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A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters
J. C. Dunn
- Vol. 3, pp 32-57
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TLDR
In this paper, two fuzzy versions of the k-means optimal, least squared error partitioning problem are formulated for finite subsets X of a general inner product space, and the extremizing solutions are shown to be fixed points of a certain operator T on the class of fuzzy, k-partitions of X, and simple iteration of T provides an algorithm which has the descent property relative to the LSE criterion function.Abstract:
Two fuzzy versions of the k-means optimal, least squared error partitioning problem are formulated for finite subsets X of a general inner product space. In both cases, the extremizing solutions are shown to be fixed points of a certain operator T on the class of fuzzy, k-partitions of X, and simple iteration of T provides an algorithm which has the descent property relative to the least squared error criterion function. In the first case, the range of T consists largely of ordinary (i.e. non-fuzzy) partitions of X and the associated iteration scheme is essentially the well known ISODATA process of Ball and Hall. However, in the second case, the range of T consists mainly of fuzzy partitions and the associated algorithm is new; when X consists of k compact well separated (CWS) clusters, Xi , this algorithm generates a limiting partition with membership functions which closely approximate the characteristic functions of the clusters Xi . However, when X is not the union of k CWS clusters, the limi...read more
Citations
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SC3: consensus clustering of single-cell RNA-seq data
Vladimir Yu. Kiselev,Kristina Kirschner,Michael T. Schaub,Michael T. Schaub,Tallulah S. Andrews,Andrew Yiu,Tamir Chandra,Tamir Chandra,Kedar Nath Natarajan,Kedar Nath Natarajan,Wolf Reik,Wolf Reik,Wolf Reik,Mauricio Barahona,Anthony R. Green,Martin Hemberg +15 more
TL;DR: It is demonstrated that SC3 is capable of identifying subclones from the transcriptomes of neoplastic cells collected from patients and achieves high accuracy and robustness by combining multiple clustering solutions through a consensus approach.
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Some new indexes of cluster validity
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An extensive comparative study of cluster validity indices
TL;DR: The results of an experimental work that compares 30 cluster validity indices in many different environments with different characteristics can serve as a guideline for selecting the most suitable index for each possible application and provide a deep insight into the performance differences between the currently available indices.
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A Robust Fuzzy Local Information C-Means Clustering Algorithm
TL;DR: A variation of fuzzy c-means (FCM) algorithm that provides image clustering that incorporates the local spatial information and gray level information in a novel fuzzy way, called fuzzy local information C-Means (FLICM).
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A Convergence Theorem for the Fuzzy ISODATA Clustering Algorithms
TL;DR: The theory of Zangwill is used to prove that arbitrary sequences generated by these (Picard iteration) procedures always terminates at a local minimum, or at worst, always contains a subsequence which converges to aLocal minimum of the generalized least squares objective functional which defines the problem.
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