Question

we plan to use the pca algorithm on a data set of 2-dimensional feature vectors. then we find out that all the features vectors happen to fall onto the same straight line in the 2-d space. what will be the first principal vector e1 and the second largest eigen value λ2 from the pca algorithm

Answer 1

One of the most often used methods of linear dimension reduction is principal component analysis (PCA). It can be used both on its own and as a starting point for further dimension reduction techniques.

By projecting the data onto a set of orthogonal axes, the projection-based PCA approach changes the data. An unsupervised linear transformation method known as Principal Component Analysis (PCA) is frequently utilized in a variety of domains, most notably for feature extraction and dimensionality reduction. Data compression, made possible by dimensionality reduction, results in less storage space being used. It speeds up computation. It also aids in removing any extraneous features. Since PCA is a variance-maximizing activity, normalization is crucial. our original data is projected in a manner that maximizes variance.

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