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K-means clustering with variable dimensions
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k-means-clustering-with-variable-dimensions.ipynb
{
"nbformat": 4,
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"metadata": {
"colab": {
"name": "K-means clustering with variable dimensions",
"provenance": [],
"collapsed_sections": [],
"authorship_tag": "ABX9TyPj3jBnrjbKT/G51QlqbYW2",
"include_colab_link": true
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"kernelspec": {
"name": "python3",
"display_name": "Python 3"
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"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/Robin-Lord/c7826161937d3448a316be5d3cd8f431/k-means-clustering-with-variable-dimensions.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "tNiB7IIb7ueX",
"colab_type": "text"
},
"source": [
"# K-means clustering data\n",
"\n",
"This notebook will help you use K-means clustering to group data, it goes with [this explanatory blog post](http://www.therobinlord.com/what-is-k-means-clustering?/) on www.therobinlord.com so if you want to know more about what actually happens in K-means clustering - go there.\n",
"\n",
"==========================================="
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "oSGTOtHd9fX-",
"colab_type": "text"
},
"source": [
"**First we need to get our data**, for the sake of consistency with [my blog post](http://www.therobinlord.com/what-is-k-means-clustering?/) we'll get the same data we're using there so first we need to get the **gspread** library to access that data."
]
},
{
"cell_type": "code",
"metadata": {
"id": "i5samlRhoQIr",
"colab_type": "code",
"colab": {}
},
"source": [
"# Lets us interact with Google Sheets\n",
"import gspread\n",
"\n",
"# Handles authorisation for you\n",
"from google.colab import auth\n",
"auth.authenticate_user()\n",
"from oauth2client.client import GoogleCredentials\n",
"\n",
"# Handles DataFrames for us\n",
"import pandas as pd\n",
"from gspread_dataframe import get_as_dataframe"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "fb7WT3l1olpM",
"colab_type": "text"
},
"source": [
"**Next we get the data we were working with.**\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "AcOz-mwKoklT",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 728
},
"outputId": "5920844a-cb74-4bf6-ae47-4d8d1d7d64b2"
},
"source": [
"# Opening up the data\n",
"gc = gspread.authorize(GoogleCredentials.get_application_default())\n",
"data = gc.open_by_url('https://docs.google.com/spreadsheets/d/18I8wyQlXrYELMoZhNf-tI5lqdq2VDjoI-jqFoi0hDow/edit?usp=sharing')\n",
"\n",
"sandwich_data = get_as_dataframe(data.worksheet(\"Sandwich_data\"), usecols=[0,1], skiprows=5, headers=1)\n",
"\n",
"# Removing the rows without data\n",
"sandwich_data = sandwich_data.dropna(axis=0, how='any')\n",
"sandwich_data"
],
"execution_count": 2,
"outputs": [
{
"output_type": "execute_result",
"data": {
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" <td>2.198211</td>\n",
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"14 5.661727 4.815616\n",
"15 1.203977 0.557554\n",
"16 9.903634 1.678977\n",
"17 2.124293 6.249030\n",
"18 7.988251 0.003995\n",
"19 2.198211 9.541700\n",
"20 7.828862 8.659528\n",
"21 3.735076 6.404364\n",
"22 5.220134 1.558261"
]
},
"metadata": {
"tags": []
},
"execution_count": 2
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Ii3gH7M27mE1",
"colab_type": "text"
},
"source": [
"**Next we import our clustering library**, [Scikit Learn](http://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html) has a KMeans clustering function that does a lot of the heavy lifting for us. Pandas is how we'll work with our data."
]
},
{
"cell_type": "code",
"metadata": {
"id": "IKQWNLMr7DGH",
"colab_type": "code",
"colab": {}
},
"source": [
"from sklearn.cluster import KMeans"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "lduyg7RV9gEp",
"colab_type": "text"
},
"source": [
"We can give KMeans a number of different settings, for instance how many clusters we want to include or how many times to try before we just go with our best attempt. If you want to see more about it and you're working in Google Colab, you can just write *KMeans?* in a cell"
]
},
{
"cell_type": "code",
"metadata": {
"id": "CUZNQL4MmQyI",
"colab_type": "code",
"cellView": "form",
"colab": {}
},
"source": [
"#@title Want more information about KMeans? Tick the box, then run this cell.\n",
"more_info = False #@param {type:\"boolean\"}\n",
"\n",
"if more_info:\n",
" KMeans?"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "lXAYmMOYwXAz",
"colab_type": "text"
},
"source": [
"**Next we set the parameters for our clustering** - we need to choose how many clusters we want (K) and how many times we want to try the process before we decide on which was the best result "
]
},
{
"cell_type": "code",
"metadata": {
"id": "xbEdVBeywlP2",
"colab_type": "code",
"cellView": "form",
"colab": {}
},
"source": [
"#@title Choose the number of clusters and repeats, then run this cell\n",
"\n",
"#@markdown Set number of clusters (K)\n",
"K = 5 #@param {type:\"number\"}\n",
"\n",
"\n",
"\n",
"\n",
"#@markdown Set number of times to try (repeats)\n",
"repeats = 300 #@param {type:\"number\"}"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "fKyIf2xmyDEC",
"colab_type": "text"
},
"source": [
"**Next we get KMeans to group our data** - it will return an object. In that object will be a list - one item for every row in our data. Each item in the list will be a number that corresponds to the group that datapoint has ended up in."
