Manifold Learning With Application And Research To Image Set Classification

With the development of science and technology,the image data are becoming not only larger in quantity but also higher in dimensionality and complexity than before.Meanwhile,these data are basically non-linear,and traditional learning algorithms cannot measure their similarities effectively.Nevertheless,the Riemannian manifold learning is much more helpful in extracting the non-linear structural information.Moreover,the traditional classification methods are based on single-shot images,while image set based classification problems attracts increasing interest,which mainly dues to more flexibility and fault-tolerance can be provided by image set.As a result,this dissertation mainly focuses on Riemannian manifold learning and its application to image set classification.Based on several traditional manifold learning algorithms for image set classification,we make studies to manifold kernel methods,dimensionality reduction methods,and multi-model metric learning methods,and propose improved algorithms.The major contributions are summarized as follows:(1)We give a detailed introduction about the basic idea and impelementation process of some classical manifold learning algorithms based on image set classification in theory.Then,we intuitively analyze and compare their differences in terms of classification ability and computation time by making experiments on some benchmark datasets.Meanwhile,we also introduce the theoretically definitions of some classical Reimannian metrics.(2)Recently,the research of neurology in the biological field has shown that the perception theory of biological neural is coincide with Riemannian manifold,and meanwhile the research has shown that Log-Gabor filter is suitable for nonlinear human eye logarithmic characteristic.Since the combination of Log-Gabor wavelet and Riemannian manifold is consistent with the process of human visual perception,a Riemannian manifold image set classification algorithm based on Log-gabor wavelet features has been proposed.The Log-Gabor filter is applied to solve the problem casued by second-order statistics,which is incapable of extracting sufficient feature information.Besides,the multi-scale and multi-direction wavelet features are useful to eliminate the redundant information of the original images and improve the discriminatory ability of the learned new feature representations.This algorithm is evaluated on some benchmark datasets,the better experimental results show its effectiveness.(3)The core idea of manifold dimensionality reduction algorithms is performing a geometry-aware dimensionality reduction from the original manifold to a lower-dimensional,more discriminative one,which leads to better results on some benchmark datasets.PML algorithm,which is based on Projection Metric and using RCG algorithm to optimize its objective function.However,its performance on some complicated datasets(e.g.YTC)is poor,and RCG is time consuming.Based on these shortcomings,the manifold dimensionality reduction algorithm based on tangent space discriminant learning is presented.Firstly,the elements which reside on Grassmann manifold are transformed into SPD manifold by adding a small perturbation to the projection matrices,then the LEM is utilized to map them into a tangent space.Finally,a fast iterative optimization algorithm based on Eigen-Decomposition is proposed to solve the objective function.The experiment results on some benchmark datasets identify the proposed algorithm is superior to PML and other baseline methods.(4)The traditional manifold learning methods usually model the given image set with a single model,which is not suitable for some complicated classification tasks.As a result,a method which combines multi-model modeling and metric learning is proposed.We first use second-order statistics and linear subspace to model the given image set into SPD manifold and Grassmann manifold,respectively.From this operation we can have complementary feature information.For these two heterogeneous spaces,the Riemannian kernels are applied to embed them into a high dimensional Hilbert space.In order to improve the discriminatory ability of the extracted features,a metric learning method is derived to fuse these new feature representations in a low dimensional common space.The achieved better results on different datasets demonstrate its effectiveness.