A new approach to numerical algorithms

In this paper we developed a new Lanczos algorithm on the Grassmann manifold. This work comes in the wake of the article by A. Edelman, T. A. Arias and S. T. Smith, “The geometry of algorithms with orthogonality constraints

Generalized Rank Pooling for Activity Recognition

Most popular deep models for action recognition split video sequences into short sub-sequences consisting of a few frames; frame-based features are then pooled for recognizing the activity. Usually, this pooling step discards the temporal order of the frames, which could otherwise be used for better recognition. Towards this end, we propose a novel pooling method, generalized rank pooling (GRP), that takes as input, features from the intermediate layers of a CNN that is trained on tiny sub-sequences, and produces as output the parameters of a subspace which (i) provides a low-rank approximation to the features and (ii) preserves their temporal order. We propose to use these parameters as a compact representation for the video sequence, which is then used in a classification setup. We formulate an objective for computing this subspace as a Riemannian optimization problem on the Grassmann manifold, and propose an efficient conjugate gradient scheme for solving it. Experiments on several activity recognition datasets show that our scheme leads to state-of-the-art performance.Comment: Accepted at IEEE International Conference on Computer Vision and Pattern Recognition (CVPR), 201

Comment: Fisher Lecture: Dimension Reduction in Regression

Comment: Fisher Lecture: Dimension Reduction in Regression [arXiv:0708.3774]Comment: Published at http://dx.doi.org/10.1214/088342307000000050 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

A bound on Grassmannian codes

We give a new asymptotic upper bound on the size of a code in the Grassmannian space. The bound is better than the upper bounds known previously in the entire range of distances except very large values.Comment: 5 pages, submitte