We call this line our first principal component. The green line has been constructed using mathematical optimization to maximize the variance between the data points as much as possible along that line. The 1D space (your line) is a subspace of the 2D coordinate system. You have essentially reduced the dimensionality of your data from 2D to 1D. Projecting data points onto a lower-dimensional subspace. If you have data in a 2-dimensional space, you could project all the data points onto a line using PCA. What is dimensionality reduction, and what is a subspace? Let’s illustrate this with an example. PCA achieves this goal by projecting data onto a lower-dimensional subspace that retains most of the variance among the data points. Principal Components Analysis, also known as PCA, is a technique commonly used for reducing the dimensionality of data while preserving as much as possible of the information contained in the original data. What is Principal Components Analysis (PCA) Lastly, we learn how to perform PCA in Python. In the second part, we will look at a more mathematical definition of Principal components analysis. We start with a simple explanation to build an intuitive understanding of PCA. In this post, we will have an in-depth look at principal components analysis or PCA.
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