Bioinformatics Advance Access originally published online on April 26, 2007
Bioinformatics 2007 23(12):1503-1510; doi:10.1093/bioinformatics/btm141
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Identifying the biologically relevant gene categories based on gene expression and biological data: an example on prostate cancer
Department of Electrical Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR
*To whom correspondence should be addressed.
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ABSTRACT |
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 TOP ABSTRACT 1 INTRODUCTION2 METHODS3 RESULTS ON SYNTHETIC...4 RESULTS ON PROSTATE...5 ConclusionsACKNOWLEDGEMENTSREFERENCES |
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Motivation: Most gene-expression based studies aim to identify genes with the capability of distinguishing different phenotypes. Although analysis at the genomic level is important, results of the molecular/cellular level are essential for understanding biological mechanisms. To deliver molecular/cellular-level results, a two-stage scheme is widely employed. This scheme just evaluates biological processes/molecular activities individually, totally overlooking the relationship between processes/activities. This treatment conflicts with the fact that most biological processes/molecular activities do not work alone. In order to deliver improved results, this shortcoming should be addressed.
Results: We design a selection model from a novel perspective to directly detect important gene functional categories (each category represents a cellular process or a molecular activity). More importantly, the correlations between gene categories are considered. Contributed by this capability, the proposed method shows its advantages over others.
Availability: the source code in Matlab is accessible via http://www.ee.cityu.edu.hk/~twschow/category_selection/category_selection.htm
Contact: ifkorf{at}ucdavis.edu
Supplementary information: http://www.ee.cityu.edu.hk/~twschow/category_selection/category_selection.htm
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1 INTRODUCTION |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS ON SYNTHETIC...4 RESULTS ON PROSTATE...5 ConclusionsACKNOWLEDGEMENTSREFERENCES |
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Gene is the basic functional and physical unit controlling and regularizing biological phenomena and human diseases. The studies at the gene level are thus essential and important. Microarray techniques enable researchers to record the expression profiles of thousands of genes simultaneously (Ekins, 1999). With the advent of these techniques, the gene-level studies have been greatly boosted. The studies include the annotation/function prediction of genes (Zhou, 2002), the analysis of gene signaling pathways (Segal, 2003), the diagnosis and prognosis of heterogeneous diseases (Lee, 2003; Yeung, 2005) and the identification of genes responsible for complex diseases (Golub, 1999; Gui, 2005; Guyon, 2002; Zhang, 2006), etc. The latter two issues, which are related to disease understanding and prediction, have been dealt with by using various supervised machine-learning methods.
In a gene expression dataset used for disease studies, each sample has a label indicating its phenotypical status (e.g. being diseased or normal or belonging to which type of disease or how to respond to a drug). According to the principle of machine learning, we generalize label of different types as response. Obviously, the genes that vary systematically with the change of response are influential and should be paid attentions on. Through discarding the unrelated and redundant genes and just focusing on the influential genes, analysis on gene expression data can be greatly simplified into a low-dimensional data domain, which is helpful to deliver precise, reliable and interpretable results. Also, focusing on the marker genes can reduce the cost of biological experiment and decision. These are the main reasons that gene selection becomes essential or even necessary.
In a gene selection scheme, genes are considered individually, either to evaluate the gene–response association or to assess the gene–gene relationship. On the other hand, most genes cannot work alone. Instead, the functionally associated genes always collaborate with each other through interaction and reaction to regularize a cellular process at a molecular level, via a signaling pathway or under a common mechanism. A series of interplays among cellular processes or molecular activities finally determine most biological phenomena and human diseases. Given this observation, there is a need to extend disease research from a gene level to a cellular/molecular level. Also the cellular/molecular results are able to offer more insights and a better understanding of the cellular mechanisms, and thus are favored by biologists.
The functional roles of genes have been studied in a huge amount of biological experiments. The confirmed results have been summarized into databases from various perspectives. In the Kyoto Encyclopedia of genes and genomes (KEGG) database, each gene is associated with the molecular signaling pathways in which it participates (Kanehisa, 1997). In the SWISS-PORT databases, a gene is labeled with a set of keywords, such as pathways and general biological processes (Boeckmann, 2003). Recently, the Gene Ontology consortium develops an excellent platform to categorize genes in the context of their cellular and molecular functions (Ashburner, 2000). In the Gene Ontology (GO), gene functions are organized into three hierarchical trees. These trees are parallel to each other and respectively stand for biological process, molecular function and cellular component. A node of tree represents a functional annotation of gene. Along the direction of top-down, the range covered by annotation is gradually narrowed. For example, in the biological process tree, the root node is named as biological process. One of its descendants is labeled with growth. Down along this direction, the annotations of nodes are in turn cell growth, regulation of cell growth, etc.
