Fuzzy rough sets (FRSs) are considered to be a powerful model for analyzing uncertainty in data. This model encapsulates two types of uncertainty: 1) fuzziness coming from the vagueness in human concept formation and 2) roughness rooted in the granulation coming with human cognition. The rough set theory has been widely applied to feature selection, attribute reduction, and classification. However, it is reported that the classical FRS model is sensitive to noisy information. To address this problem, several robust models have been developed in recent years. Nevertheless, these models do not consider a statistical distribution of data, which is an important type of uncertainty. Data distribution serves as crucial information for designing an optimal classification or regression model. Thus, we propose a data-distribution-aware FRS model that considers distribution information and incorporates it in computing lower and upper fuzzy approximations. The proposed model considers not only the similarity between samples, but also the probability density of classes. In order to demonstrate the effectiveness of the proposed model, we design a new sample evaluation index for prototype-based classification based on the model, and a prototype selection algorithm is developed using this index. Furthermore, a robust classification algorithm is constructed with prototype covering and nearest neighbor classification. Experimental results confirm the robustness and effectiveness of the proposed model.

Background modeling is a critical component for various vision-based applications. Most traditional methods tend to be inefficient when solving large-scale problems. In this paper, we introduce sparse representation into the task of large-scale stable-background modeling, and reduce the video size by exploring its discriminative frames. A cyclic iteration process is then proposed to extract the background from the discriminative frame set. The two parts combine to form our sparse outlier iterative removal (SOIR) algorithm. The algorithm operates in tensor space to obey the natural data structure of videos. Experimental results show that a few discriminative frames determine the performance of the background extraction. Furthermore, SOIR can achieve high accuracy and high speed simultaneously when dealing with real video sequences. Thus, SOIR has an advantage in solving large-scale tasks.

Metric learning plays a fundamental role in the fields of multimedia retrieval and pattern recognition. Recently, an online multikernel similarity (OMKS) learning method has been presented for content-based image retrieval (CBIR), which was shown to be promising for capturing the intrinsic nonlinear relations within multimodal features from large-scale data. However, the similarity function in this method is learned only from labeled images. In this paper, we present a new framework to exploit unlabeled images and develop a semisupervised OMKS algorithm. The proposed method is a multistage algorithm consisting of feature selection, selective ensemble learning, active sample selection, and triplet generation. The novel aspects of our work are the introduction of classification confidence to evaluate the labeling process and select the reliably labeled images to train the metric function, and a method for reliable triplet generation, where a new criterion for sample selection is used to improve the accuracy of label prediction for unlabeled images. Our proposed method offers advantages in challenging scenarios, in particular, for a small set of labeled images with high-dimensional features. Experimental results demonstrate the effectiveness of the proposed method as compared with several baseline methods.

Due to complex semantics, a sample may be associated with multiple labels in various classification and recognition tasks. Multilabel learning generates training models to map feature vectors to multiple labels. There are several significant challenges in multilabel learning. Samples in multilabel learning are usually described with high-dimensional features and some features may be sequentially extracted. Thus, we do not know the full feature set at the beginning of learning, referred to as streaming features. In this paper, we introduce fuzzy mutual information to evaluate the quality of features in multilabel learning, and design efficient algorithms to conduct multilabel feature selection when the feature space is completely known or partially known in advance. These algorithms are called multilabel feature selection with label correlation (MUCO) and multilabel streaming feature selection (MSFS), respectively. MSFS consists of two key steps: online relevance analysis and online redundancy analysis. In addition, we design a metric to measure the correlation between the label sets, and both MUCO and MSFS take label correlation to consideration. The proposed algorithms are not only able to select features from streaming features, but also able to select features for ordinal multilabel learning. However streaming feature selection is more efficient. The proposed algorithms are tested with a collection of multilabel learning tasks. The experimental results illustrate the effectiveness of the proposed algorithms.

Feature selection is viewed as an important preprocessing step for pattern recognition, machine learning, and data mining. Neighborhood is one of the most important concepts in classification learning and can be used to distinguish samples with different decisions. In this paper, a neighborhood discrimination index is proposed to characterize the distinguishing information of a neighborhood relation. It reflects the distinguishing ability of a feature subset. The proposed discrimination index is computed by considering the cardinality of a neighborhood relation rather than neighborhood similarity classes. Variants of the discrimination index, including joint discrimination index, conditional discrimination index, and mutual discrimination index, are introduced to compute the change of distinguishing information caused by the combination of multiple feature subsets. They have the similar properties as Shannon entropy and its variants. A parameter, named neighborhood radius, is introduced in these discrimination measures to address the analysis of real-valued data. Based on the proposed discrimination measures, the significance measure of a candidate feature is defined and a greedy forward algorithm for feature selection is designed. Data sets selected from public data sources are used to compare the proposed algorithm with existing algorithms. The experimental results confirm that the discrimination index-based algorithm yields superior performance compared to other classical algorithms.