How many clusters?

1. How many clusters?

Hi everyone! In this video, we will explore a way to decide how many clusters are present in our data.

2. Introduction to dendrograms

Up until this point, we have graphically looked at the number of points in our datasets to decide how many clusters to form. To decide on the number of clusters in hierarchical clustering, we can use a graphical diagram called the dendrogram. A dendrogram is a branching diagram that shows the progression in a linkage object as we proceed through the hierarchical clustering algorithm. Let us look at an example.

3. Create a dendrogram in SciPy

The first step in creating a dendrogram is to import the method from scipy-dot-cluster-dot-hierarchy. Next, we use the linkage method to create a distance matrix. Finally, we use the dendrogram method and provide the linkage object as an argument, and display the plot.

4. Dendrogram demonstration

To understand the intricacies of a dendrogram, let us look at the dendrogram that has been generated and then make corresponding clusters. Recall the hierarchical clustering algorithm, where each step was a result of merging of two closest clusters in the earlier step. The x axis represents individual points, whereas the y axis represents the distance or dissimilarity between clusters. In the dendrogram, each inverted U represents a cluster divided into its two child clusters. The inverted U at the top of the figure represents a single cluster of all the data points. The width of the U shape represents the distance between the two child clusters. A wider U, therefore, means that the two child clusters were farther away from each other as compared to a narrower U in the diagram.

5. Dendrogram demonstration - 2

Now, if you draw a horizontal line at any part of the figure, the number of vertical lines it intersects tells you the number of clusters at that stage, and the distance between those vertical lines indicates the inter-cluster distance. At the horizontal line drawn on the figure, we see that there are three clusters. When you move the line below, the number of clusters increases but the inter-cluster distance decreases. This information helps us in deciding the number of clusters. For instance, even though we haven't looked at the distribution of the data points, it seems that the top three clusters have the highest distances between them. At this point, I must reiterate that there is no right metric to decide how many clusters are ideal. For instance, it looks like choosing three clusters should be ideal for this exercise. However, one's argument for two or four clusters may stand as well. Let us look at the results of each of these three cases.

6. Two clusters

Here is the result of performing the clustering with two clusters.

7. Three clusters

Here is the result with three clusters.

8. Four clusters

And here is how 4 clusters look on the data. Although the dendorgram indicated we could go ahead with three clusters, the case with four clusters makes sense too. Therefore, an additional check of visualizing the data may be performed before deciding on the number of clusters.

9. Next up - try some exercises

Now, let us try some exercises on how to decide the number of clusters using the dendrogram!

This exercise is part of the course

Cluster Analysis in Python

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Before you are ready to classify news articles, you need to be introduced to the basics of clustering. This chapter familiarizes you with a class of machine learning algorithms called unsupervised learning and then introduces you to clustering, one of the popular unsupervised learning algorithms. You will know about two popular clustering techniques - hierarchical clustering and k-means clustering. The chapter concludes with basic pre-processing steps before you start clustering data.

Exercise 1: Unsupervised learning: basics Exercise 2: Unsupervised learning in real world Exercise 3: Pokémon sightings Exercise 4: Basics of cluster analysis Exercise 5: Pokémon sightings: hierarchical clustering Exercise 6: Pokémon sightings: k-means clustering Exercise 7: Data preparation for cluster analysis Exercise 8: Normalize basic list data Exercise 9: Visualize normalized data Exercise 10: Normalization of small numbers Exercise 11: FIFA 18: Normalize data

This chapter focuses on a popular clustering algorithm - hierarchical clustering - and its implementation in SciPy. In addition to the procedure to perform hierarchical clustering, it attempts to help you answer an important question - how many clusters are present in your data? The chapter concludes with a discussion on the limitations of hierarchical clustering and discusses considerations while using hierarchical clustering.

Exercise 1: Basics of hierarchical clustering Exercise 2: Hierarchical clustering: ward method Exercise 3: Hierarchical clustering: single method Exercise 4: Hierarchical clustering: complete method Exercise 5: Visualize clusters Exercise 6: Visualize clusters with matplotlib Exercise 7: Visualize clusters with seaborn Exercise 8: How many clusters?

Current Exercise

Exercise 9: Create a dendrogram Exercise 10: How many clusters in comic con data?Exercise 11: Limitations of hierarchical clustering Exercise 12: Timing run of hierarchical clustering Exercise 13: FIFA 18: exploring defenders

This chapter introduces a different clustering algorithm - k-means clustering - and its implementation in SciPy. K-means clustering overcomes the biggest drawback of hierarchical clustering that was discussed in the last chapter. As dendrograms are specific to hierarchical clustering, this chapter discusses one method to find the number of clusters before running k-means clustering. The chapter concludes with a discussion on the limitations of k-means clustering and discusses considerations while using this algorithm.

Exercise 1: Basics of k-means clustering Exercise 2: K-means clustering: first exercise Exercise 3: Runtime of k-means clustering Exercise 4: How many clusters?Exercise 5: Elbow method on distinct clusters Exercise 6: Elbow method on uniform data Exercise 7: Limitations of k-means clustering Exercise 8: Impact of seeds on distinct clusters Exercise 9: Uniform clustering patterns Exercise 10: FIFA 18: defenders revisited

Now that you are familiar with two of the most popular clustering techniques, this chapter helps you apply this knowledge to real-world problems. The chapter first discusses the process of finding dominant colors in an image, before moving on to the problem discussed in the introduction - clustering of news articles. The chapter concludes with a discussion on clustering with multiple variables, which makes it difficult to visualize all the data.

Exercise 1: Dominant colors in images Exercise 2: Extract RGB values from image Exercise 3: How many dominant colors?Exercise 4: Display dominant colors Exercise 5: Document clustering Exercise 6: TF-IDF of movie plots Exercise 7: Top terms in movie clusters Exercise 8: Clustering with multiple features Exercise 9: Clustering with many features Exercise 10: Basic checks on clusters Exercise 11: FIFA 18: what makes a complete player?Exercise 12: Farewell!