Hyperspectral images (HIS) classification is a high technical remote sensing tool. The goal is to reproduce a thematic map that will be compared with a reference ground truth map (GT), constructed by expecting the region. The HIS contains more than a hundred bidirectional measures, called bands (or simply images), of the same region. They are taken at juxtaposed frequencies. Unfortunately, some bands contain redundant information, others are affected by the noise, and the high dimensionality of features made the accuracy of classification lower. The problematic is how to find the good bands to classify the pixels of regions. Some methods use Mutual Information (MI) and threshold, to select relevant bands, without treatment of redundancy. Others control and eliminate redundancy by selecting the band top ranking the MI, and if its neighbors have sensibly the same MI with the GT, they will be considered redundant and so discarded. This is the most inconvenient of this method, because this avoids the advantage of hyperspectral images: some precious information can be discarded. In this paper we'll accept the useful redundancy. A band contains useful redundancy if it contributes to produce an estimated reference map that has higher MI with the GT.nTo control redundancy, we introduce a complementary threshold added to last value of MI. This process is a Filter strategy; it gets a better performance of classification accuracy and not expensive, but less preferment than Wrapper strategy.

Covering-based rough set theory is a useful tool to deal with inexact, uncertain or vague knowledge in information systems. Geometric lattice has widely used in diverse fields, especially search algorithm design which plays important role in covering reductions. In this paper, we construct four geometric lattice structures of covering-based rough sets through matroids, and compare their relationships. First, a geometric lattice structure of covering-based rough sets is established through the transversal matroid induced by the covering, and its characteristics including atoms, modular elements and modular pairs are studied. We also construct a one-to-one correspondence between this type of geometric lattices and transversal matroids in the context of covering-based rough sets. Second, sufficient and necessary conditions for three types of covering upper approximation operators to be closure operators of matroids are presented. We exhibit three types of matroids through closure axioms, and then obtain three geometric lattice structures of covering-based rough sets. Third, these four geometric lattice structures are compared. Some core concepts such as reducible elements in covering-based rough sets are investigated with geometric lattices. In a word, this work points out an interesting view, namely geometric lattice, to study covering-based rough sets.

Automatic extraction of temporal relations between event pairs is an important task for several natural language processing applications such as Question Answering, Information Extraction, and Summarization. Since most existing methods are supervised and require large corpora, which for many languages do not exist, we have concentrated our efforts to reduce the need for annotated data as much as possible. This paper presents two different algorithms towards this goal. The first algorithm is a weakly supervised machine learning approach for classification of temporal relations between events. In the first stage, the algorithm learns a general classifier from an annotated corpus. Then, inspired by the hypothesis of "one type of temporal relation per discourse'', it extracts useful information from a cluster of topically related documents. We show that by combining the global information of such a cluster with local decisions of a general classifier, a bootstrapping cross-document classifier can be built to extract temporal relations between events. Our experiments show that without any additional annotated data, the accuracy of the proposed algorithm is higher than that of several previous successful systems. The second proposed method for temporal relation extraction is based on the expectation maximization (EM) algorithm. Within EM, we used different techniques such as a greedy best-first search and integer linear programming for temporal inconsistency removal. We think that the experimental results of our EM based algorithm, as a first step toward a fully unsupervised temporal relation extraction method, is encouraging.

Properties of data are frequently seen to vary depending on the sampled situations, which usually changes along a time evolution or owing to environmental effects. One way to analyze such data is to find invariances, or representative features kept constant over changes. The aim of this paper is to identify one such feature, namely interactions or dependencies among variables that are common across multiple datasets collected under different conditions. To that end, we propose a common substructure learning (CSSL) framework based on a graphical Gaussian model. We further present a simple learning algorithm based on the Dual Augmented Lagrangian and the Alternating Direction Method of Multipliers. We confirm the performance of CSSL over other existing techniques in finding unchanging dependency structures in multiple datasets through numerical simulations on synthetic data and through a real world application to anomaly detection in automobile sensors.

It is a meaningful issue that under what condition neighborhoods induced by a covering are equal to the covering itself. A necessary and sufficient condition for this issue has been provided by some scholars. In this paper, through a counter-example, we firstly point out the necessary and sufficient condition is false. Second, we present a necessary and sufficient condition for this issue. Third, we concentrate on the inverse issue of computing neighborhoods by a covering, namely giving an arbitrary covering, whether or not there exists another covering such that the neighborhoods induced by it is just the former covering. We present a necessary and sufficient condition for this issue as well. In a word, through the study on the two fundamental issues induced by neighborhoods, we have gained a deeper understanding of the relationship between neighborhoods and the covering which induce the neighborhoods.

Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms. In this paper, we apply rough sets to matroids and study the contraction of the dual of the corresponding matroid. First, for an equivalence relation on a universe, a matroidal structure of the rough set is established through the lower approximation operator. Second, the dual of the matroid and its properties such as independent sets, bases and rank function are investigated. Finally, the relationships between the contraction of the dual matroid to the complement of a single point set and the contraction of the dual matroid to the complement of the equivalence class of this point are studied.

Neighborhood is an important concept in covering based rough sets. That under what condition neighborhoods form a partition is a meaningful issue induced by this concept. Many scholars have paid attention to this issue and presented some necessary and sufficient conditions. However, there exists one common trait among these conditions, that is they are established on the basis of all neighborhoods have been obtained. In this paper, we provide a necessary and sufficient condition directly based on the covering itself. First, we investigate the influence of that there are reducible elements in the covering on neighborhoods. Second, we propose the definition of uniform block and obtain a sufficient condition from it. Third, we propose the definitions of repeat degree and excluded number. By means of the two concepts, we obtain a necessary and sufficient condition for neighborhoods to form a partition. In a word, we have gained a deeper and more direct understanding of the essence over that neighborhoods form a partition.

At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid, as a branch of mathematics, is a structure that generalizes linear independence in vector spaces. Further, matroid theory borrows extensively from the terminology of linear algebra and graph theory. We can combine rough set theory with matroid theory through using rough sets to study some characteristics of matroids. In this paper, we apply rough sets to matroids through defining a family of sets which are constructed from the upper approximation operator with respect to an equivalence relation. First, we prove the family of sets satisfies the support set axioms of matroids, and then we obtain a matroid. We say the matroids induced by the equivalence relation and a type of matroid, namely support matroid, is induced. Second, through rough sets, some characteristics of matroids such as independent sets, support sets, bases, hyperplanes and closed sets are investigated.

Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a combinatorial generalization of linear independence in vector spaces. In this paper, we define a parametric set family, with any subset of a universe as its parameter, to connect rough sets and matroids. On the one hand, for a universe and an equivalence relation on the universe, a parametric set family is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore it can generate a matroid, called a parametric matroid of the rough set. Three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, since partition-circuit matroids were well studied through the lower approximation number, we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.

For the past few decades, man has been trying to create an intelligent computer which can talk and respond like he can. The task of creating a system that can talk like a human being is the primary objective of Automatic Speech Recognition. Various Speech Recognition techniques have been developed in theory and have been applied in practice. This paper discusses the problems that have been encountered in developing Speech Recognition, the techniques that have been applied to automate the task, and a representation of the core problems of present day Speech Recognition by using Fuzzy Mathematics.