With the availability of these databases, and driven by biological needs, it has become a trend to change the focus of gene-expression-based studies from gene identification to the detection of relevant molecular activities/cellular processes, behind which are functional categories of genes. To extract molecular/cellular-level results, most existing studies adopt a post hoc scheme. A list of influential genes is firstly selected out by using a gene-specific method. These genes are generally ranked in a descendent order of gene–response correlation. Then for each gene functional category given in biological databases, the enrichment state in the ranked gene list is estimated under statistical frameworks. The categories with significantly enrichment state are considered relevant to a given task (Al-Shahrour, 2004; Beissbarth, 2004; Draghici, 2003; Khatri, 2005; Kim, 2003; van't Veer, 2002). More recently, to enhance performance, sophisticated strategies were designed (Al-Shahrour, 2005; Barry, 2005; Mootha, 2004). After obtaining an ordered gene list, Al-Shahrour et al. (2005) analyzed the distribution of a gene functional category in that gene list. A tested category is unimportant to a given task when the genes of that category uniformly distribute in the ranked gene list. Barry et al. (2005) developed a permutation-based framework. Several permutated datasets are first generated. Based on each permutated dataset, gene–response associations are measured with a statistic approach, for instance, t-statistic. Then for a gene functional category, Wilcoxon rank sum or Kolmogorov–Smirnov statistic is used to compare the within-category association shift caused by permutation with the outside-category one. A large difference between these shifts indicates that the tested category is highly relevant to a given task. These gene-list-based models can deliver respectable and meaningful results. However, the aforementioned models, which are either oversimple or sophisticated, adopt a gene-list-based working mechanism in which identifying significant gene categories is just a sequent step of gene selection. In these approaches, gene functional categories are evaluated individually, while the relationship between gene categories has not been taken into account. This shortcoming should be justified, considering the fact that gene functional categories interplay with each other. Until now, few attempts have been done on this issue.
In this article, we present a category selection model in which gene expression data and gene functional category data are integrated together, and relevant gene categories are identified in a straightforward way. In the proposed model, the category–response and category–category associations are considered at the same time during the course of category selection. The proposed model has enhanced the performance of category selection.
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2 METHODS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS ON SYNTHETIC...4 RESULTS ON PROSTATE...5 ConclusionsACKNOWLEDGEMENTSREFERENCES |
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In order to directly select relevant gene categories, the category–response and category–category associations should be evaluated. A category, generally consisting of up to thousands genes, is represented by a high-dimensional variable. Furthermore, different category variables, covering different numbers of genes, are with different dimensionalities. With these facts, estimating category-related associations becomes very challenging. To cope with this difficulty, our method first estimates the probability distribution of each category in the gene space. This part is inspired by Yu et al. (2005). For understanding this point, please refer to Figure 1 in which several probability distribution histograms of gene categories are illustrated. Based on the obtained probability estimates, the category–category and category–response associations are measured by using a newly-introduced index. Then, a forward selection process is used to identify relevant categories. The core of this process is another newly developed evaluation criterion. With this criterion, we can identify the categories that are relevant to a given task but not redundant to the already-selected categories. The proposed methods include four sequential steps, as shown in Figure 1.
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Step A. Evaluate the gene–gene and gene–response associations based on gene expression data. During this course, Pearson's correlation and mutual information MI are used.
Step B. Estimate the probabilities of gene categories and the response variable in the gene space based upon the gene–gene/gene–response association values.
Step C. Evaluate category–category or category–response correlations based on the probabilities obtained in Step B.
Step D. Search the influential gene functional categories in a forward way according to the correlations calculated in Step C.
2.1 Gene–gene and gene–response correlation
Given a gene expression dataset, the correlation between genes can be measured by using many indices, such as Pearson's correlation, Kendall ranking correlation (Hollander, 1999) and mutual information (MI, Cover, 1994), etc. Among them, Pearson's correlation, which is reliable and efficient enough, is widely employed. Also, in most categories/pathways, induced and repressed genes exist at the same time. To account for variations in either direction, we follow other researchers (Yu, 2005; Zhou, 2002), using the absolute Pearson's correlation to measure the similarity of genes.
