WO1999034316A9 - Minimisation de puissance applicable a la classification, a la reconnaissance de diagrammes, a la fusion des donnees de capteurs, a la compression de donnees, a la reconstruction de reseaux et au traitement de signaux - Google Patents

Minimisation de puissance applicable a la classification, a la reconnaissance de diagrammes, a la fusion des donnees de capteurs, a la compression de donnees, a la reconstruction de reseaux et au traitement de signaux

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Publication number
WO1999034316A9
WO1999034316A9 PCT/US1998/027374 US9827374W WO9934316A9 WO 1999034316 A9 WO1999034316 A9 WO 1999034316A9 US 9827374 W US9827374 W US 9827374W WO 9934316 A9 WO9934316 A9 WO 9934316A9
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WO
WIPO (PCT)
Prior art keywords
data
matrices
space output
source space
output
Prior art date
Application number
PCT/US1998/027374
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English (en)
Other versions
WO1999034316A3 (fr
WO1999034316A2 (fr
Inventor
Jeff B Glickman
Abel Wolman
Original Assignee
Jeff B Glickman
Abel Wolman
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 Jeff B Glickman, Abel Wolman filed Critical Jeff B Glickman
Priority to US09/581,949 priority Critical patent/US6993186B1/en
Priority to EP98966467A priority patent/EP1064613A4/fr
Priority to CA002315814A priority patent/CA2315814A1/fr
Priority to AU23070/99A priority patent/AU2307099A/en
Priority to PCT/US1999/008768 priority patent/WO2000039705A1/fr
Priority to AU38645/99A priority patent/AU3864599A/en
Publication of WO1999034316A2 publication Critical patent/WO1999034316A2/fr
Publication of WO1999034316A9 publication Critical patent/WO1999034316A9/fr
Publication of WO1999034316A3 publication Critical patent/WO1999034316A3/fr
Priority to US09/885,342 priority patent/US6968342B2/en
Priority to US11/096,126 priority patent/US7174048B2/en
Priority to US11/097,783 priority patent/US7702155B2/en
Priority to US11/097,733 priority patent/US7272262B2/en
Priority to US12/757,561 priority patent/US7912290B2/en

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Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/213—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods
    • G06F18/2137—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods based on criteria of topology preservation, e.g. multidimensional scaling or self-organising maps

Definitions

  • An appendix of computer program source code is included and comprises 22 sheets.
  • the present invention relates to recognition, analysis, and classification of patterns in data from real world sources, events and processes. Patterns exist throughout the real world. Patterns also exist in the data used to represent or convey or store information about real world objects or events or processes. As information systems process more real world data, there are mounting requirements to build more sophisticated, capable and reliable pattern recognition systems.
  • Existing pattern recognition systems include statistical, syntactic and neural systems. Each of these systems has certain strengths which lends it to specific applications. Each of these systems has problems which limit its effectiveness.
  • Existing pattern recognition systems include statistical, syntactic and neural systems. Each of these systems has certain strengths which lends it to specific applications. Each of these systems has problems which limit its effectiveness.
  • Some real world patterns are purely statistical in nature. Statistical and probabilistic pattern recognition works by expecting data to exhibit statistical patterns. Pattern recognition by this method alone is limited. Statistical pattern recognizers cannot see beyond the expected statistical pattern. Only the expected statistical pattern can be detected.
  • Syntactic pattern recognizers function by expecting data to exhibit structure. While syntactic pattern recognizers are an improvement over statistical pattern recognizers, perception is still narrow and the system cannot perceive beyond the expected structures. While some real world patterns are structural in nature, the extraction of structure is unreliable.
  • Pattern recognition systems that rely upon neural pattern recognizers are an improvement over statistical and syntactic recognizers. Neural recognizers operate by storing training patterns as synaptic weights. Later stimulation retrieves these patterns and classifies the data.
