On Identity Tests for High Dimensional Data Using RMT

In this work, we redefined two important statistics, the CLRT test (Bai et.al., Ann. Stat. 37 (2009) 3822-3840) and the LW test (Ledoit and Wolf, Ann. Stat. 30 (2002) 1081-1102) on identity tests for high dimensional data using random matrix theories. Compared with existing CLRT and LW tests, the new tests can accommodate data which has unknown means and non-Gaussian distributions. Simulations demonstrate that the new tests have good properties in terms of size and power. What is more, even for Gaussian data, our new tests perform favorably in comparison to existing tests. Finally, we find the CLRT is more sensitive to eigenvalues less than 1 while the LW test has more advantages in relation to detecting eigenvalues larger than 1.Comment: 16 pages, 2 figures, 3 tables, To be published in the Journal of Multivariate Analysi

Divide and Fuse: A Re-ranking Approach for Person Re-identification

As re-ranking is a necessary procedure to boost person re-identification (re-ID) performance on large-scale datasets, the diversity of feature becomes crucial to person reID for its importance both on designing pedestrian descriptions and re-ranking based on feature fusion. However, in many circumstances, only one type of pedestrian feature is available. In this paper, we propose a "Divide and use" re-ranking framework for person re-ID. It exploits the diversity from different parts of a high-dimensional feature vector for fusion-based re-ranking, while no other features are accessible. Specifically, given an image, the extracted feature is divided into sub-features. Then the contextual information of each sub-feature is iteratively encoded into a new feature. Finally, the new features from the same image are fused into one vector for re-ranking. Experimental results on two person re-ID benchmarks demonstrate the effectiveness of the proposed framework. Especially, our method outperforms the state-of-the-art on the Market-1501 dataset.Comment: Accepted by BMVC201

The Grone-Merris Conjecture

In spectral graph theory, Grone and Merris conjecture that the spectrum of the Laplacian matrix of a finite graph is majorized by the conjugate degree sequence of this graph. We give a complete proof for this conjecture.Comment: The paper is accepted by Transactions of the American Mathematical Societ

Left-symmetric Algebras From Linear Functions

In this paper, some left-symmetric algebras are constructed from linear functions. They include a kind of simple left-symmetric algebras and some examples appearing in mathematical physics. Their complete classification is also given, which shows that they can be regarded as generalization of certain 2-dimensional left-symmetric algebras.Comment: 16 pages, accepted for publication in Journal of Algebr