Question

In pca, the principal components are: 2 points perpendicular to each other collinear

Answer 1

The main idea of principal component analysis (PCA) is to reduce the dimensionality of a data set consisting of many variables correlated with each other, either heavily or lightly, while retaining the variation present in the dataset, up to the maximum extent. The same is done by transforming the variables to a new set of variables, which are known as the principal components (or simply, the PCs) and are orthogonal, ordered such that the retention of variation present in the original variables decreases as we move down in the order. So, in this way, the 1st principal component retains maximum variation that was present in the original components. The principal components are the eigenvectors of a covariance matrix, and hence they are orthogonal.

Importantly, the dataset on which PCA technique is to be used must be scaled. The results are also sensitive to the relative scaling. As a layman, it is a method of summarizing data. Imagine some wine bottles on a dining table. Each wine is described by its attributes like colour, strength, age, etc. But redundancy will arise because many of them will measure related properties. So what PCA will do in this case is summarize each wine in the stock with less characteristics.

Answer 2

Principal Component Analysis:

PCA is a dimensionality-reduction procedure that is frequently employed to decrease the dimensionality of huge data batches, by transforming a huge set of variables into a neater one that still comprises the highest of the evidence in the huge set.

• PCA exist as a crowd of fundamental data variables launched in various ways, identical to the properties of actual variables.
• It is normally borrowed in Machine Learning and Data Science for dimensionality deduction.
• PCA2 is the second axes clarifying supplementary variability, and so on. So, generally, PCA1 and PCA2 will affect a large percentage of variability but never 100 percent.

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