]
},
{
"cell_type": "code",
"metadata": {
"id": "dZ438gmTwr9J",
"colab_type": "code",
"colab": {}
},
"source": [
"# Get labels from KMeans\n",
"kmeans_result = KMeans(n_clusters=K, n_init=repeats ,random_state=0).fit(sandwich_data)"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "JizkYXe-8RJ-",
"colab_type": "text"
},
"source": [
"Here we get the cluster centers it eventually landed on and turn that into a table. These points are also known as \"centroids\". This stage isn't necessary but it's interesting for us to see as we learn the process."
]
},
{
"cell_type": "code",
"metadata": {
"id": "p9QEr06b79GP",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 195
},
"outputId": "94aa1339-e532-441c-ae4d-4b49c8acd24a"
},
"source": [
"list_of_centers = kmeans_result.cluster_centers_\n",
"\n",
"kmeans_clusters = pd.DataFrame(list_of_centers,columns=[\"Sandwich width\",\"Sandwich height\"])\n",
"\n",
"kmeans_clusters"
],
"execution_count": 7,
"outputs": [
{
"output_type": "execute_result",
"data": {
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"text/plain": [
" Sandwich width Sandwich height\n",
"0 7.082905 1.116834\n",
"1 2.031574 9.121671\n",
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"4 3.840365 5.823004"
]
},
"metadata": {
"tags": []
},
"execution_count": 7
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "d1IE7SpLx3L4",
"colab_type": "text"
},
"source": [
"Here we're turning our list of labels into a table and displaying that table so we can look at it."
]
},
{
"cell_type": "code",
"metadata": {
"id": "UCp4WeWmzbY2",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 728
},
"outputId": "57a418e6-1f3b-46c5-8441-0f1721d05062"
},
"source": [
"# Show the list of labels we've created\n",
"\n",
"list_of_labels = kmeans_result.labels_\n",
"\n",
"kmeans_labels = pd.DataFrame(list_of_labels,columns=[\"Group\"])\n",
"\n",
"kmeans_labels"
],
"execution_count": 8,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/html": [
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
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],
"text/plain": [
" Group\n",
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"1 0\n",
"2 2\n",
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},
"metadata": {
"tags": []
},
"execution_count": 8
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "kG6bkZSSz1Ln",
"colab_type": "text"
},
"source": [
"**Now we add our labels to our original data so that we can use them**"
]
},
{
"cell_type": "code",
"metadata": {
"id": "U1Mlz7QNziqJ",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 728
},
"outputId": "c58df1cd-e2f2-47d2-82ad-f241453dd6b6"
},
"source": [
"grouped_sandwiches = sandwich_data.join(kmeans_labels)\n",
"grouped_sandwiches"
],
"execution_count": 9,
"outputs": [
{
"output_type": "execute_result",
"data": {
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" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>5.801256</td>\n",
" <td>0.497134</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>3.507875</td>\n",
" <td>8.790705</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>7.386901</td>\n",
" <td>1.855061</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>0.994364</td>\n",
" <td>9.797447</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>9.676991</td>\n",
" <td>5.807232</td>\n",
" <td>2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>8.666751</td>\n",
" <td>8.651484</td>\n",
" <td>2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>9.145326</td>\n",
" <td>8.437393</td>\n",
" <td>2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>1.425847</td>\n",
" <td>8.356830</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>6.435144</td>\n",
" <td>0.710601</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>3.545293</td>\n",
" <td>2.274556</td>\n",
" <td>3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>0.367717</td>\n",
" <td>3.276266</td>\n",
" <td>3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td>5.661727</td>\n",
" <td>4.815616</td>\n",
" <td>4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>1.203977</td>\n",
" <td>0.557554</td>\n",
" <td>3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>16</th>\n",
" <td>9.903634</td>\n",
" <td>1.678977</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>17</th>\n",
" <td>2.124293</td>\n",
" <td>6.249030</td>\n",
" <td>4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>18</th>\n",
" <td>7.988251</td>\n",
" <td>0.003995</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td>2.198211</td>\n",
