Sparse principal component analysis (PCA) imposes extra constraints or penalty terms to the standard PCA to achieve sparsity. In this paper, we first introduce an efficient algorithm for finding a single sparse principal component (PC) with a specified cardinality. Experiments on synthetic data, randomly generated data and real-world datasets show that our algorithm is very fast, especially on ...

Principal Component Analysis (PCA) is the most widely used unsupervised dimensionality reduction approach. In recent research, several robust PCA algorithms were presented to enhance the robustness of PCA model. However, the existing robust PCA methods incorrectly center the data using the `2-norm distance to calculate the mean, which actually is not the optimal mean due to the `1-norm used in ...

multivariate statistical techniques such as cluster analysis, multidimensional scaling and principal component analysis were applied to evaluate the temporal and spatial variations in water quality data set generated for two years (2008-2010) from six monitoring stations of veli-akkulam lake and compared with a regional reference lake vellayani of south india. seasonal variations of 14 differen...

Principal component analysis (PCA) is an unsupervised method for learning low-dimensional features with orthogonal projections. Multilinear PCA methods extend PCA to deal with multidimensional data (tensors) directly via tensor-to-tensor projection or tensor-to-vector projection (TVP). However, under the TVP setting, it is difficult to develop an effective multilinear PCA method with the orthog...

Common factor analysis (CFA) and principal component analysis (PCA) are widely used multivariate techniques. Using simulations, we compared CFA with PCA loadings for distortions of a perfect cluster configuration. Results showed that nonzero PCA loadings were higher and more stable than nonzero CFA loadings. Compared to CFA loadings, PCA loadings correlated weakly with the true factor loadings ...

Principal component analysis (PCA) is possibly one of the most widely used statistical tools to recover a low rank structure of the data. In the high-dimensional settings, the leading eigenvector of the sample covariance can be nearly orthogonal to the true eigenvector. A sparse structure is then commonly assumed along with a low rank structure. Recently, minimax estimation rates of sparse PCA ...

The method of sparse principal component analysis (S-PCA) proposed by Zou, Hastie, and Tibshirani (2006) is an attractive approach to obtain sparse loadings in principal component analysis (PCA). S-PCA was motivated by reformulating PCA as a least-squares problem so that a lasso penalty on the loading coefficients can be applied. In this article, we propose new estimates to improve S-PCA in the...