[TBD]Role of Scatter matrix in machine learning

Introduction

Laymen explanation

Technical explanation

A scatter matrix is another common analysis tool as it include several pairwise scatter plots of variables presented in a matrix format. It is also used to verify if variables are correlated and whether the correlation is positive or negative.

Types

Within-class scatter matrix

Here, is the sample mean of the k-th class.

Between-class scatter matrix

Here, m is the number of classes, is the overall sample mean, and is the number of samples in the k-th class.

Use in machine learning

• A scatter matrix is a estimation of covariance matrix when covariance cannot be calculated or costly to calculate. The scatter matrix is also used in lot of dimensionality reduction exercises. If there are k variables , scatter matrix will have k rows and k columns i.e k X k matrix.

• The maximum likelihood estimate, given n samples, for the covariance matrix of a multivariate normal distribution can be expressed as the normalized scatter matrix

• Classification problem becomes easier, if within class scatter is less and between class scatter is large

Relevance in neural networks

Reference

https://youtu.be/JlmJ5PEmIOo?t=3282

https://www.oreilly.com/library/view/hands-on-machine-learning/9781789611854/8657d409-f796-4014-923a-452ebc55d4ec.xhtml

https://medium.com/@raghavan99o/scatter-matrix-covariance-and-correlation-explained-14921741ca56

https://en.wikipedia.org/wiki/Scatter_matrix

https://youtu.be/JlmJ5PEmIOo?t=3557