  • the fixed structure of neural pattern recognizers limits their scope of recognition. While a neural system can learn on its own, it can only find the patterns that its fixed structure allows it to see. The difficulties with this fixed structure are illustrated by the well-known problem that the number of hidden layers in a neural network strongly affects its ability to learn and generalize. Additionally, neural pattern recognition results are often not reproducible. Neural nets are also sensitive to training order, often require redundant data for training, can be slow learners and sometimes never learn. Most importantly, as with statistical and syntactic pattern recognition systems, neural pattern recognition systems are incapable of discovering truly new knowledge.
  • an analyzer/classifier process for data comprises using energy minimization with one or more input matrices.
  • the data to be analyzed/classified is processed by an energy minimization technique such as individual differences multidimensional scaling (IDMDS) to produce at least a rate of change of stress/energy .
  • IDMDS individual differences multidimensional scaling
  • the rate of change of stress/energy and possibly other IDMDS output the data are analyzed or classified through patterns recognized within the data.
  • FIG. 1 is a diagram illustrating components of an analyzer according to the first embodiment of the invention.
  • FIG. 2 through FIG. 10 relate to examples illustrating use of an embodiment of the invention for data classification, pattern recognition, and signal processing.
  • the method and apparatus in accordance with the present invention provide an analysis tool with many applications.
  • This tool can be used for data classification, pattern recognition, signal processing, sensor fusion, data compression, network reconstruction, and many other purposes.
  • the invention relates to a general method for data analysis based on energy minimization and least energy deformations.
  • the invention uses energy minimization principles to analyze one to many data sets.
  • energy is a convenient descriptor for concepts which are handled similarly mathematically. Generally, the physical concept of energy is not intended by use of this term but the more general mathematical concept.
  • individual data sets are characterized by their deformation under least energy merging.
  • a number of methods for producing energy minimization and least energy merging and extraction of deformation information have been identified; these include, the finite element method (FEM), simulated annealing, and individual differences multidimensional scaling (IDMDS).
  • FEM finite element method
  • IDMDS individual differences multidimensional scaling
  • the presently preferred embodiment of the invention utilizes individual differences multidimensional scaling (IDMDS).
  • Multidimensional scaling is a class of automated, numerical techniques for converting proximity data into geometric data.
  • IDMDS is a generalization of MDS, which converts multiple sources of proximity data into a common geometric configuration space, called the common space, and an associated vector space called the source space. Elements of the source space encode deformations of the common space specific to each source of proximity data.
  • MDS and IDMDS were developed for psychometric research, but are now standard tools in many statistical software packages. MDS and IDMDS are often described as data visualization techniques. This description emphasizes only one aspect of these algorithms.
  • p is a measure of proximity between objects in S. Then the goal of MDS is to construct a mapping / from S into a metric space (X, d),
  • p(i, j) p tJ « d(f(i), f(j) that is, such that the proximity of object i to obj ect / in S is approximated by the distance in X between /(/) and f(j ) .
  • X is usually assumed to be n dimensional Euclidean space R" , with n sufficiently small.
  • IDMDS is a method for representing many points of view.
  • the different proximities p k can be viewed as giving the proximity perceptions of different judges.
  • IDMDS accommodates these different points of view by finding different maps f k for each judge.
  • These individual maps, or their image configurations, are deformations of a common configuration space whose interpoint distances represent the common or merged point of view.
  • MDS and IDMDS can be further broken down into so-called metric and nonmetric versions.
  • the transformations /( f k ) are parametric functions of the proximities p y (p ⁇ ) .
  • Nonmetric MDS or IDMDS generalizes the metric approach by allowing arbitrary admissible transformations/ ( f k ), where admissible means the association between proximities and transformed proximities (also called disparities in this context) is weakly monotone:
  • P, j ⁇ P k i implies f(p tJ ) ⁇ f ⁇ p kl ) .
  • PROXSCAL See Commandeur, J. and Heiser, W., "Mathematical derivations in the proximity scaling (PROXSCAL) of symmetric data matrices," Tech. report no.
  • PROXSCAL is a least squares, constrained majorization algorithm for IDMDS. We now summarize this algorithm, following closely the above reference.
