Geodesic Based Similarities for Approximate Spectral Clustering

Abstract

Spectral clustering has been successfully used in various applications, thanks to its properties such as no requirement of a parametric model, ability to extract clusters of different characteristics and easy implementation. However, it is often infeasible for large datasets due to its heavy computational load and memory requirement. To utilize its advantages for large datasets, it is applied to the dataset representatives (either obtained by quantization or sampling) rather than the data samples, which is called approximate spectral clustering. This necessitates novel approaches for defining similarities based on representatives exploiting the data characteristics, in addition to the traditional Euclidean distance based similarities. To address this challenge, we propose similarity measures based on geodesic distances and local density distribution. Our experiments using datasets with varying cluster statistics show that the proposed geodesic based similarities are successful for approximate spectral clustering with high accuracies.

An Approximate Spectral Clustering Ensemble for High Spatial Resolution Remote-Sensing Images

“…However, for ASC, new information types such as topology, density can be embedded into S for more effective definition for pairwise similarities of the data representatives [12], [17], [34]. A recent approach [12] uses a similarity measure (CONN) that exploits local density together with data topology on the representative level.…”

“…Recently, geodesic-based approaches are also proposed for ASC [13], [17]. To calculate geodesic distances, a preliminary step is to determine a neighborhood graph showing the neighbor representatives in the manifold.…”

“…The parameter k should be optimally set; however, k may be different for each representative. As a topology-based alternative reflecting local characteristics, CONN can be used for neighborhood graph in calculating geodesic distances to find specific number of neighbors for each representative [17]. The geodesic distance d geoadj based on CONN graph using Euclidean distances d Euc is calculated as…”

“…Due to its computational complexity, SC is performed for high spatial resolution remote-sensing images through a two-step approach called approximate SC (ASC), i.e., the SC is applied to the data representatives selected by sampling or quantization [10], [12]- [16]. The ASC enables the advantages of SC for large remote-sensing images and integrates different information types (such as distance, density, and topology) to produce an effective information representation for extraction of precise cluster structure [17]. However, it necessitates an optimum selection for similarity definition tailored to the application requirements.…”

“…First, we obtain the data representatives using neural gas [25] (instead of Nystrom approximation), to get smaller quantization errors and address out-of-sample labeling problem. Second, we use the recent similarity definitions [13], [17] exploiting various information types, rather than the traditional distance-based Gauss kernel with different parameter values. Third, we have a two-level ensemble method which obtains a fused decision for each similarity criterion and then merges these decisions into a consensus label.…”