Rough sets approach to symbolic value partition

AbstractIn data mining, searching for simple representations of knowledge is a very important issue. Attribute reduction, continuous attribute discretization and symbolic value partition are three preprocessing techniques which are used in this regard. This paper investigates the symbolic value partition technique, which divides each attribute domain of a data table into a family for disjoint subsets, and constructs a new data table with fewer attributes and smaller attribute domains. Specifically, we investigates the optimal symbolic value partition (OSVP) problem of supervised data, where the optimal metric is defined by the cardinality sum of new attribute domains. We propose the concept of partition reducts for this problem. An optimal partition reduct is the solution to the OSVP-problem. We develop a greedy algorithm to search for a suboptimal partition reduct, and analyze major properties of the proposed algorithm. Empirical studies on various datasets from the UCI library show that our algorithm effectively reduces the size of attribute domains. Furthermore, it assists in computing smaller rule sets with better coverage compared with the attribute reduction approach

Supra Soft b-Compact and Supra Soft b-Lindle÷F Spaces

The purpose of this paper is to introduce and study the concepts of supra soft b-compact and supra soft b-Lindelˆf spaces. Also we study several of their properties and characterizations in details. Furthermore, the invariance of these kinds of spaces under some types of supra soft mappings and their hereditary properties are also investigate

Granular computing based approach of rule learning for binary classification

Rule learning is one of the most popular types of machine-learning approaches, which typically follow two main strategies: ‘divide and conquer’ and ‘separate and conquer’. The former strategy is aimed at induction of rules in the form of a decision tree, whereas the latter one is aimed at direct induction of if–then rules. Due to the case that the divide and conquer strategy could result in the replicated sub-tree problem, which not only leads to overfitting but also increases the computational complexity in classifying unseen instances, researchers have thus been motivated to develop rule learning approaches through the separate and conquer strategy. In this paper, we focus on investigation of the Prism algorithm, since it is a representative one that follows the separate and conquer strategy, and is aimed at learning a set of rules for each class in the setting of granular computing, where each class (referred to as target class) is viewed as a granule. The Prism algorithm shows highly comparable performance to the most popular algorithms, such as ID3 and C4.5, which follow the divide and conquer strategy. However, due to the need to learn a rule set for each class, Prism usually produces very complex rule-based classifiers. In real applications, there are many problems that involve one target class only, so it is not necessary to learn a rule set for each class, i.e., only a set of rules for the target class needs to be learned and a default rule is used to indicate the case of non-target classes. To address the above issues of Prism, we propose a new version of the algorithm referred to as PrismSTC, where ‘STC’ stands for ‘single target class’. Our experimental results show that PrismSTC leads to production of simpler rule-based classifiers without loss of accuracy in comparison with Prism. PrismSTC also demonstrates sufficiently good performance comparing with C4.5

General set approximation and its logical applications *

Abstract To approximate sets a number of theories have appeared for the last decades. Starting up from some general theoretical pre-conditions the authors give a set of minimum requirements for the lower and upper approximations and define general partial approximation spaces. Then, these spaces are applied in logical investigations. The main question is what happens in the semantics of the first-order logic when the approximations of sets as semantic values of predicate parameters are used instead of sets as their total interpretations. On the basis of defined partial interpretations, logical laws relying on the defined general set-theoretical framework of set approximation are investigated

Some properties of soft topological spaces

AbstractFor dealing with uncertainty researchers introduced the concept of soft sets. Shabir and Naz (2011) [28], defined several basic notions on soft topology and studied many properties. In this paper, we continue investigating the properties of soft open (closed), soft nbd and soft closure. We also define and discuss the properties of soft interior, soft exterior and soft boundary which are fundamental for further research on soft topology and will strengthen the foundations of the theory of soft topological spaces

