Study On Embedding Out-of-samples For Manifold Learning

Recently, with the development of technology and application of various precision electronic equipment, we can obtain the detailed information of data. Although the high-dimensional data can describe the objective things more detail, but in the scientific research, it is not conducive to analysis the internal distribution of data sets. Therefore, the researchers pay much attention to the dimensionality reduction. The traditional dimensionality reduction methods(e.g. principal-component-analysis and linear-discriminant-analysis) can effectively deal with the data sets with linear structure and Gaussian distribution. In the practical application, the most of the original data sets are nonlinear structure, they cannot discover the intrinsic nonlinear information hidden in the high-dimensional data sets. Manifold learning is a kind of nonlinear data dimension reduction method. This approach assumes that the high dimensional samples are on the low-dimensional manifold embedded in a high dimensional space. It can effectively find and keep the intrinsic geometric structure of sample set in high dimensional space. At present, manifold learning algorithms have been widely attention and research of the scientific community.Unfortunately, a main drawback of the manifold learning methods is that they do not provide an explicit mapping function which embeds the high-dimensional data into the low-dimensional subspace. Therefore, in order to obtain the low-dimensional representations of new coming samples, the learning procedure, containing all previous samples and new samples as inputs, has to be repeatedly implemented. It is obvious that this consumes much time for subsequently arrived data. Many existing manifold learning techniques do not contain an out-of-sample extension naturally, so it is necessary to study on the ways of embedding out-of-samples for manifold learning.In this thesis, a locality-constrained sparse representation algorithm is proposed to deal with the out-of-sample embedding problem for manifold learning. In our proposed algorithm, the sparse representation is introduced, so that you can describe out-of-samples with previous samples, so as to achieve the aim of out-of-sample extension. At the same time, the local constraint is employed to preserve locality structured information of the data, so as to obtain a more accurate embedding result. To evaluate the superiority of the proposed method, our approach has been tested on four challenging face data sets including Yale, AR, CMU PIE and Extended Yale B. The experimental results show that not only the proposed method is able to achieve the competitive recognition rate than the existing methods, but also it can save more time than the traditional nonlinear dimensionality reduction method for the out-of-sample problem.