CPPCA—Compressive-Projection Principal Component Analysis James E. Fowler About CPPCA Principal component analysis (PCA) is often central to dimensionality reduction and compression in many applications, yet its data-dependent nature as a transform computed via expensive eigendecomposition often hinders its use in severely resource-constrained settings such as satellite-borne sensors. Compressive-projection principal component analysis (CPPCA) is a process that effectively shifts the computational burden of PCA from the resource-constrained encoder to a presumably more capable base-station decoder. CPPCA is driven by projections at the sensor onto lower-dimensional subspaces chosen at random, while the CPPCA decoder, given only these random projections, recovers not only the coefficients associated with the PCA transform, but also an approximation to the PCA transform basis itself. The reconstruction process at the CPPCA decoder consists of a novel eigenvector reconstruction based on a convex-set optimization driven by Ritz vectors within the projected subspaces. Publications J. E. Fowler, “Compressive-Projection Principal Component Analysis and the First Eigenvector,” in Proceedings of the IEEE Data Compression Conference, J. A. Storer and M. W. Marcellin, Eds., Snowbird, UT, March 2009, pp. 223-232. J. E. Fowler, “Compressive-Projection Principal Component Analysis for the Compression of Hyperspectral Signatures,” in Proceedings of the IEEE Data Compression Conference, J. A. Storer and M. W. Marcellin, Eds., Snowbird, UT, March 2008, pp. 83-92. J. E. Fowler, “Compressive-Projection Principal Component Analysis,” IEEE Transactions on Image Processing, vol. 18, pp. 2230-2242, October 2009. J. E. Fowler, Q. Du, W. Zhu, and N. H. Younan, “Classification Performance of Random-Projection-Based Dimensionality Reduction of Hyperspectral Imagery,” in Proceedings of the International Geoscience and Remote Sensing Symposium, Capetown, South Africa, July 2009, vol. 5, pp. 76-79. W. Li and J. E. Fowler, “Decoder-Side Dimensionality Determination for Compressive-Projection Principal Component Analysis of Hyperspectral Data,” in Proceedings of the International Conference on Image Processing, Brussels, Belgium, September 2011, pp. 329-332. J. E. Fowler and Q. Du, “Reconstructions from Compressive Random Projections of Hyperspectral Imagery,” in Optical Remote Sensing: Advances in Signal Processing and Exploitation Techniques, S. Prasad, L. M. Bruce, and J. Chanussot, Eds. Springer, 2011, ch. 3, pp. 31-48. J. E. Fowler and Q. Du, “Anomaly Detection and Reconstruction from Random Projections,” IEEE Transactions on Image Processing, vol. 21, no. 1, pp. 184-195, January 2012. Software cppca-3.3-1.tar.gz – Matlab source code for the original CPPCA algorithm (relies on the Bayesian Compressive Sensing package and l1-magic) cppca-pr-1.0-1.tar.gz – Matlab source code for the CPPCA with Partitioned Residual (CPPCA-PR) algorithm from the paper “Anomaly Detection and Reconstruction from Random Projections” (requires CPPCA) Support This material is based upon work supported by the National Science Foundation under Grant No. 0915307. Any opinions, findings and conclusions, or recomendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation (NSF). Last update: 12-dec-2012