Sparse principal component analysis (SPCA or sparse PCA) is a technique used in statistical analysis and, in particular, in the analysis of multivariate data sets. It extends the classic method of principal component analysis (PCA) for the reduction of dimensionality of data by introducing sparsity structures to the input variables.
A particular disadvantage of ordinary PCA is that the principal components are usually linear combinations of all input variables. SPCA overcomes this disadvantage by finding components that are linear combinations of just a few input variables (SPCs). This means that some of the coefficients of the linear combinations defining the SPCs, called loadings,[note 1] are equal to zero. The number of nonzero loadings is called the cardinality of the SPC.
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Sparse principal component analysis (SPCA or sparsePCA) is a technique used in statistical analysis and, in particular, in the analysis of multivariate...
Python library for machine learning which contains PCA, Probabilistic PCA, Kernel PCA, SparsePCA and other techniques in the decomposition module. Scilab...
assumptions are used to analyze each signal. Sparse approximation SparsePCA K-SVD Matrix factorization Neural sparse coding Needell, D.; Tropp, J.A. (2009)...
Robust PCA, which aims to recover a low-rank matrix L0 from highly corrupted measurements M = L0 +S0. This decomposition in low-rank and sparse matrices...
representations to assume useful properties. Examples are regularized autoencoders (Sparse, Denoising and Contractive), which are effective in learning representations...
dissertation, advised by Michael I. Jordan, included work on sparse principal components analysis (PCA) for gene expression modeling, low-rank matrix completion...
high-dimensional spaces can be undesirable for many reasons; raw data are often sparse as a consequence of the curse of dimensionality, and analyzing the data...
S2CID 13998761. Zou, Hui; Hastie, Trevor; Tibshirani, Robert (2006). "Sparse Principal Component Analysis". Journal of Computational and Graphical Statistics...
analysis (PCA), but the two are not identical. There has been significant controversy in the field over differences between the two techniques. PCA can be...
Principal component analysis (PCA) is often used for dimension reduction. Given an unlabeled set of n input data vectors, PCA generates p (which is much...
analysis (PCA) and FPCA. The two methods are both used for dimensionality reduction. In implementations, FPCA uses a PCA step. However, PCA and FPCA differ...
Following the connection between the classical scaling and PCA, metric MDS can be interpreted as kernel PCA. In a similar manner, the geodesic distance matrix...
inferring over the full model is too costly. They are typically sparsely-gated, with sparsity 1 or 2. In Transformer models, the MoE layers are often used...
Perhaps the most widely used algorithm for dimensional reduction is kernel PCA. PCA begins by computing the covariance matrix of the m × n {\displaystyle m\times...
methods of dimensionality reduction is principal component analysis (PCA). PCA involves changing higher-dimensional data (e.g., 3D) to a smaller space...
areas. For each area, it learns a separate Principal Component Analysis (PCA) basis and reconstructs the area separately. However, the reconstructed face...
orientation alignment, whereas SIFT descriptors are usually computed at sparse, scale-invariant key image points and are rotated to align orientation....
the volume of the space increases so fast that the available data become sparse. In order to obtain a reliable result, the amount of data needed often grows...
Principal Component Analysis (PCA) on the matrix A, except that PCA subtracts off the means. PCA loses the sparseness of the A matrix, which can make...
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