Fast Minimum Spanning Tree Based Clustering Algorithms on Local Neighborhood Graph

Abstract

Abstract. Minimum spanning tree (MST) based clustering algorithms have been employed successfully to detect clusters of heterogeneous nature. Given a dataset of n random points, most of the MST-based clustering algorithms first generate a complete graph G of the dataset and then construct MST from G. The first step of the algorithm is the major bottleneck which takes O(n 2 ) time. This paper proposes two algorithms namely MST-based clustering on K-means Graph and MST-based clustering on Bi-means Graph for reducing the computational overhead. The proposed algorithms make use of a centroid based nearest neighbor rule to generate a partition-based Local Neighborhood Graph (LN G). We prove that both the size and the computational time to construct the graph (LN G) is O(n 3/2 ), which is a O( √ n) factor improvement over the traditional algorithms. The approximate MST is constructed from LN G in O(n 3/2 lg n) time, which is asymptotically faster than O(n 2 ). The advantage of the proposed algorithms is that they do not require any parameter setting which is a major issue in many of the nearest neighbor finding algorithms. Experimental results demonstrate that the computational time has been reduced significantly by maintaining the quality of the clusters obtained from the MST.

Potts Clustering with Complete Shrinkage: a novel clustering methodology with its Software Package pottscompleteshrinkage in Python

“…Clustering is the method of categorising data into groups or clusters such that objects within a cluster have a high degree of similarity to one another but are quite different from objects in other clusters. The term cluster analysis itself encompasses a number of different algorithms and methods (Tree Clustering [Lin et al (2018), Liu et al (2005), Freeman (2006), Ahmed et al (2011), Lv et al (2018b), Freeman (2007), WANG et al (2009), Buttrey & Whitaker (2015), Qiu & Li (2021), Jothi et al (2015), Page (1974), Vathy-Fogarassy et al (2005), Miller & Rose (1994)], Block Clustering, k-Means Clustering Wilkin & Huang (2007) and EM algorithms) for grouping objects of similar kind into respective categories, graph-based clustering (Bai et al (2017)), hierarchical clustering (Köhn & Hubert (2014)), model-based clustering (Fraley & Raftery (1998), Fraley & Raftery (1999), Fraley & Raftery (2002)); Lloyd's K-means clustering and the progressive greedy K-means clustering (Wilkin & Huang (2007)).…”

Comparative study between deep learning and bag of visual words for wild-animal recognition

“…In a quest to improve recognition performance, the use of classical image descriptors such as the Bag-of-VisualWords (BOW) has been applied to different fields. BOW involves the extraction of features [6], [7] and construction of a codebook using an unsupervised learning algorithm such as Kmeans clustering [8], spectral clustering [9], local constrained linear coding for pooling clusters [10], and the use of the fast minimum spanning tree [11]. Finally, the extraction of feature vectors by the BOW approach can be achieved using a soft assignment scheme [12] or sparse ensemble learning methods [13].…”