MOSAIC: A Proximity Graph Approach for Agglomerative Clustering

Abstract

Representative-based clustering algorithms are quite popular due to their relative high speed and because of their sound theoretical foundation. On the other hand, the clusters they can obtain are limited to convex shapes and clustering results are also highly sensitive to initializations. In this paper, a novel agglomerative clustering algorithm called MOSAIC is proposed which greedily merges neighboring clusters maximizing a given fitness function. MOSAIC uses Gabriel graphs to determine which clusters are neighboring and approximates non-convex shapes as the unions of small clusters that have been computed using a representative-based clustering algorithm. The experimental results show that this technique leads to clusters of higher quality compared to running a representative clustering algorithm standalone. Given a suitable fitness function, MOSAIC is able to detect arbitrary shape clusters. In addition, MOSAIC is capable of dealing with high dimensional data.

Locally-scaled spectral clustering using empty region graphs

“…Carreira and Zemel apply an ensemble of minimum spanning trees to form neighborhood graphs that are more resilient to noise and varying densities [4]. Choo et al propose an agglomerate method for hierarchical clustering that merges candidate clusters that belong to the same connected component in the Gabriel graph [5].…”

A Framework for Multi-Objective Clustering and Its Application to Co-Location Mining

“…A family of clustering algorithms that support such fitness functions (CLEVER [5], SCMRG [6], and MOSAIC [7]) has been designed and implemented in our past research. Our approach measures the quality of a clustering X={x 1 ,..,x k } as the sum of rewards obtained for each cluster x i (i=1,…,k) using the reward function Reward q .…”

Towards Region Discovery in Spatial Datasets

“…In our previous work, we have defined fitness functions to search risk zones of earthquakes [4] and volcanoes [5] with respect to a single categorical attribute.…”

“…Agglomerative clustering algorithms are capable of yielding solutions with clusters of arbitrary shape by constructing unions of small convex polygons. We adapt the MOSAIC algorithm [5] that takes a set of small convex clusters as its input and greedily merges neighboring clusters as long as q(R) improves. In our experiments the inputs are generated by the SPAM algorithm.…”

“…These most relevant to our work are region-oriented clustering techniques and hotspot discovery. In our previous work, we have discussed a region discovery method that was restricted to one categorical attribute [4,5]. The integrated framework introduced in this paper is generalized to be applicable to both continuous and discrete datasets.…”