Systems and Methods for Processing High-Dimensional Data

• US 20090299705A1
• Filed: 08/28/2008
• Published: 12/03/2009
• Est. Priority Date: 05/28/2008
• Status: Active Grant

• Current Assignee: NEC Corporation
• Original Assignee: NEC Laboratories America Inc (NEC Corporation)
• Inventors: Gong, Yihong, Zhu, Shenghuo, Chi, Yun
• Granted Patent: US 8,099,381 B2
• Time in Patent Office: Days
• US Class Current: 703/2
• CPC Class Codes: G06F 16/283 Multi-dimensional databases or data warehouses, e.g. MOLAP or ROLAP

Abstract

Systems and methods are disclosed for factorizing high-dimensional data by simultaneously capturing factors for all data dimensions and their correlations in a factor model, wherein the factor model provides a parsimonious description of the data; and generating a corresponding loss function to evaluate the factor model.

Claims

1. A method for factorizing high-dimensional data, comprising:

simultaneously capturing factors for all data dimensions and their correlations in a factor model; and

generating a corresponding loss function to evaluate the factor model.

2. The method of claim 1, comprising generating a data tensor from the high dimensional input data.

3. The method of claim 1, comprising generating one or more factors and factor relationships using a factorization algorithm.

4. The method of claim 1, comprising applying the factors and their relationships to a recommendation application.

5. The method of claim 1, comprising applying the factors and their relations to the clustering application.

6. The method of claim 1, comprising applying the factors and their relations to the summarization application.

7. The method of claim 1, comprising applying a Kullback-Leibler divergence to measure an error in tensor factorization

8. The method of claim 1, comprising applying alternative algorithm to learn the model parameters.

9. The method of claim 1, comprising applying a Frobenius tensor norm to measure an error in tensor factorization.

10. The method of claim 1, comprising applying EM-style iterative algorithm for solving the non-negative tensor factorization (NTF).

11. The method of claim 1, comprising deriving a probabilistic factor model.

12. The method of claim 11, wherein the probabilistic factor model is used generate a discriminative version and a version containing regularization on result sparseness.

13. The method of claim 1, comprising approximating the data using a non-negative tensor factorization.

14. The method of claim 1, comprising minimizing errors.

15. The method of claim 14, comprising generating a set of matrices which represent the factors in different dimensions of the data.

16. The method of claim 14, comprising generating a tensor representing correlations among the factors in different dimensions of data.

17. A method for factorizing high-dimensional observed data, comprising:

a. deriving a generative model that simultaneously captures factors for all data dimensions and their correlations;

b. generating predicted data and mapping the generative model into a non-negative tensor factorization; and

c. minimizing the predetermined loss between the observed data and the predicted data and to generate a tensor that represents the correlations among the factors in different dimensions of data.

18. The method of claim 17, comprising generating a set of matrices which represent the factors in different dimensions of the data.

19. The method of claim 17, comprising generating a tensor representing correlations among the factors in different dimensions of data.

20. The method of claim 17, comprising applying EM-style iterative algorithm for solving the non-negative tensor factorization (NTF).