By always mapping data from lower dimensional space into higher or even infinite dimensional space, kernel k-means is able to organize data into groups when data of different clusters are not linearly separable. However, kernel k-means incurs the large scale computation due to the representation theorem, i.e. keeping an extremely large kernel matrix in memory when using popular Gaussianand spatial pyramid matching kernels, which largely limits its use for processing large scale data. Also, existing kernel clustering can be overfitted by outliers as well. In this paper, we introduce an Euler clustering, which can not only maintain the benefit of nonlinear modeling using kernel function but also significantly solve the large scale computational problem in kernel-based clustering. This is realized by incorporating Euler kernel. Euler kernel is relying on a nonlinear and robust cosine metric that is less sensitive to outliers. More important it intrinsically induces an empirical map which maps data onto a complex space of the same dimension. Euler clustering takes these advantages to measure the similarity between data in a robust way without increasing the dimensionality of data, and thus solves the large scale problem in kernel k-means. We evaluate Euler clustering and show its superiority against related methods on five publicly available datasets.
This paper proposes a novel robust sparse representation method, called the two-stage sparse representation (TSR), for robust recognition on a large-scale database. Based on the divide and conquer strategy, TSR divides the procedure of robust recognition into outlier detection stage and recognition stage. In the first stage, a weighted linear regression is used to learn a metric in which noise and outliers in image pixels are detected. In the second stage, based on the learnt metric, the large-scale dataset is firstly filtered into a small set according to the nearest neighbor criterion. Then a sparse representation is computed by the non-negative least squares technique. The sparse solution is unique and can be optimized efficiently. The extensive numerical experiments on several public databases demonstrate that the proposed TSR approach generally obtains better classification accuracy than the state of the art Sparse Representation Classification (SRC). At the same time, by using the TSR, a significant reduction of computational cost is reached by over fifty times in comparison with the SRC, which enables the TSR to be deployed more suitably for large-scale dataset.
Most existing robust principal component analysis (PCA) involve mean estimation for extracting low-dimensional representation. However, they do not get the optimal mean for real data, which include outliers, under the different robust distances metric learning, such as L 1 -norm and L 2,1 -norm. This affects the robustness of algorithms. Motivated by the fact that the variance of data can be characterized by the variation between each pair of data, we propose a novel robust formulation for PCA. It avoids computing the mean of data in the criterion function. Our method employs L 2 ,p-norm as the distance metric to measure the variation in the criterion function and aims to seek the projection matrix that maximizes the sum of variation between each pair of the projected data. Both theoretical analysis and experimental results demonstrate that our methods are efficient and superior to most existing robust methods for data reconstruction.
Metric learning, aiming to learn a discriminative Mahalanobis distance matrix M that can effectively reflect the similarity between data samples, has been widely studied in various image recognition problems. Most of the existing metric learning methods input the features extracted directly from the original data in the preprocess phase. What's worse, these features usually take no consideration of the local geometrical structure of the data and the noise that exists in the data, thus they may not be optimal for the subsequent metric learning task. In this paper, we integrate both feature extraction and metric learning into one joint optimization framework and propose a new bilevel distance metric learning model. Specifically, the lower level characterizes the intrinsic data structure using graph regularized sparse coefficients, while the upper level forces the data samples from the same class to be close to each other and pushes those from different classes far away. In addition, leveraging the KKT conditions and the alternating direction method (ADM), we derive an efficient algorithm to solve the proposed new model. Extensive experiments on various occluded datasets demonstrate the effectiveness and robustness of our method.
Li, Yong (Chinese Academy of Sciences) | Liu, Jing (Chinese Academy of Sciences) | Li, Zechao (Nanjing University of Science and Technology) | Zhang, Yangmuzi (University of Maryland, College Park) | Lu, Hanqing (Chinese Academy of Sciences) | Ma, Songde (Chinese Academy of Sciences)
Face recognition has been widely studied due to its importance in various applications. However, the case that both training images and testing images are corrupted is not well addressed. Motivated by the success of low-rank matrix recovery, we propose a novel semi-supervised low-rank matrix recovery algorithm for robust face recognition. The proposed method can learn robust discriminative representations for both training images and testing images simultaneously by exploiting the classwise block-diagonal structure. Specifically, low-rank matrix approximation can handle the possible contamination of data. Moreover, the classwise block-diagonal structure is exploited to promote discrimination of representations for robust recognition. The above issues are formulated into a unified objective function and we design an efficient optimization procedure based on augmented Lagrange multiplier method to solve it. Extensive experiments on three public databases are performed to validate the effectiveness of our approach. The strong identification capability of representations with block-diagonal structure is verified.