Table of Contents

## What is mutual information clustering?

Mutual information is a very popular measure for comparing clusterings. Previous work has shown that it is beneficial to make an adjust- ment for chance to this measure, by subtracting an expected value and normalizing via an upper bound. This yields the constant baseline prop- erty that enhances intuitiveness.

**How is clustering performance measured?**

The two most popular metrics evaluation metrics for clustering algorithms are the Silhouette coefficient and Dunn’s Index which you will explore next.

- Silhouette Coefficient. The Silhouette Coefficient is defined for each sample and is composed of two scores:
- Dunn’s Index.

**What is good NMI score?**

Score between 0.0 and 1.0 in normalized nats (based on the natural logarithm). 1.0 stands for perfectly complete labeling. V-Measure (NMI with arithmetic mean option). Adjusted Rand Index.

### How do you calculate cluster accuracy?

Accuracy for classification It is computed as the sum of the diagonal elements of the confusion matrix, divided by the number of samples to get a value between 0 and 1. For clustering, there is however no association provided by the clustering algorithm between the class labels and the predicted cluster labels.

**What is V measure?**

The V-measure is the harmonic mean between homogeneity and completeness: v = (1 + beta) * homogeneity * completeness / (beta * homogeneity + completeness) This metric is independent of the absolute values of the labels: a permutation of the class or cluster label values won’t change the score value in any way.

**What is mutual Info score?**

The Mutual Information score expresses the extent to which observed frequency of co-occurrence differs from what we would expect (statistically speaking). In statistically pure terms this is a measure of the strength of association between words x and y.

#### How do you calculate clusters?

Probably the most well known method, the elbow method, in which the sum of squares at each number of clusters is calculated and graphed, and the user looks for a change of slope from steep to shallow (an elbow) to determine the optimal number of clusters.

**How do you calculate mutual information?**

The mutual information can also be calculated as the KL divergence between the joint probability distribution and the product of the marginal probabilities for each variable. — Page 57, Pattern Recognition and Machine Learning, 2006. This can be stated formally as follows: I(X ; Y) = KL(p(X, Y) || p(X) * p(Y))

**What is the range of mutual information?**

First, unlike correlation, which has an absolute value within the range of 0 to 1, mutual information’s value is more open ended and can range from 0 for complete independence to infinity for a completely correlated and continuous pair of r.v. The actual value of mutual information can vary with the values of the …

## How do you test a clustering model?

Ideally you have some kind of pre-clustered data (supervised learning) and test the results of your clustering algorithm on that. Simply count the number of correct classifications divided by the total number of classifications performed to get an accuracy score.

**How do you determine the number of clusters and evaluate the clustering results?**

The optimal number of clusters can be defined as follow:

- Compute clustering algorithm (e.g., k-means clustering) for different values of k.
- For each k, calculate the total within-cluster sum of square (wss).
- Plot the curve of wss according to the number of clusters k.

**When is maximum mutual information reached in a clustering?**

Maximum mutual information is reached for a clustering that perfectly recreates the classes – but also if clusters in are further subdivided into smaller clusters (Exercise 16.7). In particular, a clustering with one-document clusters has maximum MI.

### What are the external criteria of clustering quality?

This section introduces four external criteria of clustering quality. Purity is a simple and transparent evaluation measure. Normalized mutual information can be information-theoretically interpreted. The Rand index penalizes both false positive and false negative decisions during clustering.

**Is nmi a good measure for determining the quality of clustering?**

• NMI is a good measure for determining the quality of clustering. • It is an external measure because we need the class labels of the instances to determine the NMI. • Since it’s normalized we can measure and compare the NMI between different clusterings having different number of clusters.

**Can we use purity to trade off clustering quality against number of clusters?**

High purity is easy to achieve when the number of clusters is large – in particular, purity is 1 if each document gets its own cluster. Thus, we cannot use purity to trade off the quality of the clustering against the number of clusters. A measure that allows us to make this tradeoff is normalized mutual informationor NMI: