融合协作表达和重构判别分析的数据降维算法

数据降维是处理高维数据的有效手段。子空间学 习算法由于其计算量小,性能较为出 色而广泛应用于模式识别等领域,传统的子空间学习算法均可归纳为图嵌入算法框架中。稀 疏表达是近年来的一个研究热点,并广泛应用于信号处理和模式识别等领域,但计算复杂度 较高。在稀疏表达的基础上,研究者提出了协作表达。相比稀疏表达,协作表达算法由于其 有一个闭式解,因而计算量较小且判别性能较好,可以看成是数据表达的一种有效方法。本 文从协作表达的角度来解释图嵌入算法,将图嵌入算法看作是一类回归模型。通过最小化类 内重构误差散度的同时最大化类间重构误差散度,提出了一种新的图嵌入算法,即重构判别 分析,并将它应用于该回归模型中,然后将问题归结为一广义的特征值问题,算法在某种程 度上能有效避免子空间学习过程中矩阵的奇异性问题。在人脸识别上的实验验证了算法的正 确性和有效性。

Dimensionality reduction via collaborative constrained reconstructive discrimina nt analysis

Dimensionality reduction is an effective method for treating high dime nsional data. Subspace learning is widely used in pattern recognition due to its low complexit y and desirable performance,and most of the subspace learning algorithms can be plugged into the graph embedding framework.Sparse representation gains much attention in recent years, and has wide applications in signal processing and pattern recognition,but it is time consum ing.Based on sparse representation,collaborative representation is proposed.Compared with spa rse representation,collaborative representation has a tractable closed-form solution and better discriminative power,so it i s widely used in data representation and visual classification.In this paper,the graph embedding is formulated as a manner of collaborative representation.By mini mizing the intra-class reconstructive error scatter and maximizing the inter-class recons tructive error scatter, a new graph embedding algorithm called reconstructive discriminant analysis is p roposed,and is applied in this regression model,then the solution is reduced to a generalized eigen-value problem,which to some extent can avoid the singularity problem in subspace lear ning algorithms. Various experiments on face recognition demonstrate the correctiveness and effec tiveness of the proposed algorithm.