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‎Kmeans_plus_plus.ipynb

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[[1.000e+00 1.386e+01 1.350e+00 2.270e+00 1.600e+01 9.800e+01 2.980e+00\n",
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" 3.150e+00 2.200e-01 1.850e+00 7.220e+00 1.010e+00 3.550e+00 1.045e+03]\n",
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" [2.000e+00 1.184e+01 2.890e+00 2.230e+00 1.800e+01 1.120e+02 1.720e+00\n",
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" 1.320e+00 4.300e-01 9.500e-01 2.650e+00 9.600e-01 2.520e+00 5.000e+02]]\n"
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]
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}
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],
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"source": [
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"# Write a kmeans plus plus algorithm to initialize the centroids to be used in the kmeans algorithm\n",
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"# Initialize centroids based on a probability index set by their distance from each other\n",
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"# Dataset is a numpy array and k is the number of centroids\n",
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"\n",
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"\n",
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"import numpy as np\n",
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"np.set_printoptions(precision=3)\n",
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"import matplotlib.pyplot as plt\n",
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"%matplotlib inline\n",
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"\n",
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"\n",
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"def kmeans_plus_plus(dataset, k):\n",
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" # define the shape of the dataset\n",
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" N, D = dataset.shape\n",
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" # define the centroid size\n",
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" C = np.zeros([k, D])\n",
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" # pick a random instance in the dataset\n",
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" random_index = np.random.choice(len(dataset))\n",
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" # choose a random instance\n",
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" random_instance = dataset[random_index]\n",
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" for i in range(k):\n",
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" # define the distance array to store all items in the dataset from the randomly chosen instance\n",
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" distance_array = np.linalg.norm(random_instance - dataset , axis = 1)\n",
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" # each distance proportionally increase the chances for the next data to be chosen\n",
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" prob_array = distance_array / np.sum(distance_array)\n",
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" # based on the distances, chose a random instance index\n",
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" chosen_index = np.random.choice(len(dataset) , p = prob_array)\n",
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" # assing the next instance to the centroid[i]\n",
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" C[i] = dataset[chosen_index]\n",
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" # last chosen C[i] will be the new reference to chose next instance for C[i+1]\n",
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" random_instance = C[i] \n",
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" return C\n",
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"\n",
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"# test the function \n",
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"if __name__ == '__main__':\n",
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" \n",
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" # download your copy of wine dataset from: https://archive.ics.uci.edu/ml/machine-learning-databases/wine/\n",
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" # change the format to .txt or .cvs if current data is causing any parsing error.\n",
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" \n",
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" dataset = np.loadtxt('wine.data.txt' , dtype = float, delimiter = ',')\n",
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" dataset = np.array(dataset)\n",
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" print(kmeans_plus_plus(dataset, 2))\n",
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" \n",
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" # if there was a need for standardization, this code below could be applied:\n",
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" # standardized_data = [(i - np.mean(dataset)) / (np.std(dataset)) for i in dataset]\n",
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" "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"/Users/volkansonmez/miniconda/lib/python3.7/site-packages/numpy/core/fromnumeric.py:3335: RuntimeWarning: Mean of empty slice.\n",
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" out=out, **kwargs)\n",
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"/Users/volkansonmez/miniconda/lib/python3.7/site-packages/numpy/core/_methods.py:161: RuntimeWarning: invalid value encountered in double_scalars\n",