  • PROXSCAL is a least squares approach to IDMDS which minimizes the objective function
  • MDS can be interpreted as an energy minimization process and stress can be inte ⁇ reted as an energy functional.
  • ⁇ (f,X°) ⁇ (f(p lJ ) - d IJ (X 0 )) 2 .
  • ALSCAL also produces common and source spaces, but these spaces are computed through alternating least squares without explicit use of constraints. Either form of IDMDS can be used in the present invention.
  • MDS and IDMDS have proven useful for many kinds of analyses. However, it is believed that prior utilizations of these techniques have not extended the use of these techniques to further possible uses for which MDS and IDMDS have particular utility and provide exceptional results. Accordingly, one benefit of the present invention is to incorporate MDS or IDMDS as part of a platform in which aspects of these techniques are extended. A further benefit is to provide an analysis technique, part of which uses IDMDS, that has utility as an analytic engine applicable to problems in classification, pattern recognition, signal processing, sensor fusion, and data compression, as well as many other kinds of data analytic applications.
  • Step 110 is a front end for data transformation.
  • Step 120 is a process step implementing energy minimization and deformation computations — in the presently preferred embodiment, this process step is implemented through the IDMDS algorithm.
  • Step 130 is a back end which interprets or decodes the output of the process step 120.
  • step 110 may be configured as a code
  • step 120 may be configured as second code
  • step 120 may be configured as third code, with each code comprising a plurality of machine readable steps or operations for performing the specified operations. While step 110, step 120 and step 130 have been shown as three separate elements, their functionality can be combined and/or distributed. It is to be further understood that "medium” is intended to broadly include any suitable medium, including analog or digital, hardware or software, now in use or developed in the future.
  • Step 110 of the tool 100 is the transformation of the data into matrix form.
  • the only constraint on this transformation for the illustrated embodiment is that the resulting matrices be square.
  • the type of transformation used depends on the data to be processed and the goal of the analysis. In particular, it is not required that the matrices be proximity matrices in the traditional sense associated with IDMDS.
  • time series and other sequential data may be transformed into source matrices through straight substitution into entries of symmetric matrices of sufficient dimensionality (this transformation will be discussed in more detail in an example below).
  • Time series or other signal processing data may also be Fourier or otherwise analyzed and then transformed to matrix form.
  • Step 120 of the tool 100 implements energy minimization and extraction of deformation information through IDMDS.
  • the stress function ⁇ defines an energy functional over configurations and transformations.
  • the weight vectors diag( W k ) are the contextual signature, with respect to the common space, of the k-th input source. Inte ⁇ retation of ⁇ as an energy functional is fundamental; it greatly expands the applicability of MDS as an energy minimization engine for data classification and analysis.
  • Step 130 consists of both visual and analytic methods for decoding and inte ⁇ reting the source space FT from step 120. Unlike traditional applications of IDMDS, tool 100 often produces high dimensional output. Among other things, this makes visual inte ⁇ retation and decoding of the source space problematic. Possible analytic methods for understanding the high dimensional spaces include, but are not limited to, linear programming techniques for hype ⁇ lane and decision surface estimation, cluster analysis techniques, and generalized gravitational model computations. A source space dye-dropping or tracer technique has been developed for both source space visualization and analytic postprocessing. Step 130 may also consist in recording stress/energy, or the rate of change of stress/energy, over multiple dimensions.
  • the graph of energy (rate or change or stress/energy) against dimension can be used to determine network and dynamical system dimensionality.
  • the graph of stress/energy against dimensionality is traditionally called a scree plot.
  • the use and pu ⁇ ose of the scree plot is greatly extended in the present embodiment of the tool 100.
  • Step 110 of the tool 100 converts each S k e S to matrix form M(S k ) where M S k ) is a/? dimensional real hollow symmetric matrix. Hollow means the diagonal entries of M(S k ) are zero. As indicated above, M(S k ) need not be symmetric or hollow, but for simplicity of exposition these additional restrictions are adopted. Note also that the matrix dimensionality ? is a function of the data S and the goal of the analysis. Since M(S k ) is hollow symmetric, it can be inte ⁇ reted and processed in IDMDS as a proximity (dissimilarity) matrix. Step
  • H P (R) is the set of/? dimensional hollow real symmetric matrices.
