Robust Principal Component Analysis on Graphs

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA solves the first issue with a sparse penalty term. The second issue can be handled with the matrix factorization model, which is however non-convex. Besides, PCA based clustering can also be enhanced by using a graph of data similarity. In this article, we introduce a new model called "Robust PCA on Graphs" which incorporates spectral graph regularization into the Robust PCA framework. Our proposed model benefits from 1) the robustness of principal components to occlusions and missing values, 2) enhanced low-rank recovery, 3) improved clustering property due to the graph smoothness assumption on the low-rank matrix, and 4) convexity of the resulting optimization problem. Extensive experiments on 8 benchmark, 3 video and 2 artificial datasets with corruptions clearly reveal that our model outperforms 10 other state-of-the-art models in its clustering and low-rank recovery tasks

Hemispherical confocal imaging using turtleback reflector

We propose a new imaging method called hemispherical confocal imaging to clearly visualize a particular depth in a 3-D scene. The key optical component is a turtleback reflector which is a specially designed polyhedral mirror. By combining the turtleback reflector with a coaxial pair of a camera and a projector, many virtual cameras and projectors are produced on a hemisphere with uniform density to synthesize a hemispherical aperture. In such an optical device, high frequency illumination can be focused at a particular depth in the scene to visualize only the depth with descattering. Then, the observed views are factorized into masking, attenuation, and texture terms to enhance visualization when obstacles are present. Experiments using a prototype system show that only the particular depth is effectively illuminated and hazes by scattering and attenuation can be recovered even when obstacles exist.Microsoft ResearchJapan Society for the Promotion of Science (Grants-in-Aid For Scientific Research 21680017)Japan Society for the Promotion of Science (Grants-in-Aid For Scientific Research 21650038

Precise Measurements of Direct CP Violation, CPT Symmetry, and Other Parameters in the Neutral Kaon System

We present precise tests of CP and CPT symmetry based on the full dataset of K to pipi decays collected by the KTeV experiment at Fermi National Accelerator Laboratory during 1996, 1997, and 1999. This dataset contains 16 million K to 2pi0 and 69 million K to pi+pi- decays. We measure the direct CP violation parameter Re(epsilon'/epsilon) = (19.2 pm 2.1)x10-4. We find the KL-KS mass difference Deltam = (5270 pm 12)x10^6 hbar/s and the KS lifetime tauS = (89.62 pm 0.05)x10-12 s. We also measure several parameters that test CPT invariance. We find the difference between the phase of the indirect CP violation parameter, epsilon, and the superweak phase, phi_epsilon - phi_SW = (0.40 pm 0.56) degrees. We measure the difference of the relative phases between the CP violating and CP conserving decay amplitudes for K to pi+pi- (phi+-) and for K to 2pi0 (phi00), Delta phi = (0.30 pm 0.35) degrees. From these phase measurements, we place a limit on the mass difference between K0 and K0bar, DeltaM < 4.8 x 10-19 GeV/c^2 at 95% C.L. These results are consistent with those of other experiments, our own earlier measurements, and CPT symmetry.Comment: 28 pages, 30 figures; removed extra figur