This paper introduces a novel examplar-based inpainting algorithm through investigating the sparsity of natural image patches. Two novel concepts of sparsity at the patch level are proposed for modeling the patch priority and patch representation, which are two crucial steps for patch propagation in the examplar-based inpainting approach. First, patch structure sparsity is designed to measure the confidence of a patch located at the image structure (e.g., the edge or corner) by the sparseness of its nonzero similarities to the neighboring patches. The patch with larger structure sparsity will be assigned higher priority for further inpainting. Second, it is assumed that the patch to be filled can be represented by the sparse linear combination of candidate patches under the local patch consistency constraint in a framework of sparse representation. Compared with the traditional examplar-based inpainting approach, structure sparsity enables better discrimination of structure and texture, and the patch sparse representation forces the newly inpainted regions to be sharp and consistent with the surrounding textures. Experiments on synthetic and natural images show the advantages of the proposed approach.

Microarray technology is widely used in cancer diagnosis. Successfully identifying gene biomarkers will significantly help to classify different cancer types and improve the prediction accuracy. The regularization approach is one of the effective methods for gene selection in microarray data, which generally contain a large number of genes and have a small number of samples. In recent years, various approaches have been developed for gene selection of microarray data. Generally, they are divided into three categories: filter, wrapper and embedded methods. Regularization methods are an important embedded technique and perform both continuous shrinkage and automatic gene selection simultaneously. Recently, there is growing interest in applying the regularization techniques in gene selection. The popular regularization technique is Lasso (L1), and many L1 type regularization terms have been proposed in the recent years. Theoretically, the Lq type regularization with the lower value of q would lead to better solutions with more sparsity. Moreover, the L1/2 regularization can be taken as a representative of Lq (0 < q < 1) regularizations and has been demonstrated many attractive properties. In this work, we investigate a sparse logistic regression with the L1/2 penalty for gene selection in cancer classification problems, and propose a coordinate descent algorithm with a new univariate half thresholding operator to solve the L1/2 penalized logistic regression. Experimental results on artificial and microarray data demonstrate the effectiveness of our proposed approach compared with other regularization methods. Especially, for 4 publicly available gene expression datasets, the L1/2 regularization method achieved its success using only about 2 to 14 predictors (genes), compared to about 6 to 38 genes for ordinary L1 and elastic net regularization approaches. From our evaluations, it is clear that the sparse logistic regression with the L1/2 penalty achieves higher classification accuracy than those of ordinary L1 and elastic net regularization approaches, while fewer but informative genes are selected. This is an important consideration for screening and diagnostic applications, where the goal is often to develop an accurate test using as few features as possible in order to control cost. Therefore, the sparse logistic regression with the L1/2 penalty is effective technique for gene selection in real classification problems.

Deep learning has been widely recognized as the representative advances of machine learning or artificial intelligence in general nowadays [1,2]. This can be attributed to the recent breakthroughs made by deep learning on a series of challenging applications. A deep-learning approach improves the accuracy rate of face recognition to be higher than 99%, beating the human level [3]. For speech recognition and machine translation, deep learning is approaching the performance level of a simultaneous interpreter [4]. For the game of ‘go’, it successfully beats the human world champion [5]. For diagnosis of some specific diseases, it has matched the level of medium or senior professional physicians [6]. Until now, it has been hard to find areas in which the deep-learning technique has not been tried in their respective tasks.

This paper focuses on rough set models on two universes and reveals some new properties. A revised rough set model is proposed which provides a new selection of interval structures for uncertain reasoning using rough set theory and methods.