Prashant Shekhar gives us an overview of Principal Component Analysis using R:

PCA changes the axis towards the direction of maximum variance and then takes projection on this new axis. The direction of maximum variance is represented by Principal Components (PC1). There are multiple principal components depending on the number of dimensions (features) in the dataset and they are orthogonal to each other. The maximum number of principal component is same as a number of dimension of data. For example, in the above figure, for two-dimension data, there will be max of two principal components (PC1 & PC2). The first principal component defines the most of the variance, followed by second principal component, third principal component and so on. Dimension reduction comes from the fact that it is possible to discard last few principal components as they will not capture much variance in the data.

PCA is a useful technique for reducing dimensionality and removing covariance.

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