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Find articles by Rui Fa David J. The authors have declared that no competing interests exist. Conceived and designed the experiments: Received Nov 6; Accepted Mar This article has been cited by other articles in PMC.
Abstract Successful clustering algorithms are highly dependent on parameter settings. The clustering performance degrades significantly unless parameters are properly set, and yet, it is difficult to set these parameters a priori.
SMART: Unique Splitting-While-Merging Framework for Gene Clustering
Unlike existing self-splitting algorithms, which over-cluster the dataset to a large number of clusters and then merge some similar clusters, our framework has the ability to split and merge clusters automatically during the process and produces the the most reliable clustering results, by intrinsically integrating many clustering techniques art models 7-pdf split and merge tasks.
Nevertheless, within the proposed SMART framework, many other algorithms can be derived for different clustering paradigms. The minimum message length algorithm is integrated into the framework as the clustering selection criterion.
The usefulness of the SMART framework and its algorithms is tested in demonstration datasets and simulated gene expression datasets. Moreover, two real microarray gene expression datasets are studied using this approach.
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Based on the performance of many metrics, all numerical results show that SMART is superior to compared existing self-splitting algorithms and traditional algorithms. Introduction Clustering methods have been widely used in many fields, including biology, physics, computer science, communications, artificial intelligence, image processing, and art models 7-pdf split and merge research, requiring analysis of large quantities of data to explore the relationships between individual objects within the respective datasets  — .
However, clustering is one of the most difficult and challenging problems in the realm of machine learning due to the lack of universal and rigorous mathematical definition.
The definition of clustering often depends on the specific systems or problems, e. After some pioneering works by Eisen et al. There are many families of clustering algorithms used in the gene expression analysis, including partitional clustering, hierarchical clustering, model-based clustering, self-organizing clustering .
Results of most of successful clustering algorithms strongly depend on the determined number of clusters, e. However, in many cases, a priori knowledge of the actual number of clusters is not available.
Thus, the number of clusters has to be estimated beforehand.
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The problem of determining the best number of clusters needs to be addressed in another branch of research in clustering analysis, known as clustering validation  — .
Among various clustering validation criteria, clustering validity indices, also known as relative criteria, have been employed to quantitatively evaluate the goodness of a clustering result and estimate the best number of clusters. There are two main classes of validity indices: Once an appropriate clustering validity index is selected, the general practice for determining the best number of clusters has few steps: However, this solution requires an extensive search for the number of clusters and is tedious work for large number of clusters Moreover, the initialization of clustering is also a major issue.
For some algorithms art models 7-pdf split and merge the deterministic initialization, e. For some algorithms sensitive to initialization, such as k-means with random initialization, expectation-maximization EM and self-organization map SOM they may get stuck at local minimum. art models 7-pdf split and merge
Addressing this problem requires running the algorithm repeatedly with art models 7-pdf split and merge same dataset using several different initializations. This makes such clustering algorithms more computationally unfavourable. Thus, better options would be integrative frameworks or strategies which provide an automatic and consistent clustering, so users do not have to worry about setting those data-specific parameters.
Earliest attempts of automated clustering without employing any knowledge of number of clusters were growing cell structure  and growing neural gas .
Although these algorithms are useful to visualize high dimensional data, they are not suitable for clustering because they over-fit the data.