Qihe Liu

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.

Real-time control of individual agents for crowd simulation

This paper presents a novel approach for individual agent’s motion simulation in real-time virtual environments. In our model, we focus on addressing two problems: 1) the control model for local motions. We propose to represent a combination of psychological and geometrical rules with a social and physical forces model so that it can avoid individual agent’s local collision. 2) Global path planning algorithm with moving obstacle. We propose a more efficient algorithm by extending the indicative route method. Experimental results show that the proposed approach can be tuned to simulate different types of crowd behaviors under a variety of conditions, and can naturally exhibit emergent phenomena that have been observed in real crowds.

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.

An extension to rough c-means clustering

The original form of the Rough c-means algorithm does not distinguish between data points in the boundary area. This paper presents an extended Rough c-means algorithm in which the distinction between data points in the boundary area is captured and used in the clustering procedure. Experimental results indicate that the proposed algorithm can yield more desirable clustering results in comparison to the original form of the Rough c-means algorithm.

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.

A canonical form-based approach to affine registration of DTI

Due to the orientation feature of diffusion tensor images (DTI), tensors need to be reoriented during an affine registration. There exists two active reorientation schemes: finite strain (FS) and preserving principal direction (PPD). However, FS scheme limits its application on rigid deformation and PPD scheme suffers from computation load caused by the iteration. In order to overcome these shortcomings, we propose a canonical form-based affine registration of DTI, named as CFARD. We transform voxel sets into canonical forms where an affine registration is simplified as a rigid registration, while still preserves the effects of non-rigid components. This transforming thus extends the application of FS scheme to affine deformation. Furthermore, to reduce computation load, the quaternion technique is skillfully employed to seek a closed-form solution of the optimal rotation where no iteration is required. Extensive experiments are conducted on synthetic and real DTI data from the human brain. In contrast to four existing algorithms, the proposed CFARD improves the consistency between tensor orientation and the anatomical structures after deformation, and performs a better balance between accuracy and computational complexity.

Fractal-based 3d tree modeling

In this paper, we propose an approach for generating three dimension (3D) models of trees base on fractal idea that has the benefit of offering automatically and interactively modeling. The approach can generate 3D geometry tree using botanical knowledge and the fractals, can automatically generate photorealistic tree in real-time, also provides the capability for the user to control shape of the tree in a parameterized way as compared with rule-based tree modeling systems. The approach is very useful in practices and generates visually convincing results.