Welcome to our fourth installment on Machine Learning. In this module we’re going to cover K-Means. K-Means is a clustering algorithm based on the hyperparameter “K” which dictates how many clusters there will be. A hyperparameter is just a parameter that we can adjust. Each cluster has a “centroid” or a central point that will be the anchor of our cluster. Here are the steps to the K-Means algorithm:

- Plot the data points
- Plot K centroids randomly
- Calculate distances from each point to each centroid
- Assign a label to each point equal to the centroid it’s clustered to
- Calculate the center of each cluster → that becomes the new centroid
- Repeat steps 3 to 5 until either:
- The centroid stops moving
- The data points are not assigned new centroids after an iteration
- We reach the maximum number of iterations

Video Tutorial:

Here’s a visualization of K-Means:

We’re not going to manually implement K-Means in this introductory module, we’re just going to use Python’s SKLearn module which already has an implementation for us. Let’s get into it. To start using K-Means we’ll have to install some libraries. We’ll need the `sklearn`

library which has an implementation of K-Means that we can just use, `numpy`

which contains numerical operators, `pandas`

which is the de facto data organization library for Python, and `matplotlib`

which we’ve already used many times and is the best plotting library for Python. We can install these with just one line in the command line:

`pip install sklearn numpy pandas matplotlib`

# Randomly Generated Sample Data K Means

Alright now that we’ve got our libraries installed, we’re ready to go. We’ll cover two different K-Means examples here. Example number 1 is going to be on a contrived example of randomly generated data with two centroids. Example number 2 is going to be on the digits dataset provided by `sklearn`

. As always, the first thing we’ll do is handle our imports.

```
import random
import pandas as pd
from sklearn.cluster import KMeans
import matplotlib.pyplot as plt
```

## Generate Random Sample Data

Next we’re going to randomly generate 100 data points. The points will be two clusters, one around `(0,0)`

and the other around `(5,5)`

. We’ll do this with a for loop that loops 100 times and generates a cluster around `(0,0)`

on even iterations and around `(5,5)`

on odd iterations. To randomly generate data points, we’ll create two values, an `x`

and a `y`

value. Each value will be made by generating a uniform random number between -1 and 1 and adding it to either 0 or 5. Once we’ve generated all 100 samples we’ll convert our data into a `pandas`

`DataFrame`

object for further processing.

```
samples = 100
data = []
for i in range(100):
if i%2 == 0:
base = 0
else:
base = 5
x = random.uniform(-1,1) + base
y = random.uniform(-1,1) + base
data.append([x,y])
df_rand = pd.DataFrame(data)
```

Now we can just use `sklearn`

to implement K-Means with 2 clusters. First we’ll create a K-Means object and then call its `fit_predict`

module on the `DataFrame`

we made earlier. Once we have our labels, we’ll separate out the labeled data into two separate dataframes to graph.

```
k2means = KMeans(n_clusters=2)
label_rand=k2means.fit_predict(df_rand)
flabels1 = df_rand[label_rand==1]
flabels0 = df_rand[label_rand==0]
```

## Plot Randomized Sample Data

Now all we have to do is scatter plot these with `matplotlib`

. We’ll also get the centroids using the `cluster_centers_`

attribute of the K Means object we created earlier.

```
plt.scatter(flabels1[0], flabels1[1], label=0)
plt.scatter(flabels0[0], flabels0[1], label=1)
centroids_rand = k2means.cluster_centers_
plt.scatter(centroids_rand[:,0], centroids_rand[:,1], s=80, color="black")
plt.legend()
plt.xlabel("X")
plt.ylabel("Y")
plt.title("Randomly Generated Two Centroid K Means")
plt.show()
```

Once we plot these, we should see something like the image below.

# Digits Dataset K Means

Alright now that we’ve seen a contrived example, let’s take a look at what a more real-life like example will be. For this example, we’ll be running K Means on the digits dataset. As always, we’ll start off by importing our libraries. We’ll import the `load_digits`

module from `sklearn.datasets`

to load the digits dataset. We’ll import `PCA`

from decomposition to turn this dataset with 64 features into a dataset with 2 features. PCA is Principal Component Analysis, in this example we’ll be using it for dimensionality reduction. We imported `KMeans`

and `matplotlib.pyplot`

already above but I just put them here to show you that we need those libraries for this example. We’ll also need `numpy`

for this example.

```
from sklearn.datasets import load_digits
from sklearn.decomposition import PCA
from sklearn.cluster import KMeans
import numpy as np
import matplotlib.pyplot as plt
```

We’ll start out by loading up the digits and applying PCA to turn our 64 feature dataset into a 2 feature dataset.

```
data = load_digits().data
pca = PCA(n_components=2)
df = pca.fit_transform(data)
```

## Load and Examine Data

Once we’ve transformed our data let’s apply `KMeans`

. We’ll give it 10 clusters since there are 10 digits.

```
kmeans = KMeans(n_clusters=10)
label = kmeans.fit_predict(df)
print(label)
```

The labels will be a list of numbers where each number is `KMeans`

prediction of each dataset.

This is all there is to `KMeans`

, let’s get into what it looks like when we plot it out. We’ll use `np`

, our alias for the `numpy`

library to create a set of unique labels from the labels we made earlier. Then we’ll use the `cluster_centers_`

from the K Means object we created to get the centroids. Now, for each of our unique labels, we’ll plot the data points that correspond to that label on a scatter plot. Once we’ve plotted all the labels, we’ll create a scatter plot of the centroids. For the centroids you’ll notice that I passed in an `s`

parameter. This parameter accounts for the size of the point, a regular point is size 72.

## Plot Data

Once we’ve plotted our data, we simply label our graph, add a legend, and then print it out.

```
unique_labels = np.unique(label)
centroids = kmeans.cluster_centers_
for i in unique_labels:
plt.scatter(df[label==i, 0], df[label==i, 1], label=i)
# s is a size indicator
plt.scatter(centroids[:,0], centroids[:,1], s=80, color="black")
plt.xlabel("X")
plt.ylabel("Y")
plt.title("Digits K Means")
plt.legend()
plt.show()
```

Our plot should look something like this:

That’s it, that’s all there is to K-Means. Pretty simple, you can implement it in just a few lines.

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