Shiming Xiang

Learning a Mahalanobis distance metric for data clustering and classification

Distance metric is a key issue in many machine learning algorithms. This paper considers a general problem of learning from pairwise constraints in the form of must-links and cannot-links. As one kind of side information, a must-link indicates the pair of the two data points must be in a same class, while a cannot-link indicates that the two data points must be in two different classes. Given must-link and cannot-link information, our goal is to learn a Mahalanobis distance metric. Under this metric, we hope the distances of point pairs in must-links are as small as possible and those of point pairs in cannot-links are as large as possible. This task is formulated as a constrained optimization problem, in which the global optimum can be obtained effectively and efficiently. Finally, some applications in data clustering, interactive natural image segmentation and face pose estimation are given in this paper. Experimental results illustrate the effectiveness of our algorithm.

Vehicle Detection in Satellite Images by Hybrid Deep Convolutional Neural Networks

Detecting small objects such as vehicles in satellite images is a difficult problem. Many features (such as histogram of oriented gradient, local binary pattern, scale-invariant feature transform, etc.) have been used to improve the performance of object detection, but mostly in simple environments such as those on roads. Kembhavi et al. proposed that no satisfactory accuracy has been achieved in complex environments such as the City of San Francisco. Deep convolutional neural networks (DNNs) can learn rich features from the training data automatically and has achieved state-of-the-art performance in many image classification databases. Though the DNN has shown robustness to distortion, it only extracts features of the same scale, and hence is insufficient to tolerate large-scale variance of object. In this letter, we present a hybrid DNN (HDNN), by dividing the maps of the last convolutional layer and the max-pooling layer of DNN into multiple blocks of variable receptive field sizes or max-pooling field sizes, to enable the HDNN to extract variable-scale features. Comparative experimental results indicate that our proposed HDNN significantly outperforms the traditional DNN on vehicle detection.

Efficient Image Dehazing with Boundary Constraint and Contextual Regularization

Images captured in foggy weather conditions often suffer from bad visibility. In this paper, we propose an efficient regularization method to remove hazes from a single input image. Our method benefits much from an exploration on the inherent boundary constraint on the transmission function. This constraint, combined with a weighted L1-norm based contextual regularization, is modeled into an optimization problem to estimate the unknown scene transmission. A quite efficient algorithm based on variable splitting is also presented to solve the problem. The proposed method requires only a few general assumptions and can restore a high-quality haze-free image with faithful colors and fine image details. Experimental results on a variety of haze images demonstrate the effectiveness and efficiency of the proposed method.

A unified framework for semi-supervised dimensionality reduction

In practice, many applications require a dimensionality reduction method to deal with the partially labeled problem. In this paper, we propose a semi-supervised dimensionality reduction framework, which can efficiently handle the unlabeled data. Under the framework, several classical methods, such as principal component analysis (PCA), linear discriminant analysis (LDA), maximum margin criterion (MMC), locality preserving projections (LPP) and their corresponding kernel versions can be seen as special cases. For high-dimensional data, we can give a low-dimensional embedding result for both discriminating multi-class sub-manifolds and preserving local manifold structure. Experiments show that our algorithms can significantly improve the accuracy rates of the corresponding supervised and unsupervised approaches.

Discriminative Least Squares Regression for Multiclass Classification and Feature Selection

This paper presents a framework of discriminative least squares regression (LSR) for multiclass classification and feature selection. The core idea is to enlarge the distance between different classes under the conceptual framework of LSR. First, a technique called ε-dragging is introduced to force the regression targets of different classes moving along opposite directions such that the distances between classes can be enlarged. Then, the ε-draggings are integrated into the LSR model for multiclass classification. Our learning framework, referred to as discriminative LSR, has a compact model form, where there is no need to train two-class machines that are independent of each other. With its compact form, this model can be naturally extended for feature selection. This goal is achieved in terms of L2,1 norm of matrix, generating a sparse learning model for feature selection. The model for multiclass classification and its extension for feature selection are finally solved elegantly and efficiently. Experimental evaluation over a range of benchmark datasets indicates the validity of our method.

