Graph-Based k-Means Clustering: A Comparison of the Set Median versus the Generalized Median Graph

Ferrer, Miquel; Valveny, Ernest; Serratosa, Francesc; Bardají, Itziar; Bunke, Horst

doi:10.1007/978-3-642-03767-2_42

Cited by 27 publications

(27 citation statements)

References 24 publications

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“…Nevertheless, the proposed approach takes into account all graphs of the given set in the recovery of the median graph from the median vector. This is in contrast with previous approaches [3,4], where only a small subset is used for the reconstruction. Due to the larger set of graphs, we may expect to obtain a better approximation of the median graph by this procedure.…”

Section: Introductionmentioning

confidence: 79%

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A generic framework for median graph computation based on a recursive embedding approach

Ferrer

Karatzas

Valveny

et al. 2011

Computer Vision and Image Understanding

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The median graph has been shown to be a good choice to obtain a representative of a set of graphs. However, its computation is a complex problem. Recently, graph embedding into vector spaces has been proposed to obtain approximations of the median graph. The problem with such an approach is how to go from a point in the vector space back to a graph in the graph space. The main contribution of this paper is the generalization of this previous method, proposing a generic recursive procedure that permits to recover the graph corresponding to a point in the vector space, introducing only the amount of approximation inherent to the use of graph matching algorithms. In order to evaluate the proposed method, we compare it with the set median and with the other state-of-the-art embedding-based methods for the median graph computation. The experiments are carried out using four different databases (one semi-artificial and three containing real-world data). Results show that with the proposed approach we can obtain better medians, in terms of the sum of distances to the training graphs, than with the previous existing methods.

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Section: Introductionmentioning

confidence: 79%

“…It can be seen as the representative of the set. In fact, it has been successfully applied in classical learning algorithms such as k-means clustering [3] and kNN-based classification [4]. Moreover, it can be potentially applied to any graph-based algorithm where a representative of a set of graphs in needed.…”

Section: Introductionmentioning

confidence: 99%

A generic framework for median graph computation based on a recursive embedding approach

Ferrer

Karatzas

Valveny

et al. 2011

Computer Vision and Image Understanding

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“…An example of such an approach is the k-medians algorithm [10], which employs graph edit distance as a measure of graph similarity. Other approaches take advantage of graph kernels [17], where kernel-based algorithms are applied to graphs.…”

Section: Graph-based Anomaly Detectionmentioning

confidence: 99%

Node Re-Ordering as a Means of Anomaly Detection in Time-Evolving Graphs

Rashidi

Kan

Bailey

et al. 2016

Machine Learning and Knowledge Discovery in Databases

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Abstract. Anomaly detection is a vital task for maintaining and improving any dynamic system. In this paper, we address the problem of anomaly detection in time-evolving graphs, where graphs are a natural representation for data in many types of applications. A key challenge in this context is how to process large volumes of streaming graphs. We propose a pre-processing step before running any further analysis on the data, where we permute the rows and columns of the adjacency matrix. This pre-processing step expedites graph mining techniques such as anomaly detection, PageRank, or graph coloring. In this paper, we focus on detecting anomalies in a sequence of graphs based on rank correlations of the reordered nodes. The merits of our approach lie in its simplicity and resilience to challenges such as unsupervised input, large volumes and high velocities of data. We evaluate the scalability and accuracy of our method on real graphs, where our method facilitates graph processing while producing more deterministic orderings. We show that the proposed approach is capable of revealing anomalies in a more efficient manner based on node rankings. Furthermore, our method can produce visual representations of graphs that are useful for graph compression.

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“…In particular LD-ABCD identifies clusters on a dataset that is represented through a labeled graph: graph clustering is a well-known problem and it has been addressed in many other works [10,46,18,20,21,38]. Such clusters are discovered by different agents, which operate according to a paradigm inspired by the multi-agent systems that can be found in the literature [6,36,13,12,16,2,38].…”

Section: Related Workmentioning

confidence: 99%

“…Clustering [27,37,11,39,9,26,51] is a well-established approach that can be used to this end. Among the many solutions available in this field, it is worth citing those clustering techniques based on graph-theoretical results and multi-agent systems [10,46,18,20,21,6,38,1,22]. Graph-based techniques have the fundamental advantage of mapping the original problem onto a "dimensionless" object: the graph.…”

Section: Introductionmentioning

confidence: 99%

An agent-based algorithm exploiting multiple local dissimilarities for clusters mining and knowledge discovery

et al. 2015

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We propose a multi-agent algorithm able to automatically discover relevant regularities in a given dataset, determining at the same time the set of configurations of the adopted parametric dissimilarity measure yielding compact and separated clusters. Each agent operates independently by performing a Markovian random walk on a suitable weighted graph representation of the input dataset. Such a weighted graph representation is induced by the specific parameter configuration of the dissimilarity measure adopted by the agent, which searches and takes decisions autonomously for one cluster at a time.Results show that the algorithm is able to discover parameter configurations * Corresponding Author

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Graph-Based k-Means Clustering: A Comparison of the Set Median versus the Generalized Median Graph

Cited by 27 publications

References 24 publications

A generic framework for median graph computation based on a recursive embedding approach

A generic framework for median graph computation based on a recursive embedding approach

Node Re-Ordering as a Means of Anomaly Detection in Time-Evolving Graphs

An agent-based algorithm exploiting multiple local dissimilarities for clusters mining and knowledge discovery

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