Harvard CS109A | Lecture 10: Principal Component Analysis
Key Word(s): Interaction Terms, High Dimensionality, Principal Components Analysis (PCA)
PCA • By finding the eigenvalues and eigenvectors of the covariance matrix, we find that the eigenvectors with the largest eigenvalues correspond to the dimensions that have the strongest correlation in the dataset. • This is the principal component. • PCA is a useful statistical technique that has found application in:
Learn how to use PCA to reduce dimensionality, visualize data, and learn a subspace that maximizes the projected variance. See examples of PCA applied to faces and digits, and how it relates to autoencoders and matrix factorization.
PCA using SVD algoritm •Start from m by n data matrix X •Recenter: subtract mean from each row of X-X c¬X –X •Call SVD algorithm on X c–ask for k singular vectors •Principal components:k singular vectors with highest singular values (rows of …
Learn the basics of PCA, a technique to find a low dimensional subspace that captures the variance of unlabeled data. See examples, definitions, linear algebra, and uses of PCA for dimensionality reduction and regression.
Learn the linear algebra behind PCA, a method to summarize high-dimensional data. See examples of PCA applications in neuroscience and computer graphics, and how to visualize the contributions of variables to principal components.
Principal Component Analysis (PCA) - ppt download - SlidePlayer
PCA or Karhunen- Loeve transform summarizes the variation in a (possibly) correlated multi-attribute to a set of (a smaller number of) uncorrelated components (principal components).
Learn the theory and applications of PCA, a technique to reduce the dimensionality of data by finding a low-dimensional subspace that maximizes the variance. The notes cover the intuition, formalism, algorithm, and examples of PCA, as well as the singular value decomposition.
Learn the central idea, derivation, properties and applications of PCA, a technique to reduce the dimensionality of a data set with many interrelated variables. See examples, graphs and formulas for PCA using the sample covariance matrix and linear regression.
Learn how to use PCA to extract relevant information from confusing data sets by changing the basis. This tutorial provides an intuitive explanation, a mathematical derivation and examples of PCA and its applications.
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