There is a clear latent structure in D b. However, there is a dramatic change from a to b since the patients are admitted in a random order.
The difference between V a and V b is not much since V a is already grouped by the symptom tables. The same seriations are also used to reshape the raw data matrix D a into D b. The seriations are then applied to arrange the two correlation matrices V a and a into V b and b in Figure 2b. eriation is a data analytic tool for finding a permutation or ordering of a set of objects using a data matrix. 2.2 The orted Matrix Maps with the Principle of Geometry The next step is to find proper seriations for V a and a respectively. ufficient Graph with Three Multivariate Linkages. Clustering for Variables and ubjects (d). orted Data Matrix Map and Proximity Matrix Maps (c). Original Raw Data and Proximity Matrices Maps (b). (a) (b) V a V b D a a D b b (c) (d) V c V d v v2 v3 v4 v5 D c c v v2 v3 v4 v5 D d d Figure 2. The diverging blue-red color scheme is used to represent the bi-directional property of the correlation coefficients. For the 95 patients, also the correlation matrix is used as the proximity matrix. The correlation matrix is calculated as the proximity matrix V a for the 5 symptoms. A gray spectrum is applied to project numerical numbers into gray dots with different intensities. Raw Data and Proximity Matrix Maps with uitable Color Projection The raw data matrix is denoted as D a in Figure 2a. GAP integrates the following four major steps to extract and summarize information embedded in a multivariate data set. We use a psychosis disorder data with 95 patients on 5 symptoms to illustrate the framework of a standard GAP analysis, in Figure 2. the interaction linkage between the sets of subjects and variables. theĢ linkage between p variable vectors in the n-dimensional space and 3. the linkage amongst n subject points in the p-dimensional space 2. 2 BAIC PRINCIPLE OF GAP There are three major pieces of information contained in any multivariate data set with n subjects and p variables.
First Two Eigen-Vectors for the Correlation Matrices. orted Color Maps for the Correlation Matrices (b). Converging equence of Iteratively Generated Correlation Matrices. D R () R () R (2) R (3) R (4) R (5) R (6) R (7) R (8 ) R (9) R ( ) DL DL ρ ( D) = 5 ρ ( ) = 49 ρ ( ) = 49 ρ (2 ) = 4 DL DL AH2 AH3 DL AH DL6 TH NE NA BE NC NB4 NA7 ND NA5 NB2 NB ρ (3 ) = 2 ρ (4 ) = 7 ρ (5 ) = 3 ρ (6 ) = 2 DL6 AH3 AH2AHDL TH NE BE NC NA NA7 NB NB2 NB4 NA5 ND DL DL DL DL6 AH2 AH3 DL AH DL DL6 AH2 AH3 AHDL BE NE TH NC NB2 NB NB4 NA7 NA NA5 ND TH NE BE NC NA NA5 NA7 NB NB2 NB4 ND DL DL DL6 AH3 AH2 DL DL TH NE BE AH DL DL6 AH2 AH3 AH DL NC NB2 NA NB NA5 NA7 NB4 ND TH NE BE NA NA5 NA7 NB NB2 NC ND NB4 DL DL DL DL DL6 AH3 AH2 AH DL DL6 AH3 AH2AH DL TH NE BE NC NB2 NA NB NA5 NA7 NB4 ND TH NE BE NA NA5 NA7 NB NB2 NB4 NC ND ρ (7 ) = 2 ρ (8) = 2 ρ (9 ) = 2 ρ ( ) = DL DL AH2 AH3 DL6 AH DL TH NA NA5 NA7 NB NB2 BE NB4 ND NC NE DL6 DL DL AH AH2 AH3 DL BE TH NA NA5 NA7 NB NB2 NB4 NC ND NE AH AH2 AH3 DL6 DL DL AH AH2 AH3 DL6 DL DL NA NA TH NA5 NA7 NB NB2 NB4 NC ND NE TH NA5 NA7 NB NB2 NB4 NC ND NE BE BE AH AH2 AH3 DL6 DL DL BE TH NA NA5 NA7 NB NB2 NB4 NC ND NE (a) (b) Figure. This sequence of correlation matrices is used to dynamically identify seriation and clustering for a given proximity matrix. CONVERGING EQUENCE OF CORRELATION MATRICE The computation kernel of GAP is a converging sequence of iteratively generated correlation matrices, Figure. Extensions have been added to GAP for analyzing more complicated formats such as categorical, longitudinal, and multiple-set structure. GAP has unique seriation algorithm for identifying permutations of matrices with better global sense and clustering algorithm for finding multiple clustering patterns co-exist in proximity matrices. These three maps should be cross-examined to identify important information structure embedded in the raw data matrix. Double sorted raw data matrix together with two sorted proximity matrices are then projected through appropriate color spectrums to create matrix maps. Proper seriations (permutations) are searched for rearrange these two matrices to satisfy certain properties. Given a multivariate data set, GAP first compute the proximity matrices for variables as well as for subjects.
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1 Generalized association plots (GAP): Dimension free information visualization environment for multivariate data structure Chun-houh Chen, hun-chuan Chang, Yueh-Yun Chi, and Chih-Wen Ou-Young Academia inica, Taiwan Abstract: GAP is a dimension free visualization environment for multivariate data structure.
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