Principal Component Analysis (PCA) is a dimensionality reduction technique that transforms the original variables into a new set of variables called principal components. These principal components are linear combinations of the original variables and are designed to capture the maximum variance in the data.
Principal Component 1 (PC1): This is the first principal component and it captures the largest amount of variance in the data. It is a linear combination of the original variables that explains the most variation in the dataset. In other words, PC1 is the direction in the feature space along which the data varies the most.
Principal Component 2 (PC2): This is the second principal component and it captures the second largest amount of variance in the data, subject to the constraint that it is orthogonal (uncorrelated) to PC1. PC2 is the direction in the feature space that explains the most variation in the dataset after accounting for the variation explained by PC1.
The principal components are ordered by the amount of variance they capture, with PC1 capturing the most variance, followed by PC2, and so on. By examining the principal components, we can gain insights into the underlying structure of the data and identify the most important features that contribute to the variance in the dataset.
Would you like to see the explained variance ratio for these principal components?