pca-for-clustering.ipynb

{"cells":[{"metadata":{"trusted":true},"cell_type":"code","source":"#import the data\n#standardization\n#apply PCA","execution_count":1,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"from warnings import filterwarnings\nfilterwarnings('ignore')\nimport numpy as np\nimport pandas as pd \nimport seaborn as sns\nimport matplotlib.pyplot as plt\nimport scipy as sp\nfrom sklearn.cluster import KMeans","execution_count":2,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"df=pd.read_csv(\"../input/usarrests/USArrests.csv\").copy()\ndf.index = df.iloc[:,0]\ndf = df.iloc[:,1:5]\ndf.index.name = None\ndf.head()","execution_count":3,"outputs":[{"output_type":"execute_result","execution_count":3,"data":{"text/plain":"            Murder  Assault  UrbanPop  Rape\nAlabama       13.2      236        58  21.2\nAlaska        10.0      263        48  44.5\nArizona        8.1      294        80  31.0\nArkansas       8.8      190        50  19.5\nCalifornia     9.0      276        91  40.6","text/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Murder</th>\n      <th>Assault</th>\n      <th>UrbanPop</th>\n      <th>Rape</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>Alabama</th>\n      <td>13.2</td>\n      <td>236</td>\n      <td>58</td>\n      <td>21.2</td>\n    </tr>\n    <tr>\n      <th>Alaska</th>\n      <td>10.0</td>\n      <td>263</td>\n      <td>48</td>\n      <td>44.5</td>\n    </tr>\n    <tr>\n      <th>Arizona</th>\n      <td>8.1</td>\n      <td>294</td>\n      <td>80</td>\n      <td>31.0</td>\n    </tr>\n    <tr>\n      <th>Arkansas</th>\n      <td>8.8</td>\n      <td>190</td>\n      <td>50</td>\n      <td>19.5</td>\n    </tr>\n    <tr>\n      <th>California</th>\n      <td>9.0</td>\n      <td>276</td>\n      <td>91</td>\n      <td>40.6</td>\n    </tr>\n  </tbody>\n</table>\n</div>"},"metadata":{}}]},{"metadata":{"trusted":true},"cell_type":"code","source":"#standardization","execution_count":4,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"from sklearn.preprocessing import StandardScaler\ndf=StandardScaler().fit_transform(df)\ndf[0:5,0:5]","execution_count":5,"outputs":[{"output_type":"execute_result","execution_count":5,"data":{"text/plain":"array([[ 1.25517927,  0.79078716, -0.52619514, -0.00345116],\n       [ 0.51301858,  1.11805959, -1.22406668,  2.50942392],\n       [ 0.07236067,  1.49381682,  1.00912225,  1.05346626],\n       [ 0.23470832,  0.23321191, -1.08449238, -0.18679398],\n       [ 0.28109336,  1.2756352 ,  1.77678094,  2.08881393]])"},"metadata":{}}]},{"metadata":{"trusted":true},"cell_type":"code","source":"from sklearn.decomposition import PCA\npca_fit=PCA(n_components=2).fit_transform(df)\npca_fit[0:5]","execution_count":6,"outputs":[{"output_type":"execute_result","execution_count":6,"data":{"text/plain":"array([[ 0.98556588,  1.13339238],\n       [ 1.95013775,  1.07321326],\n       [ 1.76316354, -0.74595678],\n       [-0.14142029,  1.11979678],\n       [ 2.52398013, -1.54293399]])"},"metadata":{}}]},{"metadata":{"trusted":true},"cell_type":"code","source":"#apply PCA (ex:1)","execution_count":7,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"component_df=pd.DataFrame(data= pca_fit, columns=[\"1st Component\",\"2nd Component\"])\ncomponent_df[0:5]","execution_count":8,"outputs":[{"output_type":"execute_result","execution_count":8,"data":{"text/plain":"   1st Component  2nd Component\n0       0.985566       1.133392\n1       1.950138       1.073213\n2       1.763164      -0.745957\n3      -0.141420       1.119797\n4       2.523980      -1.542934","text/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>1st Component</th>\n      <th>2nd Component</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.985566</td>\n      <td>1.133392</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1.950138</td>\n      <td>1.073213</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1.763164</td>\n      <td>-0.745957</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>-0.141420</td>\n      <td>1.119797</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>2.523980</td>\n      <td>-1.542934</td>\n    </tr>\n  </tbody>\n</table>\n</div>"},"metadata":{}}]},{"metadata":{"trusted":true},"cell_type":"code","source":"#Here,these 2 components represents 4 variables(Murder, Assault, UrbanPop,Rape)","execution_count":9,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"from sklearn.decomposition import