Inference from Clustering with Application to Gene-Expression Microarrays

Abstract

There are many algorithms to cluster sample data points based on nearness or a similarity measure. Often the implication is that points in different clusters come from different underlying classes, whereas those in the same cluster come from the same class. Stochastically, the underlying classes represent different random processes. The inference is that clusters represent a partition of the sample points according to which process they belong. This paper discusses a model-based clustering toolbox that evaluates cluster accuracy. Each random process is modeled as its mean plus independent noise, sample points are generated, the points are clustered, and the clustering error is the number of points clustered incorrectly according to the generating random processes. Various clustering algorithms are evaluated based on process variance and the key issue of the rate at which algorithmic performance improves with increasing numbers of experimental replications. The model means can be selected by hand to test the separability of expected types of biological expression patterns. Alternatively, the model can be seeded by real data to test the expected precision of that output or the extent of improvement in precision that replication could provide. In the latter case, a clustering algorithm is used to form clusters, and the model is seeded with the means and variances of these clusters. Other algorithms are then tested relative to the seeding algorithm. Results are averaged over various seeds. Output includes error tables and graphs, confusion matrices, principal-component plots, and validation measures. Five algorithms are studied in detail: K-means, fuzzy C-means, self-organizing maps, hierarchical Euclidean-distance-based and correlation-based clustering. The toolbox is applied to gene-expression clustering based on cDNA microarrays using real data. Expression pro le graphics are generated and error analysis is displayed within the context of these pro le graphics. A large amount of generated output is available over the web.

Mechanical injury of cartilage explants causes specific time‐dependent changes in chondrocyte gene expression

“…To distinguish the main expression trends, a k-means clustering algorithm was applied to the injury time-course data (28)(29)(30)(31). Each gene was grouped on the basis of correlations between the time-course expression profile and a set of randomly chosen starting genes.…”

Gene expression profiles of human chondrocytes during passaged monolayer cultivation

“…17,19 Each gene expression profile was normalized by the mean of all three passages. The standardized expression profiles were then iteratively clustered using a k means clustering technique with a Euclidean distance metric.…”

Multi-Timescale Complex Adaptation

“…The assumption that genes that are regulated similarly will have similar expression profiles allows genes to be grouped on the basis of similarities in their expression time courses (synexpression groups, Niehrs and Pollet, 1999). Many approaches for clustering gene expression data have been described (Sherlock, 2000;Dougherty et al, 2002).…”

“…In cases where information about more complex modes of regulation is available, h(⋅) can be made more complex as necessary. For example, it is straightforward to integrate computational models that describe how regulators of TF activity are regulated by extracellular signals and/or intracellular signaling (Ramkrishnan et al, 2002;Neves and Iyengar, 2002;Bhalla, 2003), or how TF activity is regulated in specific cellular process (Chen et al, 2002), into h(⋅). One demonstration of this integration may be found in Jin et al (2003), although the authors do not use a structured modeling approach in their study.…”