  • M is the set of/? dimensional hollow real symmetric matrices.
  • M is the set of/? dimensional hollow real symmetric matrices.
  • M may be a standard distance matrix whose ty ' -th entry is the Euclidean distance between "on" pixels and/.
  • FFT frequency transform
  • M(S k ) e M(S) is an input source for IDMDS.
  • the IDMDS output is a common space Z a R" and a source space W.
  • IDMDS attempts to find the lowest stress or energy configurations X k which also satisfy the constraint equation.
  • Configurations X k most similar to the source matrices M(S k ) have the lowest energy.
  • each X k is required to match the common space Z up to deformation defined by the weight matrices W k .
  • the common space serves as a characteristic, or reference object.
  • the weight space signatures are contextual; they are defined with respect to the reference object Z.
  • the contextual nature of the source deformation signature is fundamental.
  • Z- contextuality of the signature allows the tool 100 to display integrated unsupervised machine learning and generalization.
  • the analyzer/classifier learns seamlessly and invisibly.
  • Z-contextuality also allows the tool 100 to operate without a priori data models.
  • the analyzer/classifier constructs its own model of the data, the common space Z.
  • Step 130 the back end of the tool 100, decodes and inte ⁇ rets the source or classification space output W ⁇ xo .
  • IDMDS Since this output can be high dimensional, visualization techniques must be supplemented by analytic methods of inte ⁇ retation.
  • a dye-dropping or tracer technique has been developed for both visual and analytic postprocessing. This entails differential marking or coloring of source space output.
  • the specification of the dye-dropping is contingent upon the data and overall analysis goals. For example, dye-dropping may be two-color or binary allowing separating hype ⁇ lanes to be visually or analytically determined.
  • an analytic approach to separating hype ⁇ lanes using binary dye-dropping see Bosch, R. and Smith, J, "Separating hype ⁇ lanes and the authorship of the disputed federalist papers," American Mathematical Monthly, Vol. 105, 1998.
  • Discrete dye-dropping allows the definition of generalized gravitational clustering measures of the form
  • A denotes a subset of W (indicated by dye-dropping)
  • ⁇ A (x) is the characteristic function on A
  • d(-,-) is a distance function
  • p e R is a distance function
  • Such measures may be useful for estimating missing values in data bases.
  • Dye- dropping can be defined continuously, as well, producing a kind of height function on W. This allows the definition of decision surfaces or volumetric discriminators.
  • the source space also analyzable using standard cluster analytic techniques.
  • the precise clustering metric depends on the specifications and conditions of the IDMDS analysis in question.
  • the stress/energy and rate of change of stress/energy can be used as postprocessing tools.
  • Minima or kinks in a plot of energy, or the rate of change of energy, over dimension can be used to determine the dimensionality of complex networks and general dynamical systems for which only partial output information is available. In fact, this technique allows dimensionality to be inferred often from only a single data stream of time series of observed data.
  • each polygon S k was divided into 60 equal segments with the segment endpoints ordered clockwise from a fixed initial endpoint.
  • a turtle application was then applied to each polygon to compute the Euclidean distance from each segment endpoint to every other segment endpoint (initial endpoint included).
  • Let x S ' k denote the z-th endpoint of polygon S k , then the mapping Mis defined by
  • the individual column vectors ⁇ i have intrinsic interest. When plotted as functions of arc length they represent a geometric signal which contains both frequency and spatial information.
  • PROXSCAL The 16, 60 x 60 distance matrices were input into a publicly distributed version of PROXSCAL.
  • PROXSCAL was run with the following technical specifications: sources- 16, objects- 60, dimension- 4, model- weighted, initial configuration- Torgerson, conditionality- unconditional, transformations- numerical, rate of convergence- 0.0, number of iterations- 500, and minimum stress- 0.0.
  • FIG. 2 and FIG. 3 show the four dimensional common and source space output.