PCA\npca=PCA(n_components=2)\npca.fit_transform(df)\npca.explained_variance_ratio_","execution_count":10,"outputs":[{"output_type":"execute_result","execution_count":10,"data":{"text/plain":"array([0.62006039, 0.24744129])"},"metadata":{}}]},{"metadata":{"trusted":true},"cell_type":"code","source":"#It means, first component explains 62% of data variation, second component explains 24% of data variation. \n#Totally, 86% of the data variation can be explained by these two components","execution_count":11,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"#If we accept the risk of some error, we can reduce the number of variables(4) to 2(components) as it i seen. \n#We can apply this method to more complex datasets.","execution_count":12,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"#apply PCA (ex:2)","execution_count":13,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"pca = PCA(n_components = 3)\npca_fit = pca.fit_transform(df)\ncomponent_df=pd.DataFrame(data= pca_fit, columns=[\"1st Component\",\"2nd Component\",\"3rd Component\"])\ncomponent_df[0:5]","execution_count":14,"outputs":[{"output_type":"execute_result","execution_count":14,"data":{"text/plain":"   1st Component  2nd Component  3rd Component\n0       0.985566       1.133392      -0.444269\n1       1.950138       1.073213       2.040003\n2       1.763164      -0.745957       0.054781\n3      -0.141420       1.119797       0.114574\n4       2.523980      -1.542934       0.598557","text/html":"<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>1st Component</th>\n      <th>2nd Component</th>\n      <th>3rd Component</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.985566</td>\n      <td>1.133392</td>\n      <td>-0.444269</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1.950138</td>\n      <td>1.073213</td>\n      <td>2.040003</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1.763164</td>\n      <td>-0.745957</td>\n      <td>0.054781</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>-0.141420</td>\n      <td>1.119797</td>\n      <td>0.114574</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>2.523980</td>\n      <td>-1.542934</td>\n      <td>0.598557</td>\n    </tr>\n  </tbody>\n</table>\n</div>"},"metadata":{}}]},{"metadata":{"trusted":true},"cell_type":"code","source":"pca.explained_variance_ratio_","execution_count":15,"outputs":[{"output_type":"execute_result","execution_count":15,"data":{"text/plain":"array([0.62006039, 0.24744129, 0.0891408 ])"},"metadata":{}}]},{"metadata":{"trusted":true},"cell_type":"code","source":"#It means, first component explains 62% of data variation.\n#Second component explains 24% of data variation.\n#Third component explains 8% of data variation\n#Totally, 94% of the data variation can be explained by these three components","execution_count":16,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"#How can we specify the number of components?\n#We can specify the number of components according to these explained variance ratio...","execution_count":17,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"pca=PCA().fit(df)","execution_count":18,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"plt.plot(np.cumsum(pca.explained_variance_ratio_))","execution_count":19,"outputs":[{"output_type":"execute_result","execution_count":19,"data":{"text/plain":"[<matplotlib.lines.Line2D at 0x7f9882bdec50>]"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"<Figure size 432x288 with 1 Axes>","image/png":"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\n"},"metadata":{"needs_background":"light"}}]},{"metadata":{"trusted":true},"cell_type":"code","source":"#From this graph,\n#We can understand that less than 65% of the data can be explained by one component,\n#                       less than 90% of the data can be explained by two components,\n#                       more than 95% of the data can be explained by three components,\n#                                100% of the data can be explained by four components.","execution_count":20,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"Thanks to https://github.com/mvahit/DSMLBC"},{"metadata":{"trusted":true},"cell_type":"code","source":"","execution_count":null,"outputs":[]}],"metadata":{"kernelspec":{"language":"python","display_name":"Python 3","name":"python3"},"language_info":{"pygments_lexer":"ipython3","nbconvert_exporter":"python","version":"3.6.4","file_extension":".py","codemirror_mode":{"name":"ipython","version":3},"name":"python","mimetype":"text/x-python"}},"nbformat":4,"nbformat_minor":4}