Algorytmy uczenia się relacji podobieństwa z wielowymiarowych zbiorów danych

The notion of similarity plays an important role in machine learning and artificial intelligence. It is widely used in tasks related to a supervised classification, clustering, an outlier detection and planning. Moreover, in domains such as information retrieval or case-based reasoning, the concept of similarity is essential as it is used at every phase of the reasoning cycle. The similarity itself, however, is a very complex concept that slips out from formal definitions. A similarity of two objects can be different depending on a considered context. In many practical situations it is difficult even to evaluate the quality of similarity assessments without considering the task for which they were performed. Due to this fact the similarity should be learnt from data, specifically for the task at hand. In this dissertation a similarity model, called Rule-Based Similarity, is described and an algorithm for constructing this model from available data is proposed. The model utilizes notions from the rough set theory to derive a similarity function that allows to approximate the similarity relation in a given context. The construction of the model starts from the extraction of sets of higher-level features. Those features can be interpreted as important aspects of the similarity. Having defined such features it is possible to utilize the idea of Tversky’s feature contrast model in order to design an accurate and psychologically plausible similarity function for a given problem. Additionally, the dissertation shows two extensions of Rule-Based Similarity which are designed to efficiently deal with high dimensional data. They incorporate a broader array of similarity aspects into the model. In the first one it is done by constructing many heterogeneous sets of features from multiple decision reducts. To ensure their diversity, a randomized reduct computation heuristic is proposed. This approach is particularly well-suited for dealing with the few-objects-many-attributes problem, e.g. the analysis of DNA microarray data. A similar idea can be utilized in the text mining domain. The second of the proposed extensions serves this particular purpose. It uses a combination of a semantic indexing method and an information bireducts computation technique to represent texts by sets of meaningful concepts. The similarity function of the proposed model can be used to perform an accurate classification of previously unseen objects in a case-based fashion or to facilitate clustering of textual documents into semantically homogeneous groups. Experiments, whose results are also presented in the dissertation, show that the proposed models can successfully compete with the state-of-the-art algorithms.Pojęcie podobieństwa pełni istotną rolę w dziedzinach uczenia maszynowego i sztucznej inteligencji. Jest ono powszechnie wykorzystywane w zadaniach dotyczących nadzorowanej klasyfikacji, grupowania, wykrywania nietypowych obiektów oraz planowania. Ponadto w dziedzinach takich jak wyszukiwanie informacji (ang. information retrieval) lub wnioskowanie na podstawie przykładów (ang. case-based reasoning) pojęcie podobieństwa jest kluczowe ze względu na jego obecność na wszystkich etapach wyciągania wniosków. Jednakże samo podobieństwo jest pojęciem niezwykle złożonym i wymyka się próbom ścisłego zdefiniowania. Stopień podobieństwa między dwoma obiektami może być różny w zależności od kontekstu w jakim się go rozpatruje. W praktyce trudno jest nawet ocenić jakość otrzymanych stopni podobieństwa bez odwołania się do zadania, któremu mają służyć. Z tego właśnie powodu modele oceniające podobieństwo powinny być wyuczane na podstawie danych, specjalnie na potrzeby realizacji konkretnego zadania. W niniejszej rozprawie opisano model podobieństwa zwany Regułowym Modelem Podobieństwa (ang. Rule-Based Similarity) oraz zaproponowano algorytm tworzenia tego modelu na podstawie danych. Wykorzystuje on elementy teorii zbiorów przybliżonych do konstruowania funkcji podobieństwa pozwalającej aproksymować podobieństwo w zadanym kontekście. Konstrukcja ta rozpoczyna się od wykrywania zbiorów wysokopoziomowych cech obiektów. Mogą być one interpretowane jako istotne aspekty podobieństwa. Mając zdefiniowane tego typu cechy możliwe jest wykorzystanie idei modelu kontrastu cech Tversky’ego (ang. feature contrast model) do budowy precyzyjnej oraz zgodnej z obserwacjami psychologów funkcji podobieństwa dla rozważanego problemu. Dodatkowo, niniejsza rozprawa zawiera opis dwóch rozszerzeń Regułowego Modelu Podobieństwa przystosowanych do działania na danych o bardzo wielu atrybutach. Starają się one włączyć do modelu szerszy zakres aspektów podobieństwa. W pierwszym z nich odbywa się to poprzez konstruowanie wielu zbiorów cech z reduktów decyzyjnych. Aby zapewnić ich zróżnicowanie, zaproponowano algorytm łączący heurystykę zachłanna z elementami losowymi. Podejście to jest szczególnie wskazane dla zadań związanych z problemem małej liczby obiektów i dużej liczby cech (ang. the few-objects-many-attributes problem), np. analizy danych mikromacierzowych. Podobny pomysł może być również wykorzystany w dziedzinie analizy tekstów. Realizowany jest on przez drugie z proponowanych rozszerzeń modelu. Łączy ono metodę semantycznego indeksowania z algorytmem obliczania bireduktów informacyjnych, aby reprezentować teksty dobrze zdefiniowanymi pojęciami. Funkcja podobieństwa zaproponowanego modelu może być wykorzystana do klasyfikacji nowych obiektów oraz do łączenia dokumentów tekstowych w semantycznie spójne grupy. Eksperymenty, których wyniki opisano w rozprawie, dowodzą, ze zaproponowane modele mogą skutecznie konkurować nawet z powszechnie uznanymi rozwiązaniami

DOMINANT ATTRIBUTE AND MULTIPLE SCANNING APPROACHES FOR DISCRETIZATION OF NUMERICAL ATTRIBUTES

Rapid development of high throughput technologies and database management systems has made it possible to produce and store large amount of data. However, making sense of big data and discovering knowledge from it is a compounding challenge. Generally, data mining techniques search for information in datasets and express gained knowledge in the form of trends, regularities, patterns or rules. Rules are frequently identified automatically by a technique called rule induction, which is the most important technique in data mining and machine learning and it was developed primarily to handle symbolic data. However, real life data often contain numerical attributes and therefore, in order to fully utilize the power of rule induction techniques, an essential preprocessing step of converting numeric data into symbolic data called discretization is employed in data mining. Here we present two entropy based discretization techniques known as dominant attribute approach and multiple scanning approach, respectively. These approaches were implemented as two explicit algorithms in a JAVA programming language and experiments were conducted by applying each algorithm separately on seventeen well known numerical data sets. The resulting discretized data sets were used for rule induction by LEM2 or Learning from Examples Module 2 algorithm. For each dataset in multiple scanning approach, experiments were repeated with incremental scans until interval counts were stabilized. Preliminary results from this study indicated that multiple scanning approach performed better than dominant attribute approach in terms of producing comparatively smaller and simpler rule sets

CHARACTERIZATION OF SOFT B SEPARATION AXIOMS IN SOFT BI-TOPOLOGICAL SPACES

The main aim of this article is to introduce Soft b separation axioms in soft bi topological spaces. We discuss soft b separation axioms in soft bi topological spaces with respect to ordinary point and soft points. Further study the behavior of soft regular b T3 and soft normal b T4 spaces at different angles with respect to ordinary points as well as with respect to soft points. Hereditary properties are also discussed