PCA (Principal Component Analysis) is a statistical technique used to analyze data sets with multiple variables. The purpose of PCA is to reduce the dimensionality (number of variables) of the data set to simplify analysis and visualize patterns that may exist within the data.
PCA involves transforming the original variables into a new set of variables (the principal components) that are linear combinations of the original variables. The principal components are ordered by the amount of variance in the data that they explain, such that the first principal component accounts for the largest amount of variance, the second accounts for the second-largest amount, and so on.
PCA can be used in various fields such as finance, biology, chemistry, physics, economics, and social sciences. It is also utilized in machine learning, where it is used as a technique for dimensionality reduction in feature extraction.
The process of PCA involves several steps, including centering the data, computing the covariance matrix or correlation matrix, computing the eigenvectors and eigenvalues of the matrix, and finally computing the principal components. The process is usually performed using software packages such as MATLAB, R, or Python.
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