[논문]Cluster Analysis of Incomplete Microarray Data with Fuzzy Clustering

Kim, Dae-Won

doi:10.5391/jkiis.2007.17.3.397

Cluster Analysis of Incomplete Microarray Data with Fuzzy Clustering 원문보기

퍼지 및 지능시스템학회 논문지 = Journal of fuzzy logic and intelligent systems, v.17 no.3, 2007년, pp.397 - 402

Kim, Dae-Won (School of Computer Science and Engineering, Chung-Ang University)

Abstract ▼ AI-Helper

In this paper, we present a method for clustering incomplete Microarray data using alternating optimization in which a prior imputation method is not required. To reduce the influence of imputation in preprocessing, we take an alternative optimization approach to find better estimates during iterative clustering process. This method improves the estimates of missing values by exploiting the cluster Information such as cluster centroids and all available non-missing values in each iteration. The clustering results of the proposed method are more significantly relevant to the biological gene annotations than those of other methods, indicating its effectiveness and potential for clustering incomplete gene expression data.

주제어

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가설 설정

The objective of the proposed method is to classify a data set X = {xi, x2, . .

제안 방법

[1], 3, 020 significant genes obtained through two-fold change were used. The data set was preprocessed for the test by randomly removing 5-25% (5, 10, 15, and 25) of the data in order to create incomplete matrices. To cluster these incomplete data sets with conventional methods, we first estimated the missing values using the widely used KNNimpute [11] and EMimpute [12, 13].
To find better estimates of missing values and improve the clustering result during iterative clustering process, in each iteration we exploit the information of current clusters such as cluster centroids and all available non-missing values. For example, a missing value Xji is estimated using the corresponding /-th attribute value of the cluster centroid to whicli Xj is closest in each iteration.
For example, a missing value Xji is estimated using the corresponding /-th attribute value of the cluster centroid to whicli Xj is closest in each iteration. To improve the estimates during each deration, the proposed method attempts to optimize the objective function with respect to the missing values, which is often refen'ed to as the alternating optimization (AO) scheme. The objective of the proposed method is obtained by minimizing the function Jm:

이론/모형

The z-score is calculated by investigating the relation between a clustering result and the functional annotation of the genes in the cluster. To achieve this, this score uses the Saccharomyces Genome Database (SGD) annotation of the yeast 응enes, along with the gene ontology developed by the Gene Ontology Consortium [20, 21]. A higher score of z indicates that genes are better clustered by function, indicating a more biologically significant clustering result.
pointed out [12], the RMSE is limited to study the impact of missing value imputation on cluster analysis. To make this study more informative regarding how large an impact the imputation method has on cluster analysis, in the present work the clustering results obtained using the alternative imputations were evaluated by compaiing gene annotations using the z-score [19, 12]. The z-score is calculated by investigating the relation between a clustering result and the functional annotation of the genes in the cluster.

성능/효과

sets. From the comparison results for the sporulation data, the KNNimp니耸 gave better RMSE at lower missing values whereas the proposed method gave better RMSE at higher missing values. The EMimpute shows the most ineffective of the methods considered.
5. In comparison to these methods, it is evident that the proposed clustering method shows markedly better performance, giving z-scores of more than 48.5 for all missing values; it provided significantly better clustering performance than other methods, giving z 二二 55.0 at 5% and z 二二 51.9 at 10%.
By taking the alternative optimization approach, the missing values are considered as additional parameters for optimization. The evaluation results based on gene annotations have shown that the proposed method is the superior and effective method for clustering incomplete gene expression data. Besides the issues mentioned in present work, we initialized missing values with the con*esponding attributes of the cluster centroid to which the incomplete data point is closest.
The results of the ccmparison tests indicate that the proposed method gave rrarkedly better clustering performance than the other irrputation-based methods considered, highlighting the effectiveness and potential of the proposed method.

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