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Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing. The data is linearly transformed onto a new coordinate system such that the directions (principal components) capturing the largest variation in the data can be easily identified.
In ()-(), L1-norm ‖ ‖ returns the sum of the absolute entries of its argument and L2-norm ‖ ‖ returns the sum of the squared entries of its argument.If one substitutes ‖ ‖ in by the Frobenius/L2-norm ‖ ‖, then the problem becomes standard PCA and it is solved by the matrix that contains the dominant singular vectors of (i.e., the singular vectors that correspond to the highest ...
Output after kernel PCA, with a Gaussian kernel. Note in particular that the first principal component is enough to distinguish the three different groups, which is impossible using only linear PCA, because linear PCA operates only in the given (in this case two-dimensional) space, in which these concentric point clouds are not linearly separable.
A company's earnings before interest, taxes, depreciation, and amortization (commonly abbreviated EBITDA, [1] pronounced / ˈ iː b ɪ t d ɑː,-b ə-, ˈ ɛ-/ [2]) is a measure of a company's profitability of the operating business only, thus before any effects of indebtedness, state-mandated payments, and costs required to maintain its asset base.
Principal component analysis (PCA) is a widely used method for factor extraction, which is the first phase of EFA. [4] Factor weights are computed to extract the maximum possible variance, with successive factoring continuing until there is no further meaningful variance left. [4] The factor model must then be rotated for analysis. [4]
In statistics, principal component regression (PCR) is a regression analysis technique that is based on principal component analysis (PCA). PCR is a form of reduced rank regression . [ 1 ] More specifically, PCR is used for estimating the unknown regression coefficients in a standard linear regression model .
Multilinear principal component analysis (MPCA) is a multilinear extension of principal component analysis (PCA) that is used to analyze M-way arrays, also informally referred to as "data tensors". M-way arrays may be modeled by linear tensor models, such as CANDECOMP/Parafac, or by multilinear tensor models, such as multilinear principal ...
Whitening and dimension reduction can be achieved with principal component analysis or singular value decomposition. Whitening ensures that all dimensions are treated equally a priori before the algorithm is run. Well-known algorithms for ICA include infomax, FastICA, JADE, and kernel-independent component analysis, among others. In general ...