To assess the gene–response associations, the popular ways include signal-to-noise ratio (Golub, 1999), t-test and MI (refered as information gain in some literatures). The signal-to-noise ratio and t-test make use of the averages and the SDs of samples in different classes to fulfill the evaluation task. These criteria are reliable when given samples are in the normal or near-normal distribution, but they may not be good enough to tackle variables with a complex distribution. Compared with these criteria, MI is more flexible since it can reliably reflect the arbitrary relationship of variables. We thus use MI to measure the gene–response associations. Given two variable X and Y, Shannon's MI is defined as
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The above equation shows that the calculation of MI requires the estimation of p(y, x), p(x) and p(y). To estimate these probability density functions, histogram and kernel based models (e.g. Parzen window) are commonly used. In a histogram model, the probability of a data point is determined based on the frequency of that point appearing in a given dataset. Based on histograms, the integration operation in MI (1) can be simplified as a summation operation. With this simplification, histogram model can make the computation of MI much efficient. On the other hand, histogram is argued to become infeasible in high dimensional space due to the sparseness of data samples (Moon, 1995). This shortcoming, however, does not concern us because we only need 2D MIs. With the above considerations, we employ histograms to estimate the probabilities required by MI (1).
2.2 Probabilities of gene functional category in the gene space
Suppose that we have a gene set G = {g1, g2, ... , gM}, and a set of gene functional categories C = {c1, c2, ... , cK}. Each category consists of several genes in G, i.e. ci 
G (1 
i K). Given a functional category ci, to evaluate its probability density in the gene space is to determine p(ci|gj) for j = 1, 2, ... , M.
Given a gene, say gk, we evaluate the similarity of ci to gk in a way of
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(1 + MI(gk, y))6.
2.3 Category–Category Correlation and Category–response correlation
To evaluate the similarity between two categories ci and cj, we define an index as
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2.4 Forward selection process
Referring to the correlation-based feature selection index (Hall, 1999), we design the criterion rlv(TC, y) (7) to measure the classification capacity of a gene functional category set.
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Based on rlv(TC, y), we employ a forward searching process to identify relevant categories in a way of one by one. Below, this process is detailed.
- (Initialization) Set SC, the selected gene category set, empty;
- Repeat the following steps until SC reaches the desired size. For each unselected category, say c, calculate rlv(SC + c, y). Choose the category with the maximal rlv(SC + c, y). Put that category into SC.
- Output the selected set SC.
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3 RESULTS ON SYNTHETIC DATA |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS ON SYNTHETIC...4 RESULTS ON PROSTATE...5 ConclusionsACKNOWLEDGEMENTSREFERENCES |
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We compared the proposed method with the related approaches, including significance analysis of functional categories (SAFE. Barry, 2005), gene set enrichment analysis (GSEA. Mootha, 2003) and the average-based method. The first two are a typical gene-list-based scheme, in which all given genes are ranked according to their classification capabilities. Then based on the obtained gene list(s), the biological relevancy of gene category is evaluated. Both SAFE and GSEA finally estimate the significance enrichment for each gene functional category. The smaller the enrichment value, the higher relevancy of the tested category has. For SAFE, we considered the cases with P-value < 0.1 as significantly associated. For GSEA, we regarded the categories with q-value < 0.25 as biologically relevant. The average-based method extracts a hyper-gene to represent a gene category. Given a category, the expression profile of its hyper-gene is the average of the expression profiles of the genes assigned to that category. Based on the extracted hyper-genes, the selection of gene functional categories is simplified as the selection of hyper-genes. In general, any gene selection method can be employed for this issue. We chose the MI based forward searching scheme proposed by Chow et al. (2005). This MI based scheme determines the salient hyper-genes in a way of one by one. The importance of each unselected hyper-gene (say, hg) is evaluated based on MI(S + hg, y) where S is the set of the selected hyper-genes. The hyper-gene with the largest MI(S + hg, y) is selected into S. This selection process repeats until certain hyper-genes have been selected. In our Supplementary Material, the details of this MI based forward search scheme are given.
We first evaluated these methods under a synthetic scenario. The expression data we used is similar to the one mentioned by Weston et al. (2000). In this dataset, the samples are evenly distributed in the class 1 and –1. The gene variable X1 and X2 are drawn from a mixture of normal distributions: with the probability of 0.7, X1 and X2 respectively come from yN(3,1) and N(0,1) where y is the class label, that is, y = 1 or –1; with the probability of 0.3, X1 and X2 are respectively generated according to N(0,1) and yN(3,1). It can be noted that X1, which can determine the labels of 70% samples, is more important than X2.
