What is Principal Components Analysis?

Principal Component Analysis is an unsupervised learning algorithm that is used for dimensionality reduction in machine learning. It is a statistical process that transforms the observations of correlated features into a collection of linearly uncorrelated features with the support of orthogonal data. These new transformed features are known as the Principal Components.

It is a famous tool that is used for exploratory data analysis and predicting modeling. It is an approach to draw a strong design from the given dataset by decreasing the variances.

PCA works by treating the variance of each attribute because the high attribute shows the division between the classes, and therefore it reduces the dimensionality. Some real-world applications of PCA are image processing, movie recommendation systems, optimizing the power allocation in various communication channels. It is a feature extraction method, so it includes the important variables and drops the least important variable.

Principal components analysis is also called the Karhunen-Loeve, or K-L, method. It can search for k n-dimensional orthogonal vectors that can best be used to represent the data, where k ≤ n. The original data are projected onto a much smaller area, which results in dimensionality reduction. It connects the essence of attributes by making an alternative smaller set of variables. The initial data can then be projected onto this smaller set.

There are the following steps which are used in PCA is as follows −

  • The input data are normalized so that each attribute falls inside a similar range. This step helps ensure that attributes with large domains will not dominate attributes with smaller domains.

  • PCA evaluates k orthonormal vectors that support a basis for the normalized input data. These are unit vectors that each point in a direction perpendicular to the others. These vectors are defined as the principal components. The input data are a linear set of the principal components.

  • The principal components are arranged in order of decreasing “significance” or strength. The principal components essentially serve as a new set of axes for the data, providing important information about variance. That is, the sorted axes are such that the first axis displays the most variance among the data, the second axis displays the next highest variance, etc.

  • Because the components are sorted as per the decreasing order of “significance,” the size of the data can be decreased by removing the weaker components, namely, those with low variance. Using the strongest principal components, it should be possible to reconstruct a good approximation of the original data.