基于非负与低秩学习的图像分类算法研究

In recent years, nonnegative matrix factorization theory has been widely used in pattern recognition, machine learning and so on. It has a good learning ability for nonnegative features of the data, and has achieved some results in image recognition, such as face recognition. However, these methods are often use Euclidean distance as the metric which is sensitive to the noises in the data. At the same time, these methods are not fully take use of the discriminant information of the original input data, thus it is difficult to obtain good classification results in image classification, especially for the noised image data. Low-rank representation methods can effectively capture the global structure information of the data, thus it has good stability to the local noises in the data. In order to solve the above problems which are existing in the nonnegative matrix factorization methods, this study intends to fully encode the discriminant information of the data and uses low-rank representation theory to capture the global structure information of the data to improve the robustness and feature extraction abilities of algorithms. The focuses are to solve the low discriminant ability and the sensitivity of the noises of nonnegative matrix factorization methods. Through the research of this topic, it will promote the development of nonnegative matrix factorization and improve its theoretical system, so that it can well classify the high dimensional image data.

近年来，非负矩阵分解理论广泛应用于模式识别与机器学习等领域。它对数据的非负特征具有很好的学习能力，在图像识别如人脸识别等应用中取得了一定的效果。然而，此类方法往往以欧氏距离为测度，因此其对数据中的噪声很敏感，同时此类方法没有很好运用原始输入数据的鉴别信息，从而在图像分类任务中难以取得比较理想的分类效果，特别是对带有噪声的图像数据。低秩表达方法能够有效地捕捉数据的全局结构信息，从而对数据中的局部噪声具有很好的稳定性。为解决上述非负矩阵分解方法中存在的问题，本课题拟将数据的鉴别性充分编码，并运用低秩表达理论对数据全局结构信息的捕捉能力以提升算法的鲁棒性和特征提取性能，重点解决非负矩阵分解方法中的低鉴别性和对噪声的敏感性等问题。通过此课题的研究，将会促进非负矩阵分解方法的发展并完善其理论体系，使得其能很好地分类高维图像数据。

在图像分类中，待分类的图像上有着多种干扰因素，这些因素都是不可预计的。本研究主要关注如何提高带有噪声的图像分类性能。本研究的理论基础是非负矩阵分解与低秩表达学习理论，二者的结合有效地克服了以欧氏距离为测度的算法对数据中噪声的敏感性。主要研究内容包括：基于局部表达与全局表达的分类方法；基于核范数的二维局部保持投影分类方法；基于低秩嵌入的鲁棒特征提取方法。本研究发表与图像分类相关的SCI论文三篇，全部为IEEE Trans.期刊论文。项目还支持视频图像分类IEEE Trans.论文一篇。所发表的成果符合项目预期的成果数量要求与预期的技术路线，且有效地证明了项目设计的合理性与有效性。通过开展本项目的研究工作，取得了一定的科研成果，丰富了非负学习与低秩学习在图像分类中的理论研究，并推动了本领域的发展。