Method and system for analyzing multi-variate data using canonical decomposition

• US 7,171,339 B2
• Filed: 07/11/2001
• Issued: 01/30/2007
• Est. Priority Date: 07/12/2000
• Status: Expired due to Term

• Current Assignee: Cornell Research Foundation Incorporated (Cornell University)
• Original Assignee: Cornell Research Foundation Incorporated (Cornell University)
• Inventors: Schiff, Nicholas, Victor, Jonathan, Repucci, Michael
• Primary Examiner(s): NGHIEM, MICHAEL P
• Application Number:
  US10/332,478
• Publication Number:
  US 20050015205A1
• Time in Patent Office: 2,029 Days
• Field of Search: 702/179, 702/182, 702/189, 702/190, 702/196, 707/100, 707/101, 707/104.1
• US Class Current: 702/189
• CPC Class Codes: G06F 18/213 Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods
• CPC Class Codes: G06F 2218/08 Feature extraction
• CPC Class Codes: G06Q 90/00 Systems or methods specially adapted for administrative, commercial, financial, managerial or supervisory purposes, not involving significant data processing

Abstract

A canonical decomposition (CD) method that includes building a multi-variate linear autoregressive (“MLAR”) model from an original data set or from a reduced set derived by data reduction methods from the original data set. The MLAR analysis is followed by seeking a coordinate transformation of the MLAR model to obtain the best possible match with one or more canonical forms representing relationships among components. For multi-variate data with a truly hierarchical structure, CD accurately extracts the underlying sources of the system.

Claims

1. A system for determining dynamic characteristics of data, the data being causal and having translation-invariant statistics with respect to a variable, the system comprising:

means for receiving signals representing the data, the data originating from a set of components, the set of components having dynamic relationships with each other;

means for calculating a set of multi-linear autoregressive coefficients of the data, the multi-linear autoregressive coefficients yielding an array of square matrices, each square matrix reflecting the dynamic relationships among the components for a certain value of the variable;

means for transforming the square .matrices to a substantially canonical form corresponding to a selected canonical form suitable for analyzing the dynamic relationships, yielding a set of canonical form matrices representing a transformation of the components;

means for analyzing the canonical form matrices and transformed components to determine the dynamic characteristics of the data with respect to the variable; and

means for outputting the transformation of the components.

2. A system according to claim 1, wherein the dynamic relationships are hierarchical.

3. A system according to claim 1, wherein the dynamic relationships are dependent.

4. A system according to claim 1, wherein the dynamic relationships are independent.

5. A system according to claim 1, wherein the dynamic relationships are partially dependent and partially independent.

6. A computer system for analyzing signals originating from a plurality of channels dependent on a variable, the signals being causal and having translation-invariant statistics with respect to the variable, comprising:

an input for receiving the signals from a plurality of components, the signals representing multi-channel data;

a memory device for storing the data;

a processor for creating multi-variate linear autoregressive model of the components, the model representing relationships among the components, the model being stored in the memory device, the processor transforms the model so that the transformed model decorrelates and orthogonalizes random terms within the model, the transformed model having a set of autoregressive coefficients, the processor identifying an orthogonal rotation that preserves the relationships among the components in the model and the orthogonalized random terms in the transformed model, and the processor converting the autoregressive coefficients of the transformed model into a canonical form; and

an output for outputting the transformed model.

8. A computer system according to claims 6 or 7, wherein the system is used to analyze neural activity.

9. A computer system according to claims 6 or 7, wherein the system is used to analyze polygraphic biomedical time series.

10. A computer system according to claims 6 or 7, wherein the system is used to analyze electrocardiographic records.

11. A computer system according to claims 6 or 7, wherein the system is used to analyze at least one of gene expression and protein expression level time series.

12. A computer system according to claims 6 or 7, wherein the system is used to analyze geophysical data.

13. A computer system according to claims 6 or 7, wherein the system is used for financial modeling and forecasting.

14. A computer system according to claims 6 or 7, wherein the system is used to analyze inventory levels.

15. A computer system according to claims 6 or 7, wherein the system is used to analyze routing data.

16. A computer system according to claims 6 or 7, wherein the system is used to analyze network data transmission.

17. A computer system according to claims 6 or 7, wherein the system is used to analyze a quantity and a type of procedural inputs and procedural outputs.

18. A computer system according to claims 6 or 7, wherein the system is used to analyze user interfaces.

19. A computer system according to claims 6 or 7, wherein the system is used to analyze outputs of an electrical device.

20. A computer system according to claims 6 or 7, wherein the system is used to analyze telemetry signals to determine the behavior of a tracking system.

21. A computer system according to claims 6 or 7, wherein the system is used to analyze data patterns so as to improve information dispersal.

22. A computer system according to claim 21, wherein information dispersal includes marketing materials.

23. A computer system according to claim 21, wherein information dispersal includes surveys.

7. A computer characteristics of data statistics with respect to a variable, comprising:

an input for receiving signals from a plurality of components, the signals representing the data;

a memory device;

a processor for calculating a plurality of system for predicting future dynamic that is causal and has translation-invariant multi-linear autoregressive coefficients of the data to yield an array of square matrices, each square matrix reflecting relationships among the components for a certain value of the variable, the processor selecting a canonical form suitable for analyzing relationships among the components, and the processor transforming the square matrices to a substantially canonical form corresponding to the selected canonical form, yielding a plurality of canonical form matrices representing a transformation of the components; and

an output for outputtinci the transformation of the components.