Data processing: structural design – modeling – simulation – and em – Modeling by mathematical expression
Reexamination Certificate
1998-06-22
2001-08-07
Teska, Kevin J. (Department: 2123)
Data processing: structural design, modeling, simulation, and em
Modeling by mathematical expression
Reexamination Certificate
active
06272449
ABSTRACT:
BACKGROUND
Several techniques are used to model multidimensional data by mapping multidimensional input values to multidimensional output values. Such models often are used to recognize hidden predictive patterns in a data set. The kinds of problems for which a model may be used include clustering, classification and estimation of data in the data set. There are several types of models that are commonly used, such as probabilistic neural networks, generalized regression neural networks, Gaussian radial basis functions, decision trees (such as, K-D trees, neural trees and classification and regression trees), neural networks, Kohonen networks and associative algorithms.
Most modeling techniques are procedural but not declarative. In other words, a model maps input values to output values. This mapping does not convey the actual meaning or significance of what the model is doing, i.e., its behavior. It is difficult to predict how the model behaves in response to new inputs or what dimensions of the input are most relevant to the behavior of the model.
This problem is compounded when the input data includes a large number of dimensions. In order to ensure that a model is based on relevant input dimensions, various statistical techniques are used to analyze a data set that will be used to create a model in order to identify those dimensions that are salient to the problem to be modeled. A model is created using only the salient dimensions for the input. Example statistical techniques for identifying these salient dimensions include chi-squared automatic interaction detection (CHAID), correlation, principle component analysis, and sensitivity analysis.
Such techniques for identifying the salient dimensions used to create a model still do not provide an explanation of the behavior of the created model. In particular, some dimensions may be salient only in a subspace of the input data and therefore have an impact on the behavior of the model only in that subspace. To assist in understanding the behavior of a model, another kind of statistical technique, called rule induction, often is used. Rule induction is described, for example, in C4.5:
Programs for Machine Learning,
by J. Ross Quinlan, Morgan Kaufman Publishers, 1993. A computer program having the same name (“C4.5”) also is available from that author and publisher. This program uses data directly to derive rules. Other rule induction techniques use a model to derive rules. These techniques provide a tree structure that explains the behavior of a model as a collection of rules. Although these rules may help to explain the behavior of the model, the rules often are too numerous and too complex for a human to interpret as easily as one would like. It also is difficult to extract from these rules an explanation of which input values are important in each subspace of the input data that the tree defines.
SUMMARY
The present invention provides a description of the behavior of a model that indicates the sensitivity of the model in subspaces of the input space. For example, the description may indicate which dimension or dimensions of the input data are salient in the subspaces of the input space. By implementing this description using a decision tree, the subspaces and their salient dimensions are both described and determined hierarchically.
Accordingly, one aspect is a computer-implemented process for creating a description of the behavior of a model indicating sensitivity of the model in subspaces of an input space of the model. Sensitivity analysis is performed on the model to provide a sensitivity profile of the input space of the model according to sensitivity of outputs of the model to variations in data input to the model. The input space is divided into at least two subspaces according to the sensitivity profile. A sensitivity analysis is performed on the model to provide a sensitivity profile of each of the subspaces according to sensitivity of outputs of the model to variations in data input to the model.
Another aspect is a computer system for creating a description of the behavior of a model indicating sensitivity of the model in subspaces of an input space of the model. Sensitivity analysis is performed on the model to provide a sensitivity profile of the input space of the model according to sensitivity of outputs of the model to variations in data input to the model. The input space is divided into at least two subspaces according to the sensitivity profile. A sensitivity analysis is performed on the model to provide a sensitivity profile of each of the subspaces according to sensitivity of outputs of the model to variations in data input to the model.
In another aspect, a computer system for creating a description of the behavior of a model indicating sensitivity of the model in subspaces of an input space of the model includes a sensitivity analysis module and a data splitter. The sensitivity analysis module provides an indication of a sensitivity profile of the input space of the model according to sensitivity of outputs of the model to variations in data input to the model. The data splitter has a first input for receiving an input data set and a second input for receiving the indication of the sensitivity profile output by the sensitivity analysis module, and has an output for providing at least two subspaces of the input space according to a segmentation performed according to the sensitivity profile indicated by the sensitivity analysis module.
In one embodiment, the sensitivity profile is a rank order of dimensions of the input space. The input space thus may be split according to the dimension to which outputs of the model are most sensitive.
REFERENCES:
patent: 5734112 (1998-03-01), Bose et al.
patent: 5825646 (1998-10-01), Keeler et al.
patent: 5922079 (1999-07-01), Booth et al.
patent: 5993050 (1999-11-01), Miura
patent: 6058258 (2000-05-01), Cullum et al.
patent: 0 702 212 A2 (1995-09-01), None
patent: 0 791 807 A2 (1997-08-01), None
patent: WO 94/25933 (1994-11-01), None
Patterson et al., “Microwave Device Modelling Using Systematic Optimization Techniques”, IEE Colloquium on Computer Based Tools for Mocrowave Engineers, pp. 3/1-3/4, 1991.*
Chan et al., “Sensitivity Analysis of Model Output: Variance-Based Methods Make the Difference”, Proceedings of the 1997 Winter Simulation Conference, pp. 261-268. Dec. 1997.*
Salim et al., “Modeling of Magnetic Field Sensitivity of Bipolar Magnetoresistors using HSPICE”, IEEE Transactions on CAD of Integrated Circuits, vol. 14, Issue 4, pp. 464-469, Apr. 1995.*
Starzyk et al, “Automated Testing Using Circuit Decomposition”, 8th IEEE Instrumentation and Measurement Tech. Conf., pp. 514-519. May 1991.*
Lee et al., “Invariant Subspace Parametric Sensitivity (ISPS) of Structure Preserving Power System Models”, IEEE Transactions on Power Systems, vol. 11, Issue 2, pp. 845-850, May 1996.*
Swindlehurst, A. L., “Robust Algorithms for Direction-Finding in the Presence of Model Errors”, Fifth ASSP Workshop on Spectrum Estimation and Modeling, pp. 362-366, Oct. 1990.*
Sethi et al., “Structure-Driven Induction of Decision Tree Classifiers Through Neural Learning”, Pattern Recognition, vol. 30, No. 11, pp. 1893-1904, 1997.
Engelbrecht et al., “Determining The Significance Of Input Parameters Using Sensitivity Analysis”, abstract, Jun. 1995.
Guo et al., “Sensitivity Analysis and Applications to nuclear power plant”, IEEE, pp. 453-458, Jun. 1992.
Sergent Douglas W.
Teska Kevin J.
Torrent Systems, Inc.
Wolf Greenfield & Sacks P.C.
LandOfFree
Computer system and process for explaining behavior of a... does not yet have a rating. At this time, there are no reviews or comments for this patent.
If you have personal experience with Computer system and process for explaining behavior of a..., we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Computer system and process for explaining behavior of a... will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-2482820