Zhao Xiaowei, Nie Feiping, Wang Sen, Guo Jun, Xu Pengfei, Chen Xiaojiang
School of Information Science and Technology, Northwest University, Xian 71027, China
Center for Optical Imagery Analysis and Learning, Northwestern Polytechnical University, Xian 710072, China
Neural Comput. 2017 May;29(5):1352-1374. doi: 10.1162/NECO_a_00950. Epub 2017 Mar 23.
In recent years, unsupervised two-dimensional (2D) dimensionality reduction methods for unlabeled large-scale data have made progress. However, performance of these degrades when the learning of similarity matrix is at the beginning of the dimensionality reduction process. A similarity matrix is used to reveal the underlying geometry structure of data in unsupervised dimensionality reduction methods. Because of noise data, it is difficult to learn the optimal similarity matrix. In this letter, we propose a new dimensionality reduction model for 2D image matrices: unsupervised 2D dimensionality reduction with adaptive structure learning (DRASL). Instead of using a predetermined similarity matrix to characterize the underlying geometry structure of the original 2D image space, our proposed approach involves the learning of a similarity matrix in the procedure of dimensionality reduction. To realize a desirable neighbors assignment after dimensionality reduction, we add a constraint to our model such that there are exact [Formula: see text] connected components in the final subspace. To accomplish these goals, we propose a unified objective function to integrate dimensionality reduction, the learning of the similarity matrix, and the adaptive learning of neighbors assignment into it. An iterative optimization algorithm is proposed to solve the objective function. We compare the proposed method with several 2D unsupervised dimensionality methods. K-means is used to evaluate the clustering performance. We conduct extensive experiments on Coil20, AT&T, FERET, USPS, and Yale data sets to verify the effectiveness of our proposed method.
近年来，用于无标签大规模数据的无监督二维（2D）降维方法取得了进展。然而，当相似性矩阵的学习处于降维过程开始时，这些方法的性能会下降。在无监督降维方法中，相似性矩阵用于揭示数据的潜在几何结构。由于噪声数据，难以学习到最优的相似性矩阵。在这封信中，我们提出了一种用于二维图像矩阵的新降维模型：具有自适应结构学习的无监督二维降维（DRASL）。我们提出的方法不是使用预先确定的相似性矩阵来表征原始二维图像空间的潜在几何结构，而是在降维过程中学习相似性矩阵。为了在降维后实现理想的邻居分配，我们在模型中添加了一个约束，使得最终子空间中恰好有[公式：见原文]个连通分量。为了实现这些目标，我们提出了一个统一的目标函数，将降维、相似性矩阵的学习以及邻居分配的自适应学习整合到其中。提出了一种迭代优化算法来求解该目标函数。我们将所提出的方法与几种二维无监督降维方法进行了比较。使用K均值算法来评估聚类性能。我们在Coil20、AT&T、FERET、USPS和耶鲁数据集上进行了广泛的实验，以验证我们提出方法的有效性。
