Many image processing and pattern recognition problems can be formulated as binary quadratic programming (BQP) problems. However, solving a large BQP problem with a good quality solution and low computational time is still a challenging unsolved problem. Current methodologies either adopt an independent random search in a semi-definite space or perform search in a relaxed biconvex space. However, the independent search has great computation cost as many different trials are needed to get a good solution. The biconvex search only searches the solution in a local convex ball, which can be a local optimal solution. In this paper, we propose a BQP solver that alternatingly applies a deterministic search and a stochastic neighborhood search. The deterministic search iteratively improves the solution quality until it satisfies the KKT optimality conditions. The stochastic search performs bootstrapping sampling to the objective function constructed from the potential solution to find a stochastic neighborhood vector. These two steps are repeated until the obtained solution is better than many of its stochastic neighborhood vectors. We compare the proposed solver with several state-of-the-art methods for a range of image processing and pattern recognition problems. Experimental results showed that the proposed solver not only outperformed them in solution quality but also with the lowest computational complexity.

Principal Component Analysis (PCA) is one of the most widely used tools for the representation of high-dimensional data. Many different versions have been proposed to enhance the robustness of the model. Most of these ideas are not median based formulation, which is always a robust estimator in statistics. In this paper, we attempt to design a new median based PCA model based on k-medians clustering, for which each principal component is always the spatial median of the projected space. We prove that the proposed method converges. We also compare the proposed method with several state-of-the-art methods including ℓ1-PCA, RPCA and RPCA-OM. Experimental results show that the proposed k-medians clustering based PCA performs the best in many cases.

Detecting blood vessels in retinal images with the presence of bright and dark lesions is a challenging unsolved problem. In this paper, a novel multiconcavity modeling approach is proposed to handle both healthy and unhealthy retinas simultaneously. The differentiable concavity measure is proposed to handle bright lesions in a perceptive space. The line-shape concavity measure is proposed to remove dark lesions which have an intensity structure different from the line-shaped vessels in a retina. The locally normalized concavity measure is designed to deal with unevenly distributed noise due to the spherical intensity variation in a retinal image. These concavity measures are combined together according to their statistical distributions to detect vessels in general retinal images. Very encouraging experimental results demonstrate that the proposed method consistently yields the best performance over existing state-of-the-art methods on the abnormal retinas and its accuracy outperforms the human observer, which has not been achieved by any of the state-of-the-art benchmark methods. Most importantly, unlike existing methods, the proposed method shows very attractive performances not only on healthy retinas but also on a mixture of healthy and pathological retinas.

High dimensionality, noisy features and outliers can cause problems in cluster analysis. Many existing methods can handle one of the problems well but not the others. In this paper, we propose a new clustering algorithm to solve these problems. The basic idea is to control the support of the optimization procedure so that the effect produced by those contaminated samples and dimensions is greatly reduced. This is achieved by using multiple supports. Initially, a large support is used and then its size is reduced and eventually only a subgroup of data samples is considered for clustering. This procedure can filter out lots of contaminated information. Experiment results show that the proposed method effectively resolves all these problems. It outperforms existing ones for real world high dimensional datasets.

In this paper, a method is proposed for detecting blood vessels in pathological retina images. In the proposed method, blood vessel-like objects are extracted using the Laplacian operator and noisy objects are pruned according to the centerlines, which are detected using the normalized gradient vector field. The method has been tested with all the pathological retina images in the publicly available STARE database. Experiment results show that the method can avoid detecting false vessels in pathological regions and can produce reliable results for healthy regions.

In this paper, we propose a new algorithm for classification of multi-dimensional data, in which noisy features are distributed in different dimensions of different groups. This kind of datasets violate the assumption of many existing dimension reduction methods, which assume all the groups have the noisy features in the same dimensions and the pruning operation is conducted on the same dimensions of all the groups. Our strategy to resolve this problem is to use multi-classifiers. Each classifier engages different set of dimensions and carries out dimensionality reduction separately. Experiment results on six real world data sets show that the proposed algorithm has a superior to existing ones.

Existing curve tracing algorithms drive an evolving curve to the mean or median of the data. However, if the data set contains heavy noise, these algorithms may not produce correct results. In this paper, we introduce a level set based affine transform method to enhance the capability of a class of fuzzy curve tracing algorithms. The essential idea of our approach is to drive the initial curve towards the object data using level sets as well as affine transforms. Experimental results show that the proposed method can enhance fuzzy curve tracing algorithms for dealing with the data corrupted by noise.

Several cluster validity measures have been proposed for evaluating clustering results. However, existing methods may not work well for the following two kinds of data sets. The first one is that the data set contains cluster groups with different densities. The second one is that some of the cluster groups are closely positioned. In this paper, we introduce a new cluster validity index. In this method, we define the index as the ratio between the squared total length of the data eigen-axes and the between-cluster separation. Compared with existing cluster validity indices, the proposed index produces more accurate results and is able to handle the two kinds of data sets mentioned above.