Research On Some Problems Of Manifold Learning

Manifold learning is a newer research direction of machine learning and data mining in recent years, its essence is to find out the low dimensional manifold hidden in high dimensional space though learning discrete samples, and get the hidden dimensional structure of the high dimensional data to realize non-linear dimension reduction.In this dissertation, some issues about the construction of neighborhood and incremental learning are investigated in manifold learning, including the construction of dynamical neighborhood, the propagation of the "lonely points", the decomposition-composition of separated multi-manifolds with same intrinsic dimensionality and incremental learning of a batch of data. Some following innovative works are achieved in this thesis:1. Proposed the D-ISOMAP algorithm based on the dynamical neighborhood, which reconstructs the topological structure of manifolds accurately. The algorithm not only can solve the "short circuits", but also can deal with the non-convexity datasets very well. The experimental results on the synthetic data as well as the real world patterns demonstrate that the proposed approach can efficiently maintain an accurate low dimensional representation of the manifold data with less distortion, and give higher average classification rate compared to others.2. Proposed the P-ISOMAP algorithm based on propagating the tangent subspaces of the dynamical neighborhoods for "lonely points", which occur in the edges or the sparsely-sampling parts of manifolds because the distribution along the sub-manifold is not uniform or dense enough The experimental results on the synthetic data as well as the real world patterns demonstrate that the proposed approach not only solve the problem of "lonely points" effectively but also improve the ability of the dynamical neighborhood algorithm.3. Proposed the DC-ISOMAP algorithm for the separated multi-manifolds with same intrinsic dimension. The algorithm decomposes the multi-manifolds into several sub-manifolds accurately, transforms and composes the low-dimensional embeddings of the sub-manifolds, and then realizes the nonlinear dimensionality reduction of the separated multi-manifolds with same intrinsic dimension. Experimental results on synthetic data as well as real world images demonstrate the effective of our approaches.4. Proposed DKI-ISOMAP, which can efficiently applied when data are collected sequentially The algorithm updates neighborhood graph, geodesic distances matrix and low-dimensional embeddings more effectively and can be used in practices.The above mentioned contributions would further enrich the researchs of the manifold learning, and provided technology support for the study of large-scale data and data stream on image recognition, Web information retrieval and biomedicine.