Selecting a Small Set of Optimal Gestures from an Extensive Lexicon

Finding the best set of gestures to use for a given computer recognition problem is an essential part of optimizing the recognition performance while being mindful to those who may articulate the gestures. An objective function, called the ellipsoidal distance ratio metric (EDRM), for determining the best gestures from a larger lexicon library is presented, along with a numerical method for incorporating subjective preferences. In particular, we demonstrate an efficient algorithm that chooses the best $n$ gestures from a lexicon of $m$ gestures where typically $n \ll m$ using a weighting of both subjective and objective measures.Comment: 27 pages, 7 figure

Randomized Robust Subspace Recovery for High Dimensional Data Matrices

This paper explores and analyzes two randomized designs for robust Principal Component Analysis (PCA) employing low-dimensional data sketching. In one design, a data sketch is constructed using random column sampling followed by low dimensional embedding, while in the other, sketching is based on random column and row sampling. Both designs are shown to bring about substantial savings in complexity and memory requirements for robust subspace learning over conventional approaches that use the full scale data. A characterization of the sample and computational complexity of both designs is derived in the context of two distinct outlier models, namely, sparse and independent outlier models. The proposed randomized approach can provably recover the correct subspace with computational and sample complexity that are almost independent of the size of the data. The results of the mathematical analysis are confirmed through numerical simulations using both synthetic and real data