Sparse PCA (sparse principal component analysis)

Sparse PCA (sparse principal component analysis) is a specialised technique used in statistical analysis and, in particular, in the analysis of multivariate data sets.

Sparse PCA (sparse principal component analysis) is a specialised technique used in statistical analysis and, in particular, in the analysis of multivariate data sets.

Ordinary principal component analysis (PCA) uses a vector space transform used to reduce multidimensional data sets to lower dimensions for analysis. It finds linear combinations of variables (called "principal components") that correspond to directions of maximal variance in the data. The number of new variables created by these linear combinations is usually much lower than the number of variables in the original dataset. Sparse PCA finds sets of sparse vectors for use as weights in the linear combinations while still explaining most of the variance present in the data.

Several approaches have been proposed, including a regression framework,[1] a convex relaxation/semidefinite programming framework,[2] a generalized power method framework[3] an alternating maximization framework[4] forward/backward greedy search and exact methods using branch-and-bound techniques,[5] Bayesian formulation framework.[6]

References[edit]

  1. Jump up^ H. Zou and T. Hastie and R. Tibshirani (2006). "Sparse principal component analysis"Jcgs 2006 15(2): 262-286.
  2. Jump up^ Alexandre d’Aspremont, Laurent El Ghaoui, Michael I. Jordan, Gert R. G. Lanckriet (2004). "A Direct Formulation for Sparse PCA Using Semidefinite Programming"Advances in Neural Information Processing Systems (NIPS), MIT Press.
  3. Jump up^ Michel Journee, Yurii Nesterov, Peter Richtarik, Rodolphe Sepulchre (2008). "Generalized Power Method for Sparse Principal Component Analysis"CORE Discussion Paper 2008/70, Journal of Machine Learning Research 11 (2010) 517-553 0811: 4724.arXiv:0811.4724.
  4. Jump up^ Peter Richtarik, Martin Takac and S. Damla Ahipasaoglu (2012). Alternating Maximization: Unifying Framework for 8 Sparse PCA Formulations and Efficient Parallel CodesarXiv:1212.4137.
  5. Jump up^ Baback Moghaddam, Yair Weiss, Shai Avidan (2005). "Spectral Bounds for Sparse PCA: Exact and Greedy Algorithms"Advances in Neural Information Processing Systems (NIPS), MIT Press.
  6. Jump up^ Yue Guan, Jennifer Dy (2009). "Sparse Probabilistic Principal Component Analysis"Journal of Machine Learning Research Workshop and Conference Proceedings. 5: AISTATS 2009.
RELATED ARTICLESExplain
Machine Learning Methods & Algorithms
Unsupervised learning
Sparse PCA (sparse principal component analysis)
Association rule learning
Data clustering
Expectation–maximization algorithm
FastICA
Generative topographic map
Hierarchical clustering
IBSEAD - distributed autonomous entity systems based Interaction
Information bottleneck method
Partitional clustering
Radial basis function network
Self-organizing map
Stochastic gradient descent
Vector quantization (VQ)
Graph of this discussion
Enter the title of your article


Enter a short (max 500 characters) summation of your article
Enter the main body of your article
Lock
+Comments (0)
+Citations (0)
+About
Enter comment

Select article text to quote
welcome text

First name   Last name 

Email

Skip