This is a correction to a typographical error in (11) in [1] which present the calculation of the sum of the multiple significant interdependence redundancy measure. Equation (11) in [1] should be: $$k=\arg\max\nolimits_{k\in\{2,\ldots,p\}}\sum_{r=1}^k \sum_{A_i\in\{C_r-\eta_r\}}R(A_i:\eta_r).$$(11)We remark that the experimental results reported in [1] are based on (11) above not (11) in [1].

This correspondence presents a two-stage classification learning algorithm. The first stage approximates the class-conditional distribution of a discrete space using a separate mixture model, and the second stage investigates the class posterior probabilities by training a network. The first stage explores the generative information that is inherent in each class by using the Chow-Liu (CL) method, which approximates high-dimensional probability with a tree structure, namely, a dependence tree, whereas the second stage concentrates on discriminative learning to distinguish between classes. The resulting learning algorithm integrates the advantages of both generative learning and discriminative learning. Because it uses CL dependence-tree estimation, we call our algorithm CL-Net. Empirical tests indicate that the proposed learning algorithm makes significant improvements when compared with the related classifiers that are constructed by either generative learning or discriminative learning.

Classification of data with imbalanced class distribution has posed a significant drawback of the performance attainable by most standard classifier learning algorithms, which assume a relatively balanced class distribution and equal misclassification costs. This learning difficulty attracts a lot of research interests. Most efforts concentrate on bi-class problems. However, bi-class is not the only scenario where the class imbalance problem prevails. Reported solutions for bi-class applications are not applicable to multi-class problems. In this paper, we develop a cost-sensitive boosting algorithm to improve the classification performance of imbalanced data involving multiple classes. One barrier of applying the cost-sensitive boosting algorithm to the imbalanced data is that the cost matrix is often unavailable for a problem domain. To solve this problem, we apply Genetic Algorithm to search the optimum cost setup of each class. Empirical tests show that the proposed cost-sensitive boosting algorithm improves the classification performances of imbalanced data sets significantly.

Associative classification is a new classification approach integrating association mining and classification. It becomes a significant tool for knowledge discovery and data mining. However, high-order association mining is time consuming when the number of attributes becomes large. The recent development of the AdaBoost algorithm indicates that boosting simple rules could often achieve better classification results than the use of complex rules. In view of this, we apply the AdaBoost algorithm to an associative classification system for both learning time reduction and accuracy improvement. In addition to exploring many advantages of the boosted associative classification system, this paper also proposes a new weighting strategy for voting multiple classifiers.

This paper presents an attribute clustering method which is able to group genes based on their interdependence so as to mine meaningful patterns from the gene expression data. It can be used for gene grouping, selection, and classification. The partitioning of a relational table into attribute subgroups allows a small number of attributes within or across the groups to be selected for analysis. By clustering attributes, the search dimension of a data mining algorithm is reduced. The reduction of search dimension is especially important to data mining in gene expression data because such data typically consist of a huge number of genes (attributes) and a small number of gene expression profiles (tuples). Most data mining algorithms are typically developed and optimized to scale to the number of tuples instead of the number of attributes. The situation becomes even worse when the number of attributes overwhelms the number of tuples, in which case, the likelihood of reporting patterns that are actually irrelevant due to chances becomes rather high. It is for the aforementioned reasons that gene grouping and selection are important preprocessing steps for many data mining algorithms to be effective when applied to gene expression data. This paper defines the problem of attribute clustering and introduces a methodology to solving it. Our proposed method groups interdependent attributes into clusters by optimizing a criterion function derived from an information measure that reflects the interdependence between attributes. By applying our algorithm to gene expression data, meaningful clusters of genes are discovered. The grouping of genes based on attribute interdependence within group helps to capture different aspects of gene association patterns in each group. Significant genes selected from each group then contain useful information for gene expression classification and identification. To evaluate the performance of the proposed approach, we applied it to two well-known gene expression data sets and compared our results with those obtained by other methods. Our experiments show that the proposed method is able to find the meaningful clusters of genes. By selecting a subset of genes which have high multiple-interdependence with others within clusters, significant classification information can be obtained. Thus, a small pool of selected genes can be used to build classifiers with very high classification rate. From the pool, gene expressions of different categories can be identified.

Association and classification are two important tasks in data mining and knowledge discovery. Intensive studies have been carried out in both areas. But, how to apply discovered event associations to classification is still seldom found in current publications. Trying to bridge this gap, this paper extends our previous paper on significant event association discovery to classification. We propose to use weight of evidence to evaluate the evidence of a significant event association in support of, or against, a certain class membership. Traditional weight of evidence in information theory is extended here to measure the event associations of different orders with respect to a certain class. After the discovery of significant event associations inherent in a data set, it is easy and efficient to apply the weight of evidence measure for classifying an observation according to any attribute. With this approach, we achieve flexible prediction.

Decision support nowadays is more and more targeted to large scale complicated systems and domains. The success of a decision support system relies mainly on its capability of processing large amounts of data and efficiently extracting useful knowledge from the data, especially knowledge which is previously unknown to the decision makers. With a large scale system, traditional knowledge acquisition models become inefficient and/or more biased, due to the subjectivity of the experts or the pre-assumptions of certain ideas or algorithmic procedures. Today, with the rapid development of computer technologies, the capability of collecting data has been greatly advanced. Data becomes the most valuable resource for an organization. We present a fundamental framework toward intelligent decision support by analyzing a large amount of mixed-mode data (data with a mixture of continuous and categorical values) in order to bridge the subjectivity and objectivity of a decision support process. By considering significant associations of artifacts (events) inherent in the data as patterns, we define patterns as statistically significant associations among feature values represented by joint events or hypercells in the feature space. We then present an algorithm which automatically discovers statistically significant hypercells (patterns) based on: 1) a residual analysis, which tests the significance of the deviation when the occurrence of a hypercell differs from its expectation, and 2) an optimization formulation to enable recursive discovery. By discovering patterns from data sets based on such an objective measure, the nature of the problem domain will be revealed. The patterns can then be applied to solve specific problems as being interpreted or inferred with.

To uncover qualitative and quantitative patterns in a data set is a challenging task for research in the area of machine learning and data analysis. Due to the complexity of real-world data, high-order (polythetic) patterns or event associations, in addition to first-order class-dependent relationships, have to be acquired. Once the patterns of different orders are found, they should be represented in a form appropriate for further analysis and interpretation. The authors propose a novel method to discover qualitative and quantitative patterns (or event associations) inherent in a data set. It uses the adjusted residual analysis in statistics to test the significance of the occurrence of a pattern candidate against its expectation. To avoid exhaustive search of all possible combinations of primary events, techniques of eliminating the impossible pattern candidates are developed. The detected patterns of different orders are then represented in an attributed hypergraph which is lucid for pattern interpretation and analysis. Test results on artificial and real-world data are discussed toward the end of the paper.