WO2000025230A3 - Determining a tangent space and filtering data onto a manifold - Google Patents

Determining a tangent space and filtering data onto a manifold Download PDF

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Publication number
WO2000025230A3
WO2000025230A3 PCT/US1999/024849 US9924849W WO0025230A3 WO 2000025230 A3 WO2000025230 A3 WO 2000025230A3 US 9924849 W US9924849 W US 9924849W WO 0025230 A3 WO0025230 A3 WO 0025230A3
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WO
WIPO (PCT)
Prior art keywords
data
fit
constraints
base point
tangent space
Prior art date
Application number
PCT/US1999/024849
Other languages
French (fr)
Other versions
WO2000025230A2 (en
Inventor
Joel M Macauslan
Juan Luis Sanchez
Original Assignee
Speech Technology And Applied
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Speech Technology And Applied filed Critical Speech Technology And Applied
Priority to AU11317/00A priority Critical patent/AU1131700A/en
Publication of WO2000025230A2 publication Critical patent/WO2000025230A2/en
Publication of WO2000025230A3 publication Critical patent/WO2000025230A3/en

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Classifications

    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10L—SPEECH ANALYSIS OR SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING; SPEECH OR AUDIO CODING OR DECODING
    • G10L25/00—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00
    • G10L25/48—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00 specially adapted for particular use
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations

Abstract

A technique for determining the number of constraints on a set of input data, or equivalently the topological dimension, especially when such data are produced by a nonlinear system, such as a pathological vocal system or econometric data and the like. The technique characterizes the tangent space about a predetermined base point by identifying a maximal set of non-redundant nonlinear fits to the data. It needs only a modest number of data points and does not assume prior knowledge of the functional form of the true constraints, other than smoothness. Each fit is equivalent to a set of contours (including curves, surfaces, and other manifolds), with the data themselves all lying along the zero-value contour of the fit. For each fit, the gradient of the fit at the base point in the uphill direction across the contours identifies the constraint direction. Considering all fits simultaneously, the number of constraint directions that are linearly independent provides the number of constraints in the neighborhood of the base point. The remaining unconstrained directions define the tangent space, and its dimensionality, which is precisely the number of linearly independent unconstrained directions, is precisely the inferred topological dimensionality of the original data.
PCT/US1999/024849 1998-10-26 1999-10-25 Determining a tangent space and filtering data onto a manifold WO2000025230A2 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
AU11317/00A AU1131700A (en) 1998-10-26 1999-10-25 Determining a tangent space and filtering data onto a manifold

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US10569098P 1998-10-26 1998-10-26
US60/105,690 1998-10-26

Publications (2)

Publication Number Publication Date
WO2000025230A2 WO2000025230A2 (en) 2000-05-04
WO2000025230A3 true WO2000025230A3 (en) 2000-07-27

Family

ID=22307256

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/US1999/024849 WO2000025230A2 (en) 1998-10-26 1999-10-25 Determining a tangent space and filtering data onto a manifold

Country Status (2)

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AU (1) AU1131700A (en)
WO (1) WO2000025230A2 (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2019051113A1 (en) * 2017-09-06 2019-03-14 BigML, Inc. Prediction characterization for black box machine learning models

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0421566A2 (en) * 1989-10-04 1991-04-10 Stanley Electric Co., Ltd. System for generating approximate curves and system for memorizing curves
US5493516A (en) * 1991-03-22 1996-02-20 The Secretary Of State For Defence In Her Britannic Majesty's Government Of The United Kingdom Of Great Britain And Northern Ireland Dynamical system analyzer

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0421566A2 (en) * 1989-10-04 1991-04-10 Stanley Electric Co., Ltd. System for generating approximate curves and system for memorizing curves
US5493516A (en) * 1991-03-22 1996-02-20 The Secretary Of State For Defence In Her Britannic Majesty's Government Of The United Kingdom Of Great Britain And Northern Ireland Dynamical system analyzer

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
BIGLIERI E ET AL: "SVD ALGORITHMS AND THEIR APPLICATION TO DIGITAL SIGNAL PROCESSING", PROCEEDINGS OF THE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS,US,NEW YORK, IEEE, vol. CONF. 18, 1985, pages 1399 - 1402, XP000758378 *
BROOMHEAD D S ET AL.: "Topological Dimension and Local Coordinates from Time Series Data", JOURNAL OF PHYSICS A, vol. 20, no. 9, 21 June 1987 (1987-06-21), pages L563 - L569, XP002135740 *

Also Published As

Publication number Publication date
WO2000025230A2 (en) 2000-05-04
AU1131700A (en) 2000-05-15

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