![]() ![]() The size of each eigenvector is encoded in the corresponding eigenvalue and indicates how much the data vary along the principal component. ![]() In fact, the result of running PCA on the set of points in the diagram consist of 2 vectors called eigenvectors which are the principal components of the data set. Hence, PCA allows us to find the direction along which our data varies the most. This means that if you know the position of a point along the blue line you have more information about the point than if you only knew where it was on Feature 1 axis or Feature 2 axis. Moreover, you could also see that the points vary the most along the blue line, more than they vary along the Feature 1 or Feature 2 axes. ![]() For example, in the above case it is possible to approximate the set of points to a single line and therefore, reduce the dimensionality of the given points from 2D to 1D. Dimensionality Reduction is the process of reducing the number of the dimensions of the given dataset. A key point of PCA is the Dimensionality Reduction. However, if you have a better look you will see that there is a linear pattern (indicated by the blue line) which is hard to dismiss. Here some could argue that the points are set in a random order. Each dimension corresponds to a feature you are interested in. Consider that you have a set of 2D points as it is shown in the figure above. ![]()
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