Generally, in a gene expression data, there are many irrelevant genes. To simulate this, we generated 20 genes according to the distribution N(0,1). These variables are just background noise and irrelevant to distinguish the samples from different classes. Also, we generated redundant genes. In detail, given X1, we drew five genes in a way of X1 + 0.2N(0,1). These five genes are highly redundant to X1. Similarly, around X2, other five redundant genes were built. After adding the 10 redundant and the 20 irrelevant genes, we finally got a 32-gene dataset X. Also, suppose that, in X, the 32 genes are arranged in a way of
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In GO, the gene categories show a hierarchical tree structure in which each node covers the genes associated to itself and all its descendants. To simulate GO tree, we constructed six gene categories, as illustrated in Figure 2. S6 is not a representative category and was rejected from our study. Details about representative category will be detailed later. Also, based on our generation mechanism, we observe that (1) of the five tested categories, S2, S3, S4 and S5 are useful since they contain informative genes, while S1, having no informative gene, is unrelated to this classification task; (2) S2, S3 and S4 are redundant to each other because all of them contain X1 or the genes close to X1. Among these categories, S2 is the best due to the highest purity, i.e. S2 includes no irrelevant gene and the fewest redundant genes; (3) as X1 is more influential than X2, the categories including X1 are more important than the ones having X2. According to the above observations, the correct order of category selection is (S2/S3/S4) 
S5. Also, the result S2 S5 is the most desired since S2 is better than S3 and S4.
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We generated 1000 datasets, and run the compared methods on each of them. In Table 1, the statistical results across 1000 trails are summarized. It is noted that all the methods can put S2/S3/S4 on the first place with a high probability. Also GSEA may have bias to large categories since the probability of S2 being selected out in the first place is zero. Let us see the category selected in the second place. It is known that following S2/S3/S4 should be S5. S5 is useful but slightly less important than S2/S3/S4. Such S5 poses great challenge to SAFE and GSEA, as indicated by the results presented in the third column of Table 1. Actually, in all trials, SAFE always assigned S5 with P-value > 0.1. In the estimates of GSEA, FDR q-values of S5 were always larger than those of S2, S3 and S4. These estimation results means that, in all trials, both SAFE and GSEA could not correctly consider S5 as the second important category.
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Furthermore, we added noise genes into S5 such that S5 = {X8, X9, five genes randomly selected from (X13, ... , X32)}. As shown in Table 1 (b), with the noise-mixing S5, the good performance of our method can be kept, whilst the average-based method is badly affected. Through the average operation, the useful genes will be masked by noise ones. This is the direct reason that, in the average-based method, the accuracy of selecting S2
S5 greatly decreases to 49.4% from 61.9% obtained in the pervious example.
S3 is the combination of S2 and seven noise genes, {X13 
X19}, as shown in Figure 2. In the estimates of SAFE, the significance P-values of S2 and S3 were 0.04 and 0.63, respectively. Also, the P-values of the original S5 (in the first example) and the noise-mixing S5 (of the second example) were respectively 0.26 and 0.47 on average. These comparisons indicate that irrelevant genes may greatly undermine the performance of SAFE. To sum up, we have the following conclusions. (1) All the methods except GSEA can successfully identify the categories with great importance and high purity, such as S2. (2) The proposed method and the average-based method outperform SAFE and GSEA when one is dealing with useful but slightly unimportant categories, for instance, S5. (3) The proposed method and GSEA can exhibit the advantage over others on identifying noise-mixing categories, e.g. noise-mixed S5.
It is worth noting that, in a real dataset, ideal categories, like S2, rarely exist. Thus, the capability of handling noise-mixing categories is very important, even crucial, for gene category selection.
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4 RESULTS ON PROSTATE DATA |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS ON SYNTHETIC...4 RESULTS ON PROSTATE...5 ConclusionsACKNOWLEDGEMENTSREFERENCES |
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4.1 Data
We applied our method to a prostate cancer data. Prostate cancer is one of the most well-studied cancers. A lot of published clinical results can be used for evaluating our data analysis results. We used the gene expression dataset provided by Singh et al. (2002). This dataset, collected in the platform of Affymetrix HG U95A arrays, consists of 102 samples and records expression profiles of 9527 genes. As to gene-functional categories, we used GO annotation database (Ashburner, 2000) and KEGG gene pathway database (Kanehisa, 1997). Due to the hierarchical structure of GO, there must exists redundant GO terms. Here, a GO term is considered as redundant when most genes covered by it can be associated to their children. Redundant GO terms contain little exclusive information. To efficiently analyze GO terms, we filtered the redundant GO terms out and restricted our study to representative GO terms. We considered a term (say, r) as representative when, out of all genes associated to r, there exist genes that cannot be covered by the r's descendants. Given a GO term (say H), assume that there are totally w genes annotated either with it or with its descendants. Among these w genes, z genes are directly annotated with H itself, while others are associated to its descendants. The uniqueness of H can be calculated as z/w. A large uniqueness indicates that H is a representative term in that most genes related to H cannot be shared by H 's children. In this study, we considered the GO terms with uniqueness >0.5 as representative. Also, in order to avoid uncertainty, the gene-functional categories with less than 10 genes were out of our consideration.