Semi-supervised orthogonal discriminant analysis via label propagation

Trace ratio is a natural criterion in discriminant analysis as it directly connects to the Euclidean distances between training data points. This criterion is re-analyzed in this paper and a fast algorithm is developed to find the global optimum for the orthogonal constrained trace ratio problem. Based on this problem, we propose a novel semi-supervised orthogonal discriminant analysis via label propagation. Differing from the existing semi-supervised dimensionality reduction algorithms, our algorithm propagates the label information from the labeled data to the unlabeled data through a specially designed label propagation, and thus the distribution of the unlabeled data can be explored more effectively to learn a better subspace. Extensive experiments on toy examples and real-world applications verify the effectiveness of our algorithm, and demonstrate much improvement over the state-of-the-art algorithms.

Edge-Directed Single-Image Super-Resolution Via Adaptive Gradient Magnitude Self-Interpolation

Super-resolution from a single image plays an important role in many computer vision systems. However, it is still a challenging task, especially in preserving local edge structures. To construct high-resolution images while preserving the sharp edges, an effective edge-directed super-resolution method is presented in this paper. An adaptive self-interpolation algorithm is first proposed to estimate a sharp high-resolution gradient field directly from the input low-resolution image. The obtained high-resolution gradient is then regarded as a gradient constraint or an edge-preserving constraint to reconstruct the high-resolution image. Extensive results have shown both qualitatively and quantitatively that the proposed method can produce convincing super-resolution images containing complex and sharp features, as compared with the other state-of-the-art super-resolution algorithms.

Learning Consistent Feature Representation for Cross-Modal Multimedia Retrieval

The cross-modal feature matching has gained much attention in recent years, which has many practical applications, such as the text-to-image retrieval. The most difficult problem of cross-modal matching is how to eliminate the heterogeneity between modalities. The existing methods (e.g., CCA and PLS) try to learn a common latent subspace, where the heterogeneity between two modalities is minimized so that cross-matching is possible. However, most of these methods require fully paired samples and suffer difficulties when dealing with unpaired data. Besides, utilizing the class label information has been found as a good way to reduce the semantic gap between the low-level image features and high-level document descriptions. Considering this, we propose a novel and effective supervised algorithm, which can also deal with the unpaired data. In the proposed formulation, the basis matrices of different modalities are jointly learned based on the training samples. Moreover, a local group-based priori is proposed in the formulation to make a better use of popular block based features (e.g., HOG and GIST). Extensive experiments are conducted on four public databases: Pascal VOC2007, LabelMe, Wikipedia, and NUS-WIDE. We also evaluated the proposed algorithm with unpaired data. By comparing with existing state-of-the-art algorithms, the results show that the proposed algorithm is more robust and achieves the best performance, which outperforms the second best algorithm by about 5% on both the Pascal VOC2007 and NUS-WIDE databases.

Semi-Supervised Classification via Local Spline Regression

This paper presents local spline regression for semi-supervised classification. The core idea in our approach is to introduce splines developed in Sobolev space to map the data points directly to be class labels. The spline is composed of polynomials and Greens functions. It is smooth, nonlinear, and able to interpolate the scattered data points with high accuracy. Specifically, in each neighborhood, an optimal spline is estimated via regularized least squares regression. With this spline, each of the neighboring data points is mapped to be a class label. Then, the regularized loss is evaluated and further formulated in terms of class label vector. Finally, all of the losses evaluated in local neighborhoods are accumulated together to measure the global consistency on the labeled and unlabeled data. To achieve the goal of semi-supervised classification, an objective function is constructed by combining together the global loss of the local spline regressions and the squared errors of the class labels of the labeled data. In this way, a transductive classification algorithm is developed in which a globally optimal classification can be finally obtained. In the semi-supervised learning setting, the proposed algorithm is analyzed and addressed into the Laplacian regularization framework. Comparative classification experiments on many public data sets and applications to interactive image segmentation and image matting illustrate the validity of our method.

Nonlinear Dimensionality Reduction with Local Spline Embedding

This paper presents a new algorithm for nonlinear dimensionality reduction (NLDR). Our algorithm is developed under the conceptual framework of compatible mapping. Each such mapping is a compound of a tangent space projection and a group of splines. Tangent space projection is estimated at each data point on the manifold, through which the data point itself and its neighbors are represented in tangent space with local coordinates. Splines are then constructed to guarantee that each of the local coordinates can be mapped to its own single global coordinate with respect to the underlying manifold. Thus, the compatibility between local alignments is ensured. In such a work setting, we develop an optimization framework based on reconstruction error analysis, which can yield a global optimum. The proposed algorithm is also extended to embed out of samples via spline interpolation. Experiments on toy data sets and real-world data sets illustrate the validity of our method.