Yangqing Jia

Trace Ratio Problem Revisited

Dimensionality reduction is an important issue in many machine learning and pattern recognition applications, and the trace ratio (TR) problem is an optimization problem involved in many dimensionality reduction algorithms. Conventionally, the solution is approximated via generalized eigenvalue decomposition due to the difficulty of the original problem. However, prior works have indicated that it is more reasonable to solve it directly than via the conventional way. In this brief, we propose a theoretical overview of the global optimum solution to the TR problem via the equivalent trace difference problem. Eigenvalue perturbation theory is introduced to derive an efficient algorithm based on the Newton-Raphson method. Theoretical issues on the convergence and efficiency of our algorithm compared with prior literature are proposed, and are further supported by extensive empirical results.

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.

Normalized tree partitioning for image segmentation

In this paper, we propose a novel graph based clustering approach with satisfactory clustering performance and low computational cost. It consists of two main steps: tree fitting and partitioning. We first introduce a probabilistic method to fit a tree to a data graph under the sense of minimum entropy. Then, we propose a novel tree partitioning method under a normalized cut criterion, called normalized tree partitioning (NTP), in which a fast combinatorial algorithm is designed for exact bipartitioning. Moreover, we extend it to k-way tree partitioning by proposing an efficient best-first recursive bipartitioning scheme. Compared with spectral clustering, NTP produces the exact global optimal bipartition, introduces fewer approximations for k-way partitioning and can intrinsically produce superior performance. Compared with bottom-up aggregation methods, NTP adopts a global criterion and hence performs better. Last, experimental results on image segmentation demonstrate that our approach is more powerful compared with existing graph-based approaches.

Finding image exemplars using fast sparse affinity propagation

In this paper, we propose a novel approach to organize image search results obtained from state-of-the-art image search engines in order to improve user experience. We aim to discover exemplars from search results and simultaneously group the images. The exemplars are delivered to the user as a summary of search results instead of the large amount of unorganized images. This gives the user a brief overview of search results with a small amount of images, and helps the user to further find the images of interest. We adopt the idea of affinity propagation and design a fast sparse affinity propagation algorithm to find exemplars that best represent the image search results. Experiments on real-world data demonstrate the effectiveness of our method both visually and quantitatively.

Front-view vehicle detection by Markov chain Monte Carlo method

In this paper, we propose a new vehicle detection approach based on Markov chain Monte Carlo (MCMC). We mainly discuss the detection of vehicles in front-view static images with frequent occlusions. Models of roads and vehicles based on edge information are presented, the Bayesian problems formulations are constructed, and a Markov chain is designed to sample proposals to detect vehicles. Using the Monte Carlo technique, we detect vehicles sequentially based on the idea of maximizing a posterior probability (MAP), performing vehicle segmentation in the meantime. Our method does not require complex preprocessing steps such as background extraction or shadow elimination, which are required in many existing methods. Experimental results show that the method has a high detection rate on vehicles and can perform successful segmentation, and reduce the influence caused by vehicle occlusion.

Learning distance metric for semi-supervised image segmentation

Semi-supervised image segmentation is an important issue in many image processing applications, and has been a popular research area recently, the most popular are graph-based methods. However, parameter selection in these methods is still largely heuristic. In this paper, we introduce distance metric learning into graph-based semi-supervised segmentation to automatically obtain good results for images with different appearances. We first derive the optimization problem with respect to the distance metric as well as the segmentation labels, and use gradient descent method to find a local optimum solution. Experiments on general images and the fungal disease analysis application have shown that our method provides a steady performance under casual user annotations and different image appearances.

Augmented tree partitioning for interactive image segmentation

In this paper, we propose a new fast semi-supervised image segmentation method based on augmented tree partitioning. Unlike many existing methods that use a graph structure to model the image, we use a tree-based structure called the augmented tree, which is built up by augmenting several abstract label nodes to the minimum spanning tree of the original graph. We then model image segmentation as the partitioning problem on the augmented tree. Dynamic programming is used to efficiently solve the optimization problem. Experimental results show that our method gives competitive segmentation results, and the speed is much faster than graph- based methods.

Local Regularized Least-Square Dimensionality Reduction

In this paper, we propose a new nonlinear dimensionality reduction algorithm by adopting regularized least-square criterion on local areas of the data distribution. We first propose a local linear model to describe the characteristic of the low-dimensional coordinates of the neighborhood centered in each data point, and use regularized least-square criterion to evaluate the fitness of the low-dimensional embedding. Next, we form an optimization task similar to the graph Laplacian and efficiently retrieve the solution via eigenvalue decomposition. The relationship between our method and the Laplacian Eigenmaps are discussed, and experimental results are presented.

Distortion-Free Nonlinear Dimensionality Reduction

Nonlinear Dimensionality Reduction is an important issue in many machine learning areas where essentially low-dimensional data is nonlinearly embedded in some high-dimensional space. In this paper, we show that the existing Laplacian Eigenmaps method suffers from the distortion problem, and propose a new distortion-free dimensionality reduction method by adopting a local linear model to encode the local information. We introduce a new loss function that can be seen as a different way to construct the Laplacian matrix, and a new way to impose scaling constraints under the local linear model. Better low-dimensional embeddings are obtained via constrained concave convex procedure. Empirical studies and real-world applications have shown the effectiveness of our method.