Research On Manifold Alignment Algorithms Based On The Discovering Of The Corre Lations

In machine learning and pattern recognition, the acquisition, storage, and the need deal with data is often exist in high-dimensional space, such as high resolution image data, video, audio, etc. In recent years, the manifold learning and algorithm has achieved great success and become one of research hot spots. Although the manifold learning algorithm is widely used, they can only deal with a single manifold. In the real world of many applications, such as, cross- language information retrieval, image and text of matching and pose estimation, etc, needed deal with two or more data sets. In order to solve this problem, scholars have proposed manifold alignment algorithm which can deal with from different data sets mapped to a common low dimensional space, and the local geometrical structure of each data set unchanged, simultaneously match the corresponding instance.In the manifold alignment algorithm, the key step is how to accurately build correction between the manifold samples which determine the effectiveness of the manifold alignment algorithm. Therefore, in order to improve matching accuracy, this paper makes further improvements the manifold alignment algorithm which had been existed. Specifically, the main work includes:1. In the unsupervised algorithm, there is no corresponding point, so discover the correlation between the manifold samples is very important. We propose a basic assumption: for the points sampled from two manifolds which have strong correlations, their neighbors also have stronger correlations. Based on this assumption, this paper propose a new unsupervised manifold alignment algorithm which using the local neighborhood correlation to construct the relationship between the data sample points from different manifolds, and then projecting multiple manifold data to a common low-dimensional space while preserve the discovering of the correlation.2. In the semi-supervised algorithm, require a small set of corresponding pairs for initial alignment, but use global structure or local structure could not accurately discover the correlation between the manifold samples. Using the global geometric distances to construct the relationship between the data points sample from different manifolds, and modifying the relationship by the similarity between the local geometries of the sample points, this paper proposes a new algorithm to discover the correlations between the data points sampled from different manifolds more accurately. Further, this paper proposes a new semi-supervised manifold alignment algorithm, using the known correspondences information and the discovered correlation between the sample points, and projecting multiple manifold data to a common low-dimensional space.3. In the manifold learning algorithm, maximum variance unfolding(MVU) method is classical which use the correlation between neighborhood as the constraint condition. MVU method learns the data from similarities, preserving both local distances and angles between the pairs of all neighbors of each point in the data set. But MVU method can only deal with a single manifold, so we consider linking the two or more manifold, then use maximum variance unfolding, through semi-definite programming(SDP) learning a gram matrix which obtained a low dimensional manifold, finally match the corresponding examples.Finally, the effectiveness of the three proposed algorithm is validated by the experiments on real-world data sets.