The given genes involve totally 3152 biological process GO terms. After filtering out the redundant and uncertain ones, we remained 621 representative GO terms for study. In KEGG dataset, totally 155 pathways are given. After rejecting the categories having no more than 10 genes, we finally left 124 pathways for analysis.
4.2 Results and evaluations
In the experiment, we first evaluated the classification capability of the selected gene functional categories. That is, based on a set of selected gene functional categories, we built the classifiers and evaluated the quality of the tested gene category set according to the performance of these classifiers. Considering that a category contains redundant or irrelevant genes, we did not employ all involved genes for building classifiers. Instead, from a selected category, we identified the best gene to represent it. The best gene here means the gene with the high classification capability. There are many ways to measure the classification capability of genes, such as signal-to-noise ratio, t-test and MI. We used MI to identify representative gene of a category (say, C) in a way of
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Besides the view of machine learning, we evaluated the obtained results from the biological view. Prostate cancer has been studies for many years. Many conclusions have been published and clinically confirmed. SuperArray Bioscience Corporation presents a relatively comprehensive summary in which 263 genes are suggested to be (potentially) responsible for prostate cancer (http://www.superarray.com/gene_array_product/HTML/OHS-403.html). Below, these prostate-cancer-related genes are called as PCR genes.
Based on PCR genes, we extracted the PCR annotations and PCR pathways by using a popular statistics framework. Concretely, given a functional annotation, say C, we recorded the number of genes given in the gene expression dataset are mentioned in C. We also counted the number of genes, out of the 263 PCR genes, could be associated to C. With these values and under the scheme of hyper-geometric distribution, the significance P-value of C enriched by the PCR gene list was computed. A small P-value means that C is significantly related to prostate cancer. We adjusted the obtained P-values to account for multiple hypothesis test using a false discovery rate (FDR) scheme (Benjamini, 2001). Then, with the condition that a PCR annotation has adjusted P-value < 0.05 and contains at least five genes, we obtained 58 PCR annotations in total. Similarly, we identified 13 PRC pathways. The 13 PCR pathways and the 58 PCR annotations are the basis of our evaluation. Our PCR annotation list includes many widely-recognized PCR cellular processes, for example, the apoptosis related ones (GO:0006916 anti-apoptosis and GO:0008637 apoptotic mitochondrial changes), the insulin related ones (GO:0008286 insulin receptor signaling pathway), the cell growth/proliferation related ones (GO:0008284 positive regulation of cell proliferation, GO:0016049 cell growth). Our PCR pathway list also contains the pathways that have been stated to play important roles in prostate cancers, such as apoptosis (path:hsa04210), MAPK signaling pathway (path:hsa04010) and Focal adhesion (path:hsa04510). In the Supplementary Material, the full lists of PCR annotation and pathways are given.
To evaluate a selection result, we calculated the amount of the PCR annotation/pathway included. In the cases that GO annotations are involved, the hierarchical relationship between annotations was considered. That is, a category was marked as PCR, either when it is a PCR annotation or when it is the no-more-than-2-generations ancestor/descendant of a PCR annotation. Clearly, the more PCR items a selection result has, the better that result is. In Figure 4, the comparative results are illustrated. By these results, the advantages of our method can be clearly indicated. Also, in Tables 2 and 3, detailed results of our method are listed. The PCR items are marked by a symbol of asterisk. The obtained results are remarkably encouraging since many selected annotations/pathways are either in the PCR annotation/pathway list or supported by the published clinical results.
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5 Conclusions |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS ON SYNTHETIC...4 RESULTS ON PROSTATE...5 ConclusionsACKNOWLEDGEMENTSREFERENCES |
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In this article, we present a method to identify the relevant gene functional categories. In this method, the category–category relationship is taken into account. Contributed by this capability, the proposed approach can deliver the improved results. Our method currently employs a correlation-based index to evaluate a category set. In the further work, we will develop new evaluation indices based on sophisticated concepts, such as MI, in order to further enhance the selection performance.
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ACKNOWLEDGEMENTS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS ON SYNTHETIC...4 RESULTS ON PROSTATE...5 ConclusionsACKNOWLEDGEMENTSREFERENCES |
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The work described in this article was wholly supported by a grant by CityU of Project No. 7001998-570.
Conflict of Interest: none declared.
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FOOTNOTES |
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Associate Editor: Alfonso Valencia
Received on July 10, 2006; revised on April 2, 2007; accepted on April 6, 2007
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