Sparse approximation

About: Sparse approximation is a research topic. Over the lifetime, 18037 publications have been published within this topic receiving 497739 citations. The topic is also known as: Sparse approximation.

SLIM: Sparse Linear Methods for Top-N Recommender Systems

Abstract: This paper focuses on developing effective and efficient algorithms for top-N recommender systems. A novel Sparse Linear Method (SLIM) is proposed, which generates top-N recommendations by aggregating from user purchase/rating profiles. A sparse aggregation coefficient matrix W is learned from SLIM by solving an `1-norm and `2-norm regularized optimization problem. W is demonstrated to produce high quality recommendations and its sparsity allows SLIM to generate recommendations very fast. A comprehensive set of experiments is conducted by comparing the SLIM method and other state-of-the-art top-N recommendation methods. The experiments show that SLIM achieves significant improvements both in run time performance and recommendation quality over the best existing methods.

Blessing of Dimensionality: High-Dimensional Feature and Its Efficient Compression for Face Verification

Abstract: Making a high-dimensional (e.g., 100K-dim) feature for face recognition seems not a good idea because it will bring difficulties on consequent training, computation, and storage. This prevents further exploration of the use of a high dimensional feature. In this paper, we study the performance of a high dimensional feature. We first empirically show that high dimensionality is critical to high performance. A 100K-dim feature, based on a single-type Local Binary Pattern (LBP) descriptor, can achieve significant improvements over both its low-dimensional version and the state-of-the-art. We also make the high-dimensional feature practical. With our proposed sparse projection method, named rotated sparse regression, both computation and model storage can be reduced by over 100 times without sacrificing accuracy quality.

Toward a Practical Face Recognition System: Robust Alignment and Illumination by Sparse Representation

Abstract: Many classic and contemporary face recognition algorithms work well on public data sets, but degrade sharply when they are used in a real recognition system. This is mostly due to the difficulty of simultaneously handling variations in illumination, image misalignment, and occlusion in the test image. We consider a scenario where the training images are well controlled and test images are only loosely controlled. We propose a conceptually simple face recognition system that achieves a high degree of robustness and stability to illumination variation, image misalignment, and partial occlusion. The system uses tools from sparse representation to align a test face image to a set of frontal training images. The region of attraction of our alignment algorithm is computed empirically for public face data sets such as Multi-PIE. We demonstrate how to capture a set of training images with enough illumination variation that they span test images taken under uncontrolled illumination. In order to evaluate how our algorithms work under practical testing conditions, we have implemented a complete face recognition system, including a projector-based training acquisition system. Our system can efficiently and effectively recognize faces under a variety of realistic conditions, using only frontal images under the proposed illuminations as training.

Comparing Measures of Sparsity

Abstract: Sparsity of representations of signals has been shown to be a key concept of fundamental importance in fields such as blind source separation, compression, sampling and signal analysis. The aim of this paper is to compare several commonly-used sparsity measures based on intuitive attributes. Intuitively, a sparse representation is one in which a small number of coefficients contain a large proportion of the energy. In this paper, six properties are discussed: (Robin Hood, Scaling, Rising Tide, Cloning, Bill Gates, and Babies), each of which a sparsity measure should have. The main contributions of this paper are the proofs and the associated summary table which classify commonly-used sparsity measures based on whether or not they satisfy these six propositions. Only two of these measures satisfy all six: the pq-mean with p les 1, q > 1 and the Gini index.

Appearance-only SLAM at large scale with FAB-MAP 2.0

Abstract: We describe a new formulation of appearance-only SLAM suitable for very large scale place recognition. The system navigates in the space of appearance, assigning each new observation to either a new or a previously visited location, without reference to metric position. The system is demonstrated performing reliable online appearance mapping and loop-closure detection over a 1000 km trajectory, with mean filter update times of 14 ms. The scalability of the system is achieved by defining a sparse approximation to the FAB-MAP model suitable for implementation using an inverted index. Our formulation of the problem is fully probabilistic and naturally incorporates robustness against perceptual aliasing. We also demonstrate that the approach substantially outperforms the standard term-frequency inverse-document-frequency (tf-idf) ranking measure. The 1000 km data set comprising almost a terabyte of omni-directional and stereo imagery is available for use, and we hope that it will serve as a benchmark for future systems.