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Understanding K-Means Clustering {#tutorial_py_kmeans_understanding}
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In this chapter, we will understand the concepts of K-Means Clustering, how it works etc.
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We will deal this with an example which is commonly used.
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### T-shirt size problem
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Consider a company, which is going to release a new model of T-shirt to market. Obviously they will
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have to manufacture models in different sizes to satisfy people of all sizes. So the company make a
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data of people's height and weight, and plot them on to a graph, as below:
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![image](images/tshirt.jpg)
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Company can't create t-shirts with all the sizes. Instead, they divide people to Small, Medium and
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Large, and manufacture only these 3 models which will fit into all the people. This grouping of
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people into three groups can be done by k-means clustering, and algorithm provides us best 3 sizes,
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which will satisfy all the people. And if it doesn't, company can divide people to more groups, may
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be five, and so on. Check image below :
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![image](images/tshirt_grouped.jpg)
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### How does it work ?
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This algorithm is an iterative process. We will explain it step-by-step with the help of images.
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Consider a set of data as below ( You can consider it as t-shirt problem). We need to cluster this
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![image](images/testdata.jpg)
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**Step : 1** - Algorithm randomly chooses two centroids, \f$C1\f$ and \f$C2\f$ (sometimes, any two data are
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taken as the centroids).
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**Step : 2** - It calculates the distance from each point to both centroids. If a test data is more
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closer to \f$C1\f$, then that data is labelled with '0'. If it is closer to \f$C2\f$, then labelled as '1'
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(If more centroids are there, labelled as '2','3' etc).
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In our case, we will color all '0' labelled with red, and '1' labelled with blue. So we get
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following image after above operations.
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![image](images/initial_labelling.jpg)
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**Step : 3** - Next we calculate the average of all blue points and red points separately and that
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will be our new centroids. That is \f$C1\f$ and \f$C2\f$ shift to newly calculated centroids. (Remember, the
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images shown are not true values and not to true scale, it is just for demonstration only).
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And again, perform step 2 with new centroids and label data to '0' and '1'.
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So we get result as below :
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![image](images/update_centroid.jpg)
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Now **Step - 2** and **Step - 3** are iterated until both centroids are converged to fixed points.
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*(Or it may be stopped depending on the criteria we provide, like maximum number of iterations, or a
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specific accuracy is reached etc.)* **These points are such that sum of distances between test data
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and their corresponding centroids are minimum**. Or simply, sum of distances between
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\f$C1 \leftrightarrow Red\_Points\f$ and \f$C2 \leftrightarrow Blue\_Points\f$ is minimum.
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\f[minimize \;\bigg[J = \sum_{All\: Red\_Points}distance(C1,Red\_Point) + \sum_{All\: Blue\_Points}distance(C2,Blue\_Point)\bigg]\f]
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Final result almost looks like below :
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![image](images/final_clusters.jpg)
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So this is just an intuitive understanding of K-Means Clustering. For more details and mathematical
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explanation, please read any standard machine learning textbooks or check links in additional
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resources. It is just a top layer of K-Means clustering. There are a lot of modifications to this
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algorithm like, how to choose the initial centroids, how to speed up the iteration process etc.
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-# [Machine Learning Course](https://www.coursera.org/course/ml), Video lectures by Prof. Andrew Ng
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(Some of the images are taken from this)