Matrix re-ordering and visualization in the presence of data hierarchies
AssigneeInternational Business Machines Corporation
InventorsAbderrahim Labbi, Michail Vlachos, Christos Boutsidis
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Abstract
Exemplary embodiments include a method for re-ordering and visualizing a matrix in the presence of a data hierarchy stored on a computer system, the method including receiving a matrix, in the computer system, the matrix having rows and columns, reordering the matrix so that groups of related rows and columns are brought in adjacent matrix positions, wherein reordering the matrix A obeys constraints imposed by the data hierarchy on at least one of the rows and the columns and reordering the hierarchy on at least one of the rows and columns, wherein affinities in the data hierarchy are extracted by the reordering of the data hierarchy.
Claims24
A method for re-ordering and visualizing a matrix in the presence of a data hierarchy stored on a computer system, the method comprising:
- receiving, in the computer system, a matrix having a plurality of sub-matrices and having rows and columns;
- identifying a plurality of data hierarchies that correspond to the plurality of sub-matrices;
- identifying hierarchical constraints from the plurality of data hierarchies;
- generating a bipartite graph for the matrix;
- computing an adjacency matrix for the matrix;
- computing a Laplacian matrix from the adjacency matrix;
- computing a Fielder vector from the Laplacian matrix;
- reordering the columns of the matrix;
- reordering the rows of the matrix;
- reordering the data hierarchy on the columns of the matrix;
- and
- reordering the data hierarchy on the rows of the matrix,
- wherein the matrix, the plurality of sub-matrices and the identified plurality of data hierarchies are reordered so that groups of related rows and columns are brought in adjacent matrix positions, wherein reordering the matrix, the plurality of sub-matrices and the identified plurality of data hierarchies, obeys the identified constraints imposed by the data hierarchy on at least one of the rows and the columns,
- wherein affinities in the data hierarchy are extracted by the reordering of the data hierarchy.
A computer program product for re-ordering and visualizing a matrix in the presence of data hierarchies stored on a computer system, the computer program product including a non-transitory computer readable medium having instructions for causing the computer system to implement a method, the method comprising:
- receiving, in the computer system, a matrix having a plurality of sub-matrices and having rows and columns;
- identifying a plurality of data hierarchies that correspond to the plurality of sub-matrices;
- identifying hierarchical constraints from the plurality of data hierarchies;
- generating a bipartite graph for the matrix;
- computing an adjacency matrix for the matrix;
- computing a Laplacian matrix from the adjacency matrix;
- computing a Fielder vector from the Laplacian matrix;
- reordering the columns of the matrix;
- reordering the rows of the matrix;
- reordering the data hierarchy on the columns of the matrix;
- and
- reordering the data hierarchy on the rows of the matrix,
- wherein the matrix, the plurality of sub-matrices and the identified plurality of data hierarchies are reordered while obeying the identified constraints of the data hierarchy.
A method for re-ordering and visualizing a matrix in the presence of data hierarchies stored on a computer system, the method comprising:
- receiving a first data set;
- receiving a second data set;
- identifying data hierarchies for the first and second data sets;
- identifying hierarchical constraints from the identified data hierarchies;
- generating a sparse matrix representing the first and second data sets;
- and
- reordering the sparse matrix to reveal interactions between the first and second data sets to generate a re-ordered hierarchy, wherein the reordering obeys the identified constraints imposed by the data hierarchies, wherein the reordering comprises:
- generating a bipartite graph for the sparse matrix;
- computing an adjacency matrix for the sparse matrix;
- computing a Laplacian matrix from the adjacency matrix;
- computing a Fielder vector from the Laplacian matrix;
- reordering the columns of the sparse matrix;
- reordering the rows of the sparse matrix;
- reordering the data hierarchy on the columns of the sparse matrix;
- and
- reordering the data hierarchy on the rows of the sparse matrix.
A computer program product for re-ordering and visualizing a matrix in the presence of data hierarchies stored on a computer system, the computer program product including a non-transitory computer readable medium having instructions for causing the computer system to implement a method, the method comprising:
- receiving a first data set;
- receiving a second data set;
- identifying data hierarchies for the first and second data sets;
- identifying hierarchical constraints from the identified data hierarchies;
- generating a sparse matrix representing the first and second data sets;
- and
- reordering the sparse matrix to reveal interactions between the first and second data sets to generate a re-ordered hierarchy, wherein the reordering obeys the identified constraints imposed by the data hierarchies, wherein the reordering comprises:
- generating a bipartite graph for the sparse matrix;
- computing an adjacency matrix for the sparse matrix;
- computing a Laplacian matrix from the adjacency matrix;
- computing a Fielder vector from the Laplacian matrix;
- reordering the columns of the sparse matrix;
- reordering the rows of the sparse matrix;
- reordering the data hierarchy on the columns of the sparse matrix;
- and
- reordering the data hierarchy on the rows of the sparse matrix.
Dependencies are inferred from the claim text.