Parametric assumptions of data

When we say parametric assumptions, we are referring to base assumptions that algorithms make about the shape of the data. In the previous chapter, while exploring principal component analysis (PCA), we discovered that the end result of the algorithm produced components that we could use to transform data through a single matrix multiplication. The assumption that we were making was that the original data took on a shape that could be decomposed and represented by a single linear transformation (the matrix operation). But what if that is not true? What if PCA is unable to extract useful features from the original dataset? Algorithms such as PCA and linear discriminate analysis (LDA) will always be able to find features, but they may not be useful at all. Moreover, these algorithms rely on a predetermined equation and will always output the same features each and every time they are run. This is why we consider both LDA and PCA as being linear transformations...