2 Linear Algbraic Tools in Machine Learning and Data Science
Chapter 4 from Math and Architectures of Deep Learning by Krishnendu Chaudhury
As mentioned earlier, finding patterns in large volumes of high dimensional data is the name of the game in machine learning and data science. The data often appears in the form of large matrices (a toy example of this is shown in section 2.3 and also in equation 2.1). The rows of the data matrix would represent feature vectors for individual input instances. The number of columns would match the size of the feature vector. The number of rows would match the number of observed input instances. The geometrical representation of such an input matrix would be a set of points (the number of points matches the number of rows in the matrix). The number of dimensions of the space would match the number of columns in the data matrix). The distribution of these points is usually not uniformly random - meaning these points are not spread all over the space. Rather they will occupy a rather small sub-region of that space. Such a skewed distribution of points is shown in Figure 4.2 as a toy instance. Instead of being distributed all over the 2D space, the points are lying within a long and very narrow elliptic shape.