A Fuzzy Graph Framework for Initializing k-Means

Abstract

k-Means is among the most significant clustering algorithms for vectors chosen from an underlying space S. Its applications span a broad range of fields including machine learning, image and signal processing, and Web mining. Since the introduction of k-Means, two of its major design parameters remain open to research. The first is the number of clusters to be formed and the second is the initial vectors. The latter is also inherently related to selecting a density measure for S. This article presents a two-step framework for estimating both parameters. First, the underlying vector space is represented as a fuzzy graph. Afterwards, two algorithms for partitioning a fuzzy graph to non-overlapping communities, namely Fuzzy Walktrap and Fuzzy Newman-Girvan, are executed. The former is a low complexity evolving heuristic, whereas the latter is deterministic and combines a graph communication metric with an exhaustive search principle. Once communities are discovered, their number is taken as an estimate of the true number of clusters. The initial centroids or seeds are subsequently selected based on the density of S. The proposed framework is modular, allowing thus more initialization schemes to be derived. The secondary contributions of this article are HI, a similarity metric for vectors with numerical and categorical entries and the assessment of its stochastic behavior, and TD, a metric for assessing cluster confusion. The aforementioned framework has been implemented mainly in C# and partially in C++ and its performance in terms of efficiency, accuracy, and cluster confusion was experimentally assessed. Post-processing results conducted with MATLAB indicate that the evolving community discovery algorithm approaches the performance of its deterministic counterpart with considerably less complexity.

Agrupamento De Dados Mistos Baseados No Algoritmo K-Means: Uma Revisão Sistemática Da Literatura

“…Bishnu and Bhattacherjee (2016) apresentaram uma generalização do k-modes para dados mistos com o objetivo de aplicar o algoritmo proposto em uma análise de custo de software. Drakopoulos et al (2016) abordaram o problema de inicialização dos centroides no k-means para dados mistos por meio de algoritmos fuzzy que dividem o conjunto de dados em grids e pela densidade determinam o ponto de centroide. Além disso, o artigo também propõe um índice de qualidade externo de agrupamento para dados mistos.…”

Blockchain For Mobile Health Applications: Acceleration With GPU Computing

“…The advantages of and the ways for visualising the TensorFlow computations are Wongsuphasawat et al (2018). For tensor applications in social network analysis such as multiway digital influence estimation see Drakopoulos et al (2017), community structure discovery Drakopoulos et al (2018a), and graph based k-means initialization Drakopoulos et al (2016). Finally, for a genetic algorithm for clustering tensors containing linguistic and spatial data see Drakopoulos et al (2019).…”

Extending Fuzzy Cognitive Maps with Tensor-Based Distance Metrics

“…Given that the trained fuzzy cognitive maps can be represented as a fuzzy graph, clustering can be performed by fuzzy community discovery algorithms [27][28][29]. In Reference [30] fuzzy graphs have been used in a technique for estimating the number of clusters and their respective centroids. C-means fuzzy clustering has been applied to epistasis analysis [31] and image segmentation [32].…”