Principal component analysis

Q: How deeply does Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI cover principal component analysis?

Defines weighted linear components and their visualization role, but stops short of algorithmic or mathematical derivation.

As explained in Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI

A linear dimensionality-reduction method that represents data using orthogonal components formed as weighted combinations of the original features.

Principal component analysis (PCA) reduces a numeric dataset to a few summary features called components. Each component is a weighted combination of the original features, making complex tabular data easier to visualize. section 2.4.3

Use PCA as an exploratory step: plot the reduced dimensions to look for patterns, isolated clusters, or possible anomalies before modeling. Because PCA is linear, it may miss nonlinear structure; compare it with SVD, t-SNE, or UMAP when appropriate. section 2.4.3

How Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI covers it

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Related concepts

dimensionality reductionkind of · Dimensionality reduction is the transformation of data into a representation with fewer dimensions while retaining selected information, structure, or relationships.
covariance matrixuses · A covariance matrix is a square matrix whose diagonal entries are variances and whose off-diagonal entries are pairwise covariances among variables.
varianceuses · Variance is the expected squared deviation of a random variable from its mean, measuring the spread of its distribution.
principal componentproduces · A principal component is an orthogonal direction in transformed data space that captures a ranked amount of variation in the data.
singular value decompositionuses · Singular value decomposition is a matrix factorization that expresses a matrix as the product of orthogonal or unitary matrices and a diagonal matrix of nonnegative singular values.

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