" <td>9.541700</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20</th>\n",
" <td>7.828862</td>\n",
" <td>8.659528</td>\n",
" <td>2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>21</th>\n",
" <td>3.735076</td>\n",
" <td>6.404364</td>\n",
" <td>4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>22</th>\n",
" <td>5.220134</td>\n",
" <td>1.558261</td>\n",
" <td>0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Sandwich width Sandwich height Group\n",
"0 6.038829 0.353439 0\n",
"1 7.889089 2.277203 0\n",
"2 7.398768 8.508832 2\n",
"3 5.801256 0.497134 0\n",
"4 3.507875 8.790705 1\n",
"5 7.386901 1.855061 0\n",
"6 0.994364 9.797447 1\n",
"7 9.676991 5.807232 2\n",
"8 8.666751 8.651484 2\n",
"9 9.145326 8.437393 2\n",
"10 1.425847 8.356830 1\n",
"11 6.435144 0.710601 0\n",
"12 3.545293 2.274556 3\n",
"13 0.367717 3.276266 3\n",
"14 5.661727 4.815616 4\n",
"15 1.203977 0.557554 3\n",
"16 9.903634 1.678977 0\n",
"17 2.124293 6.249030 4\n",
"18 7.988251 0.003995 0\n",
"19 2.198211 9.541700 1\n",
"20 7.828862 8.659528 2\n",
"21 3.735076 6.404364 4\n",
"22 5.220134 1.558261 0"
]
},
"metadata": {
"tags": []
},
"execution_count": 9
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "kgjGRkgf0eXM",
"colab_type": "text"
},
"source": [
"I want to be able to see our data in a colour-coordinated graph like we did in GSheets so **next we take our DataFrame, create a smaller version for each of our groups, and plot each of those in turn.**"
]
},
{
"cell_type": "code",
"metadata": {
"id": "173A2mC1ycRR",
"colab_type": "code",
"cellView": "both",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 367
},
"outputId": "ee8863f2-e668-4007-fdef-56ed72fe92a5"
},
"source": [
"# Choosing which colours we want for each group\n",
"colour_map=[\"#ea4335\",\"#fbbc04\",\"#34a853\",\"#ff6d01\",\"#46bdc6\"]\n",
"\n",
"\n",
"# Counting out our number of groups\n",
"group_list = [num for num in range(K)]\n",
"\n",
"# Initially plotting each of our centroids points on the graph\n",
"# we don't have to do this but we're making it line up with our GSheets graph\n",
"ax = kmeans_clusters.plot(kind='scatter', x='Sandwich width', y='Sandwich height',color=\"Black\",label=\"Clusters\");\n",
"\n",
"\n",
"# Now we're labelling each of the centroids we added to the graph.\n",
"# Again this isn't necessary but it's good for us to see and lines up with\n",
"# our GSheets process.\n",
"for num in group_list:\n",
" # Create a unique label\n",
" mylabel = 'Group '+str(num)\n",
"\n",
" # Add an annotation at the relevant point on the graph\n",
" width = list_of_centers[num][0]\n",
" height = list_of_centers[num][1]\n",
" ax.annotate(mylabel, (width, height))\n",
"\n",
"# For each of our groups\n",
"for num in group_list:\n",
" # Create a temporary dataframe which is the same as\n",
" # grouped_sandwiches filtered to just the rows where\n",
" # 'Group' is the same as our number\n",
" temp_df = grouped_sandwiches[(grouped_sandwiches['Group']==num)]\n",
"\n",
" # Getting our colour for this group\n",
" group_colour = colour_map[num]\n",
"\n",
" # Create a new label for this data\n",
" mylabel = 'Group '+str(num)\n",
"\n",
" # If we're not doing this for the last time\n",
" if num<K-1:\n",
"\n",
" # Add this series to the object we already created\n",
" ax = temp_df.plot(kind='scatter', x='Sandwich width', y='Sandwich height',color=group_colour,label=mylabel, ax=ax);\n",
"\n",
" \n",
"\n",
" # If we ARE doing this for the last time\n",
" else:\n",
" print (\"Higher than K\")\n",
" # Create our graph\n",
" scatter = temp_df.plot(title=\"Clustered sandwich sizes\", kind='scatter', x='Sandwich width', y='Sandwich height',color=group_colour,label=mylabel, ax=ax, figsize=(10,5));\n",
" # Format the legend label\n",
" col, lab = ax.get_legend_handles_labels()\n",
" ax.legend(col, lab, bbox_to_anchor=(1, 1))\n",
" fig = scatter.get_figure()\n",
"fig.savefig(\"scatter.png\")"
],
"execution_count": 10,
"outputs": [
{
"output_type": "stream",
"text": [
"Higher than K\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
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SEfV9y5cvR1xcHBISEurbZs6cCX9/fwBATk4O5s2bB61Wi8DAQEybNg379u1r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\nB9nafHFHHNPoAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 720x360 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "BQpdOyGInFRt",
"colab_type": "code",
"colab": {}
},
"source": [
""
],
"execution_count": 0,
"outputs": []
}
]
}
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