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Title:
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POLAR SORT: COMBINING MULTIDIMENSIONAL
SCALING AND POLAR COORDINATES
FOR MATRIX REORDERING |
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Author(s):
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Celmar Guimarães da Silva |
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ISBN:
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978-989-8533-91-3 |
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Editors:
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Katherine Blashki and Yingcai Xiao |
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Year:
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2019 |
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Edition:
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Single |
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Keywords:
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Heatmaps, Information Visualization, Visualization Design and Evaluation Methods |
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Type:
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Full Paper |
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First Page:
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239 |
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Last Page:
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246 |
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Language:
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English |
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Cover:
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Full Contents:
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click to dowload 
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Paper Abstract:
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Matrix reordering algorithms aim to permute rows and columns of a matrix (or a matrix-based visualization, such as a
heatmap) in order to reveal data patterns that could not be perceivable in some orderings of its columns and rows. Finding
a good permutation, according to some evaluation criteria, is not straightforward, and many approaches try to find out a
good tradeoff between algorithm execution time and output quality. This work argues that using multidimensional scaling
and polar coordinates helps to find row and column orderings that reveal Band and Circumplex patterns if they are
present in some permutation of a matrix. The proposed O(n3) method Polar Sort uses classical MDS to find an initial
2-dimensional projection of rows (or columns) of the input matrix. After that, the method sorts the projected points
according to their angular coefficients in a polar coordinate system whose center is the barycenter of these points. The
algorithm then replicates this order to the correspondent rows (or columns). Experiments with synthetic data indicates
that Polar Sort produces high-quality results for uncovering Band and Circumplex patterns, and that its mean execution
time is as fast as the fastest tested methods for matrices with size 200 × 200. This paper also presents real-world
examples in which Polar Sort shows those patterns. |
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