Clustering of change patterns using Fourier coefficients
Clustering of change patterns using Fourier coefficients
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DOI：
10.1093/bioinformatics/btm568
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发表时间：
2008-01-15
期刊：
影响因子：
5.8
通讯作者：
Kim, Haseong
中科院分区：
文献类型：
--
作者：
Kim, Jaehee;Kim, Haseong
动机：要了解基因的行为，很重要的一点是探索基因表达模式在一段时间内如何变化，因为生物相关的基因组可以共享相同的变化模式。人们已经提出了许多聚类算法来对观测数据进行分组。然而，由于底层功能的复杂性，关于基于变化模式的数据分组的研究并不多。在本研究中，寻找相似变化模式的问题被归结为利用导数傅立叶系数进行聚类。样本傅立叶系数不仅提供了关于基本函数的信息，而且还降低了维度。此外，由于它们的极限分布是多元正态分布，结合统计属性的基于模型的聚类方法是合适的。结果：本工作的目的是发现具有相似变化模式的具有相似生物学特性的基因组。我们开发了一个使用导数傅立叶系数的统计模型来识别相似的基因表达变化模式。我们使用一种基于模型的方法对导数的傅里叶级数估计进行聚类。在我们提出的模型中，基于模型的方法比其他方法更有优势，因为样本傅立叶系数渐近服从多元正态分布。在我们的模型中，变化模式是用傅立叶表示法自动估计的。我们的模型在模拟和真实基因数据集上进行了测试。仿真结果表明，基于样本傅里叶系数的基于模型的聚类方法比K-均值聚类具有更低的聚类错误率。即使在重复时间点很少的情况下，也可以得到相同的结果。我们还将我们的模型应用于酵母细胞周期微阵列表达数据的变化模式与阿尔法因子同步的聚类。结果表明，与概率邻域数据聚类方法一样，基于模型的聚类结果具有生物学上的可解释性。我们期望我们提出的傅立叶分析可以作为一种有用的工具来对基因进行分类和解释可能的生物变化模式。
Motivation: To understand the behavior of genes, it is important to explore how the patterns of gene expression change over a time period because biologically related gene groups can share the same change patterns. Many clustering algorithms have been proposed to group observation data. However, because of the complexity of the underlying functions there have not been many studies on grouping data based on change patterns. In this study, the problem of finding similar change patterns is induced to clustering with the derivative Fourier coefficients. The sample Fourier coefficients not only provide information about the underlying functions, but also reduce the dimension. In addition, as their limiting distribution is a multivariate normal, a model-based clustering method incorporating statistical properties would be appropriate.Results: This work is aimed at discovering gene groups with similar change patterns that share similar biological properties. We developed a statistical model using derivative Fourier coefficients to identify similar change patterns of gene expression. We used a model-based method to cluster the Fourier series estimation of derivatives. The model-based method is advantageous over other methods in our proposed model because the sample Fourier coefficients asymptotically follow the multivariate normal distribution. Change patterns are automatically estimated with the Fourier representation in our model. Our model was tested in simulations and on real gene data sets. The simulation results showed that the model-based clustering method with the sample Fourier coefficients has a lower clustering error rate than K-means clustering. Even when the number of repeated time points was small, the same results were obtained. We also applied our model to cluster change patterns of yeast cell cycle microarray expression data with alpha-factor synchronization. It showed that, as the method clusters with the probability-neighboring data, the model-based clustering with our proposed model yielded biologically interpretable results. We expect that our proposed Fourier analysis with suitably chosen smoothing parameters could serve as a useful tool in classifying genes and interpreting possible biological change patterns.