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Principal Components Analysis

Chapter 18 Principal Components AnalysisPrincipal Components Analysis (PCA) is one of a family of techniques for takinghigh-dimensional data, and using the dependencies between the variables to representit in a more tractable, lower-dimensional form, without losing too much is one of the simplest and most robust ways of doing suchdimensionalityreduction. It is also one of the oldest, and has been rediscovered many times inmany fields, so it is also known as the Karhunen-Lo ve transformation, the Hotellingtransformation, the method of empirical orthogonal functions, and singular valuedecomposition1. We will call it Mathematics of Principal ComponentsWe start withp-dimensional vectors, and want to summarize them by projectingdown into aq-dimensional subspace.

Principal components analysis (PCA) is one of a family of techniques for taking ... The second principal component is the direction which ... “assume the different rows of the data frame are statistically independent”. This is because no such assumption is required for principal components. All it does is say

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