Haze is one of the major factors that degrade outdoor images. Removing haze from an image is a challenge problem. In this paper, a two-peak channel prior model is proposed for general image dehazing. Firstly, the estimation of medium transmission function is derived and analyzed comprehensively. Secondly, a new calculation method estimating atmospheric light is proposed for more robust dehazing with a new compensation parameter. The experimental results illustrate that the proposed method is able to achieve more satisfied dehazing results than two state-of-the-art methods.

Identifying cancer molecular patterns with high accuracy from high-dimensional proteomic profiles presents a challenge for statistical learning and oncology research. In this study, we develop a nonnegative principal component analysis and propose a nonnegative principal component analysis based support vector machine with a sparse coding to conduct effective feature selection and high-performance proteomic pattern classification. We demonstrate the superiority of our algorithm by comparing it with six peer algorithms on four benchmark proteomic tumor profiles under 100 trials of 50% holdout cross validations. We also rigorously show that the over-fitting problem associated with support vector machines can be overcome by nonnegative principal component analysis with exceptional sensitivities and specificities. Moreover, we illustrate that nonnegative principal component analysis can be employed to capture meaningful biomarkers.

As a well-established feature selection algorithm, principal component analysis (PCA) is often combined with the state-of-the-art classification algorithms to identify cancer molecular patterns in microarray data. However, the algorithm's global feature selection mechanism prevents it from effectively capturing the latent data structures in the high-dimensional data. In this study, we investigate the benefit of adding nonnegative constraints on PCA and develop a nonnegative principal component analysis algorithm (NPCA) to overcome the global nature of PCA. A novel classification algorithm NPCA-SVM is proposed for microarray data pattern discovery. We report strong classification results from the NPCA-SVM algorithm on five benchmark microarray data sets by direct comparison with other related algorithms. We have also proved mathematically and interpreted biologically that microarray data will inevitably encounter overfitting for an SVM/PCA-SVM learning machine under a Gaussian kernel. In addition, we demonstrate that nonnegative principal component analysis can be used to capture meaningful biomarkers effectively.

Although entropy and relative entropy (K-L distance) are widely applied in many bioinformatics areas, there is no method given to compute the multispecies gene entropy yet. This paper presents the first multispecies gene entropy estimation method from the data mining point of view. In this study, a self-organizing map (SOM) is employed to mine a multispecies gene set to obtain the probability distribution of each gene in the feature space, which is the approximation of its corresponding probability distribution in the original sequence space. The multispecies gene entropy is computed by the probability distribution of a gene in the feature space. The phylogenetic applications of the multispecies gene entropy are investigated in an example of resolving incongruence between gene trees and species trees. It is found that genes with nearest K-L distances to the minimum entropy gene are more likely to be phylogenetically informative. A K-L distance based gene concatenation approach under gene clustering is proposed to resolve the gene tree and species tree problem. Under the same testing dataset, the K-L distance based approach not only avoids the ad-hoc mechanism of the original gene concatenation method but also is easy to extend to other dataset and free from prohibitive phylogenetic computing from large number of taxa.

For a collection of sets in R d we consider the task of finding all sets in the collection that cover or contain a given point. The algorithms introduced in this paper are based on quadtrees and their generalizations to R d . The advantages of our new splitting algorithm to find the covering sets of a point over the basic algorithm are detailed by means of hit rates and the expected depth traversed in the quadtree search, numerically and theoretically. This solves a difficult problem faced by mesh-free discretizations of partial differential equations.