An automatic graph layout procedure to visualize correlated data

Abstract

Abstract. This paper introduces an automatic procedure to assist on the interpretation of a large dataset when a similarity metric is available. We propose a visualization approach based on a graph layout methodology that uses a Quadratic Assignment Problem (QAP) formulation. The methodology is presented using as testbed a time series dataset of the Standard & Poor's 100, one the leading stock market indicators in the United States. A weighted graph is created with the stocks represented by the nodes and the edges' weights are related to the correlation between the stocks' time series. A heuristic for clustering is then proposed; it is based on the graph partition into disconnected subgraphs allowing the identification of clusters of highly-correlated stocks. The final layout corresponds well with the perceived market notion of the different industrial sectors. We compare the output of this procedure with a traditional dendogram approach of hierarchical clustering.

An Information Theoretic Clustering Approach for Unveiling Authorship Affinities in Shakespearean Era Plays and Poems

“…We utilised an unsupervised graph-based clustering method called MST-kNN to cluster plays and poems in the data set generated by the Intelligent Archive. The non-parametric MST-kNN algorithm [21] (see also its external-memory variant in [22] and a GPU-based data-parallel variant in [23] , [24] and several applications in [25] – [28] ), takes as input a weighted undirected complete graph ( G ) and computes two proximity graphs: a minimum spanning tree ( ) and a k-nearest neighbour graph ( ), where the value of is automatically determined by Equation 1 . …”

An adaptive memetic algorithm for feature selection using proximity graphs

“…The RNG, which we denote as G RNG ( V , E RNG , W RNG ), is constructed as follows: an edge e i j is included in E RNG if and only if d i j ≤ max { d ix , d xj }, ∀ x ≠ i , j , where d i j is the distance between objects i and j . We refer the reader to more information about these proximity graphs (as well as the Gabriel graph and Delaunay triangulation) in the works of Bose et al and Inostroza‐Ponta et al…”

“…An edge e i j ∈ E is included in E k-NN if the distance between v i and v j is among the kth smallest distances from v i to other nodes in V. The RNG, which we denote as G RNG (V,E RNG ,W RNG ), is constructed as follows: an edge e i j is included in E RNG if and only if d i j ≤ max {d ix ,d xj }, ∀ x ≠ i, j, where d i j is the distance between objects i and j. We refer the reader to more information about these proximity graphs (as well as the Gabriel graph and Delaunay triangulation) in the works of Bose et al 23 and Inostroza-Ponta et al 25 Next, we explain how a proximity graph is constructed from a given data set. Let H m,n be an m × n matrix, where m represents the number of features, n indicates the number of samples, and h i j holds the value of feature i in sample j.…”

An Integrated QAP-Based Approach to Visualize Patterns of Gene Expression Similarity

“…From G C , the new QAP instance is created as was describe in section 2. To tackle the QAP problem, we use a memetic algorithm described in [10]. The memetic algorithm will produce a solution for the QAP, which will correspond to the layout of the data.…”

“…To find a solution to the QAP instances, we used the Memetic Algorithm described in [10]. The methods were coded in Java, and run in a Pentium IV (2,3 GHz) workstation.…”