测度学习及其应用研究

Presently, we have witnessed a growing interest in the research for metric learning in machine learning, which is widely applied to pattern recognition, information retrieve, dimensionality reduction and computer vision. This project deals with three crucial problems in metric learning and its application. The main work is described as follows. Firstly, metric learning algorithms available, which adopt the Mahalanobis distance, have a problem of local representation. To remedy it, this project proposes two schemes. One is related to locally and nonlinearly empirical mapping model and the other concerns the model of class dependence. Both schemes make a balance between global and local representation in the objective function of metric learning, which is expected to have good performance. Secondly, it would result in overfitting problem when enhancing the model representation or introducing the local information into the metric learning algorithms. To solve it, we use two methods. One method is a common way used in statistical learning theory, or the regularization method. The other method is similar to that used in the face recognition tasks, which deals with the regular and irregular information, respectively. We discuss the computational complexity. In metric learning, the semi-definite constraint induces a large computational complexity in the training procedure and K nearest neighbor algorithm results in a large computational complexity in the test procedure. Thus, this project tries to construct efficient metric learning algorithms by developing decomposition algorithm, greedy algorithm, one-class SVM, sparse learning algorithm and low rank learning algorithm. Finally, we deal with the unablanced data learning problem in metric learning. All metric learning methods will be applied to image classification and/or image segmentation.

近年来测度学习已成为了机器学习领域研究的一个方向，这是由于测度在模式识别、信息检索、数据降维和低维可视化、机器视觉等领域有着广泛应用。本项目围绕测度学习及其应用展开研究。主要研究内容包括：针对目前测度学习中所采用全局马氏矩阵局域表示能力不足的问题，提出采用局域相关非线性经验映射模型以及类别相关测度模型，同时在优化准则中兼顾全局和局域的平衡，以期更好解决此问题；针对模型表示能力扩充以及引入局域信息后带来的学习算法过拟合问题，我们将采用类似统计学习理论中模型正则约束方法和类似人脸识别中规则信息和不规则信息分别处理的方法来研究该问题；针对目前测度学习中半正定约束引起的大训练复杂度和KNN 算法引起的大测试复杂度这两个难点，我们将通过采用分解算法、贪婪算法、1 类SVM 方法、稀疏和低秩学习方法来研究更加有效的测度学习和检验算法；研究测度学习中的不平衡问题的解决方法；应用为图像分类和分割。

本项目对测度学习及其应用展开了研究。主要完成的工作包括两个方面：有监督度量学习和相似性学习。在有监督学习方面：提出了有监督稀疏邻域保持嵌入方法；提出基于双图的判别邻域嵌入方法；提出基于类别信息的邻域保持嵌入算法；提出局部平衡的判别近邻嵌入算法；提出相似平衡的判别邻域嵌入算法；提出隐空间邻域分量分析以及隐空间判别邻域嵌入方法等。在相似性学习方面：提出基于余弦相似性的集成方法；提出基于多支持向量数据描述的相似性学习；提出基于一类支持向量机的快速相似性学习以及提出针对不平衡数据的支持向量机相似性学习方法等。这些方法模型被应用到图像分类和癌症分类中，并获得较好的性能。在本项目的研究期间，在高质量的学术期刊和会议上发表论文56篇，申请发明专利73项，获得发明专利授权20项,获得软件著作权19项，培养硕士研究生10名，博士研究生2名。项目主持人获得2015年江苏省科技进步奖二等奖一项。