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" ret = ret.dtype.type(ret / rcount)\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[ 0. 17592402.704 4545800.928 2633614.463 1341434.153\n",
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" 916424.194 684095.537 415042.347 674861.281 353365.048\n",
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" 657438.809 187113.672 492970.971 565012.338 138874.119]\n"
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]
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},
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{
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"data": {
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\n",
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"text/plain": [
96+
"<Figure size 432x288 with 1 Axes>"
97+
]
98+
},
99+
"metadata": {
100+
"needs_background": "light"
101+
},
102+
"output_type": "display_data"
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}
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],
105+
"source": [
106+
"# the Within-Cluster-Sum-of-Squares amount normally goes down as the number of clusters increase\n",
107+
"# the ideal number of clusters can be chosen if the WCSS graph achieves a clear elbow shape\n",
108+
"\n",
109+
"def k_means(dataset, k): # return the WCSS value for chosen k clusters\n",
110+
" # Initialize the WCSS value to 0\n",
111+
" WCSS = 0\n",
112+
" # create an array to collect the indices of the groups\n",
113+
" final_array = np.zeros(len(dataset))\n",
114+
" # initialize the centroids based on the kmeansplusplus function. If data is too big, just choose k random instances\n",
115+
" C = kmeans_plus_plus(dataset, k)\n",
116+
" # create an old C initialized with zeros\n",
117+
" C_old = np.zeros(C.shape)\n",
118+
" # define the error function\n",
119+
" parameter_gradient = np.linalg.norm(C-C_old)\n",
120+
" # count the number of epochs performed until the error is zero, put an iterator\n",
121+
" epoch = 0\n",
122+
" # continue to assign new C until the distance btw C_new and C_old is very small\n",
123+
" while parameter_gradient > 1e-4: \n",
124+
" # loop over the dataset to measure the instance distances with C\n",
125+
" # assign the group number for each instance based on the shortest distance from the instance to the C\n",
126+
" for i in range(len(dataset)):\n",
127+
" distance = np.linalg.norm((dataset[i] - C), axis = 1) # axis 1 will output distance array with size k\n",
128+
" centroid_index = np.argmin(distance) # the closest centroid_index from the instance \n",
129+
" final_array[i] = centroid_index # assign the centroid index as group number to an array \n",
130+
" # assign the current C as C_old to update the new C\n",
131+
" C_old = np.copy(C)\n",
132+
" # loop over each index of the centroid\n",
133+
" for i in range(k):\n",
134+
" # list of items with the same group numbers are assigned to sub_groups\n",
135+
" sub_group = [dataset[j] for j in range(len(dataset)) if final_array[j] == i]\n",
136+
" # take the mean of the sub-group and \n",
137+
" mean_of_sub_group = np.mean(sub_group, axis = 0)\n",
138+
" # assign the new values to C\n",
139+
" C[i] = mean_of_sub_group\n",
140+
" # update the parameter gradient after assigning the new C \n",
141+
" parameter_gradient = np.linalg.norm(C - C_old) # when C does not change, we reach to zero error \n",
142+
" # update epoch value\n",
143+
" epoch += 1\n",
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"\n",
145+
" # To measure WCSS, sum up the square of the \"distances from all group data to their mean\"\n",
146+
" for j in range(k):\n",
147+
" grouped_data = [dataset[i] for i in range(len(dataset)) if final_array[i] == j]\n",
148+
" mean_of_grouped_data = np.mean(grouped_data, axis = 0) # outputs number of attributes\n",
149+
" for i in range(len(grouped_data)):\n",
150+
" WCSS += np.sum((grouped_data[i] - mean_of_grouped_data)**2) \n",
151+
" \n",
152+
" \n",
153+
" # return the final cluster coordinates, the array carrying indices of all data points, and the WCSS with given k\n",
154+
" return epoch, C, final_array, WCSS\n",
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"\n",
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"\n",
157+
"if __name__ == '__main__':\n",
158+
" dataset = np.loadtxt('wine.data.txt' , dtype = float, delimiter = ',')\n",
159+
" dataset = np.array(dataset)\n",
160+
" np.random.seed(1)\n",
161+
" k = 15\n",
162+
" def run_k_means():\n",
163+
" WCSS_list = np.zeros(k)\n",
164+
" for i in range(1, k):\n",
165+
" epoch, C, final_array, WCSS = k_means(dataset, i)\n",
166+
" WCSS_list[i] = WCSS\n",
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"\n",
168+
" return WCSS_list\n",
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"\n",
170+
" result = run_k_means()\n",
171+
" print(result)\n",
172+
" plt.plot(np.arange(1, k), result[1:])\n",
173+
" "
174+
]
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},
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{
177+
"cell_type": "code",
178+
"execution_count": null,
179+
"metadata": {},
180+
"outputs": [],
181+
"source": []
182+
}
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],
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"metadata": {
185+
"kernelspec": {
186+
"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
191+
"codemirror_mode": {
192+
"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
197+
"name": "python",
198+
"nbconvert_exporter": "python",
199+
"pygments_lexer": "ipython3",
200+
"version": "3.7.7"
201+
}
202+
},
203+
"nbformat": 4,
204+
"nbformat_minor": 2
205+
}

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