation to generate reference data\n", "simulation=10\n", "\n", "var=locals()\n", "\n", "for i in range(simulation):\n", "\n", " var['ref'+str(i)]=get_reference_data(x[[i for i in x.columns if i!='label']])" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "gap_stat=[]\n", "gap_std=[]\n", "for i in range(2,8):\n", " \n", " #avoid using label as one of the features\n", " x['label']=kmeans(x[[i for i in x.columns if i!='label']],\n", " df,knum=i)\n", " \n", " #get expectation of gap statistic from all reference data\n", " mc_simu=[]\n", " for j in range(simulation):\n", " var['ref'+str(j)]['label']=kmeans(var['ref'+str(j)][[i for i in x.columns if i!='label']],\n", " x,knum=i)\n", " \n", " mc_simu.append(get_inertia(var['ref'+str(j)])) \n", " \n", " gap_stat.append(np.mean([np.log(i) for i in mc_simu])-np.log(get_inertia(x)))\n", " gap_std.append((1+1/simulation)**0.5*np.std([np.log(i) for i in mc_simu]))" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x360 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#visualize gap statistic\n", "ax=plt.figure(figsize=(10,5)).add_subplot(111)\n", "ax.spines['top'].set_visible(False)\n", "ax.spines['right'].set_visible(False)\n", " \n", "plt.errorbar([i for i in range(2,8)],gap_stat,gap_std,\n", " c='#05386b',capsize=5)\n", "ind=None\n", "for i in range(len(gap_stat)-1):\n", " if gap_stat[i]+gap_std[i+1]>gap_stat[i+1]:\n", " ind=i\n", " break\n", "\n", "plt.plot(ind+2,gap_stat[ind],\n", " lw=0,c='#fc4445',alpha=0.8,\n", " marker='*',markersize=20,label='Optimal')\n", "\n", "plt.legend(loc=0)\n", "plt.ylabel('Gap Statistic')\n", "plt.xlabel('Numbers of Cluster')\n", "plt.title('Gap Statistic')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }