Matrix Visualization and Information Mining

Chen, Chun-Houh; Hwu, Hai‐Gwo; Jang, Wen-Jung; Kao, Chiun-How; Tien, Yong Ming; Tzeng, ShengLi; Wu, Hanming

doi:10.1007/978-3-7908-2656-2_6

Cited by 18 publications

(19 citation statements)

References 24 publications

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“…Data is often represented in a matrix form, and research community has developed numerous methods for matrix visualization (Chen et al 2004;Wu et al 2010). In this contribution, we use banded matrices to visualize the data and the results of a data mining process in a way that the results become easily understandable to the domain specialist.…”

Section: Data Clustering and Visualization Using Banded Matricesmentioning

confidence: 99%

Explaining mixture models through semantic pattern mining and banded matrix visualization

et al. 2016

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This paper presents an approach to semi-automated data analysis, supported by tools for pattern construction, exploration and explanation. The proposed three-part methodology for multiresolution 0-1 data analysis consists of data clustering with mixture models, extraction of rules from clusters, as well as data and rule visualization using banded matrices. The results of the three-part process: clusters, rules from clusters, and banded structure of the data matrix are finally merged in a unified visual banded matrix display. The incorporation of multiresolution data is enabled by the supporting ontology, describing the relationships between the different resolutions, which is used as background knowledge in the semantic pattern mining process of descriptive rule induction. The presented experimental use case highlights the usefulness of the proposed methodology for analyzing complex DNA copy number amplification data, studied in previous research, for which we provide new insights in terms of induced semantic patterns and cluster/pattern visualization. The methodology is

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Section: Data Clustering and Visualization Using Banded Matricesmentioning

confidence: 99%

Explaining mixture models through semantic pattern mining and banded matrix visualization

et al. 2016

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“…In case of (0, 1)-matrices, the Robinson property is best known as the Consecutive One Property. Seriation is of importance in archeological dating [39,44,50], clustering hypertext orderings [11], numerical ecology [48,58], sparse matrix ordering [5], musicology [37], matrix visualization methods [18,19], and DNA sequencing [10,17,49]. For example, if biological experiments were error-free, the genomic reconstruction problem would be precisely testing the Consecutive One Property.…”

Section: Seriation Problemmentioning

confidence: 99%

Seriation in the Presence of Errors: A Factor 16 Approximation Algorithm for l ∞-Fitting Robinson Structures to Distances

Chepoi

Seston

2009

Algorithmica

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The classical seriation problem consists in finding a permutation of the rows and the columns of the distance (or, more generally, dissimilarity) matrix d on a finite set X so that small values should be concentrated around the main diagonal as close as possible, whereas large values should fall as far from it as possible. This goal is best achieved by considering the Robinson property: a distance d R on X is Robinsonian if its matrix can be symmetrically permuted so that its elements do not decrease when moving away from the main diagonal along any row or column. If the distance d fails to satisfy the Robinson property, then we are lead to the problem of finding a reordering of d which is as close as possible to a Robinsonian distance.In this paper, we present a factor 16 approximation algorithm for the following NP-hard fitting problem: given a finite set X and a dissimilarity d on X, we wish to find a Robinsonian dissimilarity d R on X minimizing the l ∞ -error d − d R ∞ = max x,y∈X {|d(x, y) − d R (x, y)|} between d and d R .

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“…Hurley (2004) [17] also studied related issues with examples in scatterplot matrix and parallel coordinate plots. Chen (2002) [5] called this concept the relativity of a statistical graph with discussions on several important aspects of the corresponding mechanism in ( [6], [27], [28], [29]). For the seriation problem, one has to decide which algorithms to be applied to rows and columns, based on Jaccard Coefficient…”

Section: Seriation Of Proximity Matrices and Raw Data Matrixmentioning

confidence: 99%

“…There are three major tasks in a GAP ( [5], [6], [28], [29]) approach matrix visualization: color coding for raw data matrix with calculation of two corresponding proximity matrices, for columns (variables) and rows (subjects). There are essentially two types of binary data, symmetric and asymmetric.…”

Section: Introductionmentioning

confidence: 99%

“…Matrix visualization ( [3], [5], [6], [14], [27], [28], [29]) is a graphical technique for visualizing and exploring simultaneously the associations of subjects, variables and their interactions. In addition to helping answer whether the grouping of subjects is meaningful, it also shows which variables are highly correlated to each other due to similarity of their subject distributions.…”

Section: Introductionmentioning

confidence: 99%

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Selection of Proximity Measures for Matrix Visualization of Binary Data

Tzeng¹,

Chen

2009

2009 2nd International Conference on Biomedical Engineering and Informatics

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Exploratory data analysis (EDA: Tukey, 1977) has been introduced and extensively used for more than 30 years yet boxplot and scatterplot are still the major EDA tools for visualizing continuous data in the 21st century. On the other hand, multiple correspondence analysis (MCA) type of methods and mosaic plots are most popular in practice for visualizing multivariate binary and nominal data. But all these methods loose their efficiency when data dimensionality gets really high (hundreds/thousands), particularly when data is of non-continuous nature.Matrix visualization (MV) instead can simultaneously explore the associations of up to thousands of variables, subjects, and their interactions, without reducing dimension. MV permutes rows and columns of the raw data matrix together with two corresponding proximity matrices by suitable seriation (reordering) algorithms. These permuted matrices are then displayed as matrix maps through suitable color spectra for extracting the subject-clusters, variablegroups, and the subjects/variables interaction patterns.For binary data, conventional visualization techniques (boxplot, scatterplot (matrix), mosaic display, parallel coordinate plot, etc.) basically cannot provide users much visual information while the binary generalized association plots (bGAP), by integrating matrix visualization with suitably chosen proximity for binary data, can effectively present complex patterns for thousands of binary variables for thousands of subjects in one matrix visualization.

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Matrix Visualization and Information Mining

Cited by 18 publications

References 24 publications

Explaining mixture models through semantic pattern mining and banded matrix visualization

Explaining mixture models through semantic pattern mining and banded matrix visualization

Seriation in the Presence of Errors: A Factor 16 Approximation Algorithm for l ∞-Fitting Robinson Structures to Distances

Selection of Proximity Measures for Matrix Visualization of Binary Data

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