Replicator Graph Clustering

Abstract

In this paper we introduce an efficient, effective and scalable clustering method denoted as Replicator Graph Clustering. Our method takes measures of similarity between pairs of data points (i. e. an affinity matrix) as input and identifies a set of clusters and unique cluster assignments in a fully unsupervised manner, where the cluster granularity is adaptable by a single parameter. We provide clustering results in three subsequent steps: (a) diffusing affinities by finding personalized evolutionary stable strategies of non-cooperative games (b) building a mutual k-nearest neighbor graph representing the underlying manifold and (c) applying a graph based clustering strategy which identifies the final clusters. Individual steps have low computational complexity which leads to an efficient clustering method, scaling well with an increasing number of data points. Experimental evaluation demonstrates competitive performance to state-of-the-art in several application fields.

Deep Feature Aggregation and Image Re-Ranking With Heat Diffusion for Image Retrieval

“…Anisotropic diffusion has been applied to many computer vision problems, such as image segmentation [8], [9], saliency detection [12], [13], and clustering [14], [15]. In these applications, diffusion is used for finding central points by capturing the intrinsic manifold structure of the data.…”

“…This means we only need to store k + 1 image vectors (query as well as k results), and matrices of size k × k contained in Eq. (14). In practice, both image vector dimensions and k are relatively small (a few hundreds), showing the low memory usage of HeR.…”

Geometry-Aware Neighborhood Search for Learning Local Models for Image Superresolution

“…As our study has close links with the clustering of lowdimensional data, we now give a brief overview of some clustering methods for data on manifolds. The RGC method [18], from which the proposed AGNN method has been inspired, first constructs a data graph. An initial affinity matrix is then computed based on the pairwise similarities between data samples.…”

“…: Set of training samples yj ∈ Y: Test sample c1, c2, κ: Algorithm parameters 2: AGNN Algorithm: 3: Form affinity matrix A of training samples with respect to (6). 4: Diffuse the affinities in A to obtain A * as proposed in the RGC method [18]. 5: Initialize the affinity vector a between test sample yj and the training samples as in (8).…”

“…We first present an adaptive scheme, called Adaptive Geometry-driven Nearest Neighbor search (AGNN). Our method is inspired by the Replicator Graph Clustering (RGC) [18] algorithm and can be regarded as an out-of-sample extension of RGC for local model learning. Given a test sample, the AGNN method computes a diffused affinity measure between each test sample and the training samples in a manner that is coherent with the overall topology of the data graph.…”