Research On The Methods And Applications Of Multiview Metric And Regression Learning

Distance metric and regression learning play an important role in machine learning,pattern recognition and computer vision. Many tasks such as image classification, clus-tering, content-based image annotation and retrieval depend critically on the choice of anappropriate distance metric. Regression learning provide an effective tool for distancemetric learning and image processing problems. So, the distance metric and regressionlearning is important in theory and application. However, most of the traditional algo-rithms in metric and regression learning only focus on the problem on the single dataset.With the rapid development of internet and the rising popularity of digital cameras, dataoften have different observations or descriptions, which present the multimodal property.In order to analysis and process multimodal data effectively, this paper will focus on mul-tiview metric and regression learning problems. Nowadays the work on multiview metricand regression learning has just started, all existing work are global methods. Recently,researchers observe that, compared with global methods, the estimation error rate is alsolocalized by localizing the prediction function, and thus it appears to be more robust andflexible. In addition, learning in local manner can sufficiently boost the capacity powers.In this thesis, we study multiview metric and regression learning with local and globalcombination, and explore their applications. The contents of the thesis can be dividedinto four sections that are detailed as follows:1. We propose a two stage multiview metric learning with global consistency andlocal smoothness. To study the shared latent space of the multi-view observations, theconnections between data from different views are implicity established. The learningprocess is decomposed into a two-stage: In the first stage, based on the spectral graphtheory, our method get the common low-dimensional embeddings for all labeled corre-spondence pairs; In the second stage, based on regularized local linear regression, ourmethod learn the relationships between input space of each observation and the shared la-tent space for unlabeled and test data. Furthermore, graph-Laplacian regularization termis incorporated to keep the learned metric vary smoothly. The proposed method formu-lates global and local metric learning as two convex optimization problems, which couldbe efficiently solved with closed-form solutions. Experimental results with application to pose and expression alignment demonstrate the effectiveness of the proposed method.2. We propose a unified framework for multiview metric learning via instance-specific canonical correlation analysis. Based on canonical correlation analysis (CCA),we propose instance-specific canonical correlation analysis, which achieves locality andnonlinearity at the same time. Unlike the work above, the proposed method does not needa two stage learning process, and thus establish a unified framework. First, we propose aleast squares solution for CCA which will set the stage for the proposed method. Second,based on the framework of least squares regression, CCA is extended to approximates thenonlinear data by computing the instance specific projections along the smooth curve ofthe manifold. Furthermore, the proposed method can be extended to semi-supervised set-ting by exploiting the unlabeled data to further improve the performance. The optimiza-tion problem is proved to be jointly convex and could be solved efficiently by alternatingoptimization. And the globally optimal solutions could be achieved with theoretical guar-antee.3. To confront with the big data problem, we propose parametric local multiviewhamming distance metric learning First, discrete local multimodal hashing functions aredefined to project data from input features to binary codes. And the hashing distancein the discrete space is computed. To balance locality and computational efficiency, wepropose to approximate the local hashing function for each point as a linear weightedcombination of a small set of projection basis associated with a set of anchor points. Andthe error bound for approximated local hashing projection is verified. Then the objectivefunction with local and global combination is established, and conjugate gradient methodand sequential learning process are exploited for efficient optimization. Experiments re-sults on cross-media retrieval task demonstrate local hash functions can better model thecomplex structure of large-scale datasets, and achieve higher empirical query accuracythan global-based ones.4.Besides the study on multiple datasets, we further discuss multiview models onsingle dataset with local and global combination. We propose a unified framework forprogressive image denoising via multiview kernel regression. We first construct a multi-scale representation of the target image, then progressively recover the degraded imagein the scale space from coarse to fine. On one hand, within each scale, a graph Laplacianregularization model represented by the implicit kernel is learned which simultaneously minimizes the least square error on the measured samples and preserves the global mani-fold structure of the image data space. On the other hand, between two successive scales,the proposed model is learned in a projected high dimensional feature space through theexplicit kernel mapping to describe the inter-scale correlation, in which the local structureregularity is learned and propagated from coarser to finer scales. Moreover, in our methodthe objective functions are formulated in the same form for intra-scale and inter-scale pro-cessing, but with different solutions obtained in different feature spaces. Therefore, theconsistency of local and global correlation in image can be better exploited and com-bined. Experiment results demonstrate the proposed method achieves comparable andeven better results for image denoising problems.