Methods for mapping data into lower dimensions
Methods and systems for creating ensembles of hypersurfaces in high-dimensional feature spaces, and to machines and systems relating thereto. More specifically, exemplary aspects of the invention relate to methods and systems for generating supervised hypersurfaces based on user domain expertise, machine learning techniques, or other supervised learning techniques. These supervised hypersurfaces may optionally be combined with unsupervised hypersurfaces derived from unsupervised learning techniques. Lower-dimensional subspaces may be determined by the methods and systems for creating ensembles of hypersurfaces in high-dimensional feature spaces. Data may then be projected onto the lower-dimensional subspaces for use, e.g., in further data discovery, visualization for display, or database access. Also provided are tools, systems, devices, and software implementing the methods, and computers embodying the methods and/or running the software, where the methods, software, and computers utilize various aspects of the present invention relating to analyzing data.
1. A method for analysis of a high-dimensional feature space comprising labelled data, comprising:
generating a first supervised hypersurface and a first vector normal to the first hypersurface using supervised learning techniques on said labelled data;
generating a second unsupervised hypersurface and a second vector normal to the second hypersurface using unsupervised learning techniques on said labelled data after removing the labels;
selecting a subspace comprising the supervised hypersurface and unsupervised hypersurface;
projecting data from the high-dimensional feature space onto the orthonormal basis that spans the selected subspace comprising the first vector normal to the first hypersurface and the second vector normal to the second hypersurface; and
outputting the projected data into a computer memory.
2. The method of claim 1 , wherein the lower-dimensional subspace comprises a new model of the data from the high-dimensional feature space.
3. The method of claim 1 , wherein the projected data is used to conduct further analysis of the projected data.
4. The method of claim 3 , wherein the further analysis is selected from the group consisting of data discovery, data display, and database exploration.
5. The method of claim 1 , wherein the projected data is used to generate a visual data display on a display means.
6. The method of claim 1 , wherein the data projected onto the lower dimensional subspace is used to represent an svm or learning machine.
7. The method of claim 6 , wherein the data projected onto the lower dimensional subspace is used to represent a combination of an svm or learning machine and an unsupervised learning method in a single visual subspace model.
8. The method of claim 1 , wherein the supervised learning techniques is a machine learning solution.
9. A computer program product comprising a non-transitory computer usable medium having control logic stored therein for causing a computer comprising a process to analyze a high-dimensional feature space comprising labelled data, the control logic comprising:
first computer readable program code means for generating a first supervised hypersurface and a first vector normal to the first hypersurface using supervised learning techniques on said labelled data;
second computer readable program code means for generating a second unsupervised hypersurface and a second vector normal to the second hypersurface using unsupervised learning techniques on said labelled data after removing the labels;
third computer readable program code means for selecting a subspace comprising the supervised hypersurface and unsupervised hypersurface;
fourth computer readable program code means for projecting data from the high-dimensional feature space onto the orthonormal basis that spans the selected subspace comprising the first vector normal to the first hypersurface and the second vector normal to the second hypersurface; and
fifth computer readable program code means for outputting the projected data on an output device.
10. A method for projecting high-dimensional data from a high-dimensional data space onto a lower-dimensional subspace comprising:
generating one or more axes from high-dimensional data comprising labelled data, wherein said axes include at least one vector chosen from the following: a vector normal to a hypersurface in said high-dimensional data space, said hypersurface being derived using supervised means based on a vector created from a hypothetical data pattern, or derived using supervised means based on a vector selected from an actual data pattern;
generating one or more axes from high-dimensional data, wherein said axes include at least one vector normal to an unsupervised hypersurface in said high-dimensional data space, said unsupervised hypersurface being derived using unsupervised means on said labelled data after removing the labels;
orthonormalizing the vectors with respect to one another and projecting the high-dimensional data onto said orthonormalized vectors to form a lower-dimensional subspace; and
outputting the lower-dimensional subspace into a computer memory.
11. The method of claim 10 , wherein the projected data is used to generate a visual data display on a display means.
12. The method of claim 10 , wherein the data projected onto the lower dimensional subspace is used to represent an svm or learning machine, or a combination of an svm or learning machine and an unsupervised learning method.
13. The method of claim 10 , wherein the supervised means are machine learning techniques.
14. A computer program product comprising a non-transitory computer usable medium having control logic stored therein for causing a computer comprising a process to analyze a high-dimensional feature space, the control logic comprising:
first computer readable program code means for generating one or more axes from high-dimensional data comprising labelled data, wherein said axes include at least one vector chosen from the following: a vector normal to a hypersurface in said high-dimensional data space, said hypersurface being derived using supervised means based on a vector created from a hypothetical data pattern, or derived using supervised means based on a vector selected from an actual data pattern;
second computer readable program code means for generating one or more axes from high-dimensional data, wherein said axes include at least one vector normal to an unsupervised hypersurface in said high-dimensional data space, said unsupervised hypersurface being derived using unsupervised means on said labelled data after removing the labels;
third computer readable program code means for orthonormalizing the vectors with respect to one another and projecting the high-dimensional data onto said orthonormalized vectors to form lower-dimensional subspaces; and
fourth computer readable program code means for outputting the lower-dimensional subspaces into a computer memory.
15. A graphic method of indexing a database comprising:
generating a lower-dimensional subspace using data from the database;
projecting data from the database onto the lower-dimensional subspace
graphically representing data from the database in the subspace;
enabling access of database records by selection of the graphical representation of the data from the database; and
outputting the generated index of the database into a computer memory.
16. A method for detecting deviations in data from a complex typical state and identifying data features responsible for the deviations from the typical state, comprising:
generating a first hypersurface and a first vector normal to the first hypersurface and a second hypersurface and a second vector normal to the second hypersurface derived from data consisting of typical data from a high-dimensional feature space using learning methods consisting of unsupervised learning methods;
selecting a lower-dimensional subspace comprising the hypersurfaces;
projecting data from the high-dimensional feature space onto the orthonormal basis that spans the selected subspace comprising the first vector normal to the first hypersurface and the second vector normal to the second hypersurface to generate a lower-dimensional typical model;
comparing additional data samples to the lower-dimensional typical model;
identifying which data features of the compared data samples do not match the typical model; and
outputting the projected typical model into a computer memory.
17. The method of claim 16 , wherein the typical model is progressively generated as examples are added to the model by calculating a vector orthogonal to a hypersurface in the high-dimensional feature space that reflects the differences of the data features of the example from the model, and incorporating that vector into the typical model subspace.
18. The method of claim 16 , wherein the method is used to detect deviations from typical in data sets.
19. The method of claim 16 , wherein the method is used to monitor equipment.
20. The method of claim 16 , wherein the method is used to conduct data surveillance.
21. The method of claim 1 , wherein hypothetical or actual data patterns are used to create a lower-dimensional subspace.
22. The method of claim 10 , wherein the projected data is used to conduct further analysis of the projected data.
23. The method of claim 10 , wherein the further analysis is selected from the group consisting of data discovery, data display, and database exploration.