Fan Min

Rough sets approach to symbolic value partition

In 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.

Minimal attribute space bias for attribute reduction

Attribute reduction is an important inductive learning issue addressed by the Rough Sets society.Most existing works on this issue use the minimal attribute bias, i.e., searching for reducts with the minimal number of attributes. But this bias does not work well for datasets where different attributes have different sizes of domains. In this paper, we propose a more reasonable strategy called the minimal attribute space bias, i.e., searching for reducts with the minimal attribute domain sizes product. In most cases, this bias can help to obtain reduced decision tables with the best space coverage, thus helpful for obtaining small rule sets with good predicting performance. Empirical study on some datasets validates our analysis.

The M -relative reduct problem

Since there may exist many relative reducts for a decision table, some attributes that are very important from the viewpoint of human experts may fail to be included in relative reduct(s) computed by certain reduction algorithms. In this paper we present the concepts of M-relative reduct and core where M is a user specified attribute set to deal with this problem. M-relative reducts and cores can be obtained using M-discernibility matrices and functions. Their relationships with traditional definitions of relative reduct and core are closely investigated

Knowledge reduction in inconsistent decision tables

In this paper, we introduce a new type of reducts called the A-Fuzzy-Reduct, where the fuzzy similarity relation is constructed by means of cosine-distances of decision vectors and the parameter A is used to tune the similarity precision level. The A-Fuzzy-Reduct can eliminate harsh requirements of the distribution reduct, and it is more flexible than the maximum distribution reduct, the traditional reduct, and the generalized decision reduct. Furthermore, we prove that the distribution reduct, the maximum distribution reduct, and the generalized decision reduct can be converted into the traditional reduct. Thus in practice the implementations of knowledge reductions for the three types of reducts can be unified into efficient heuristic algorithms for the traditional reduct. We illustrate concepts and methods proposed in this paper by an example.

OFFD: Optimal Flexible Frequency Discretization for Naïve Bayes Classification

Incremental Flexible Frequency Discretization (IFFD) is a recently proposed discretization approach for Naive Bayes (NB). IFFD performs satisfactory by setting the minimal interval frequency for discretized intervals as a fixed number. In this paper, we first argue that this setting cannot guarantee optimal classification performance in terms of classification error. We observed empirically that an optimal minimal interval frequency existed for each dataset. We thus proposed a sequential search and wrapper based incremental discretization method for NB: named Optimal Flexible Frequency Discretization (OFFD). Experiments were conducted on 17 datasets from UCI machine learning repository and performance was compared between NB trained on the data discretized by OFFD, IFFD, PKID, and FFD respectively. Results show that OFFD works better than these alternatives for NB. Experiments between NB discretized on the data with OFFD and C4.5 showed that our new method outperforms C4.5 on most of the datasets we have tested.

Intra-cluster similarity index based on fuzzy rough sets for fuzzy c-means algorithm

Cluster validity indices have been used to evaluate the quality of fuzzy partitions. In this paper, we propose a new index, which uses concepts of Fuzzy Rough sets to evaluate the average intra-cluster similarity of fuzzy clusters produced by the fuzzy c-means algorithm. Experimental results show that contrasted with several well-known cluster validity indices, the proposed index can yield more desirable cluster number estimation.

Reduction based symbolic value partition

Theory of Rough Sets provides good foundations for the attribute reduction processes in data mining. For numeric attributes, it is enriched with appropriately designed discretization methods. However, not much has been done for symbolic attributes with large numbers of values. The paper presents a framework for the symbolic value partition problem, which is more general than the attribute reduction, and more complicated than the discretization problems.We demonstrate that such problem can be converted into a series of the attribute reduction phases. We propose an algorithm searching for a (sub)optimal attribute reduct coupled with attribute value domains partitions. Experimental results show that the algorithm can help in computing smaller rule sets with better coverage, comparing to the standard attribute reduction approaches.