  • the common space configuration appears to be a multifaceted representation of the original polygons. It forms a simple closed path in four dimensions which, when viewed from different angles, or, what is essentially the same thing, when deformed by the weight matrices, produces a best, in the sense of minimal energy, representation of each of the two dimensional polygonal figures. The most successful such representation appears to be that of the triangle projected onto the plane determined by dimensions 2 and 4.
  • the different types of polygons are arranged, and hence, classified, along different radii. Magnitudes within each such radial classification indicate polygon size or scale with the smaller polygons located nearer the origin.
  • the contextual nature of the polygon classification is embodied in the common space configuration.
  • this configuration looks like a single, carefully bent wire loop.
  • this loop of wire looks variously like a triangle, a square, a pentagon, or a hexagon.
  • Example B Classification of non-regular polygons
  • the polygons in Example A were regular.
  • the perimeter of each figure S k was divided into 30 equal segments with the preprocessing transformation M computed as in Example A. This produced 6, 30 x 30 source matrices which were input into PROXSCAL with technical specifications the same as those above except for the number of sources, 6, and objects, 30.
  • FIG. 4 and FIG. 5 show the three dimensional common and source space outputs.
  • the common space configuration again, has a "holographic" or faceted quality; when illuminated from different angles, it represents each of the polygonal figures.
  • this change of viewpoint is encoded in the source space weight vectors. While the weight vectors encoding triangles and rectangles are no longer radially arranged, they can clearly be separated by a hype ⁇ lane and are thus accurately classified by the analysis tool as presently embodied.
  • This example relates to signal processing and demonstrates the analysis tool's invariance with respect to phase and frequency modification of time series data. It also demonstrates an entry-wise approach to computing the preprocessing transformation M.
  • the set S ⁇ S,,...,S 12 ⁇ consisted of sine, square, and sawtooth waveforms.
  • This preprocessing produced 12, 9 x 9 source matrices which were input to PROXSCAL with the following technical specifications: sources- 12, objects- 9, dimension- 8, model- weighted, initial configuration- Torgerson, conditionality- unconditional, transformations- ordinal, approach to ties- secondary, rate of convergence- 0.0, number of iterations- 500, and minimum stress- 0.0.
  • data while metric or numeric, was transformed as if it were ordinal or nonmetric.
  • the use of nonmetric IDMDS has been greatly extended in the present embodiment of the tool 100.
  • FIG. 6 shows the eight dimensional source space output for the time series data.
  • Example D Sequences, Fibonacci, etc.
  • the data set S ⁇ £, ,.. ,,S 9 ⁇ in this example consisted of nine sequences with ten elements each; they are shown in Table 1, FIG. 8. Sequences 1-3 are constant, arithmetic, and Fibonacci sequences respectively. Sequences 4-6 are these same sequences with some error or noise introduced. Sequences 7-9 are the same as 1-3, but the negative 1 's indicate that these elements are missing or unknown.
  • the resulting 10 x 10 source matrices where input to PROXSCAL configured as follows: sources- 9, objects- 10, dimension- 8, model- weighted, initial configuration- simplex, conditionality- unconditional, transformations- numerical, rate of convergence- 0.0, number of iterations- 500, and minimum stress- 0.0.
  • FIG. 9 shows dimensions 5 and 6 of the eight dimensional source space output.
  • the sequences are clustered, hence classified, according to whether they are constant, arithmetic, or Fibonacci based. Note that in this projection, the constant sequence and the constant sequence with missing element coincide, therefore only two versions of the constant sequence are visible.
  • Example E Missing value estimation for bridges This example extends the previous result to demonstrate the applicability of the analysis tool to missing value estimation on noisy, real-world data.
  • the data set consisted of nine categories of bridge data from the National Bridge Inventory (NBI) of the Federal Highway Administration. One of these categories, bridge material (steel or concrete), was removed from the database. The goal was to repopulate this missing category using the technique of the presently preferred embodiment to estimate the missing values.
  • NBI National Bridge Inventory
  • One hundred bridges were arbitrarily chosen from the NBI. Each bridge defined an eight dimensional vector of data with components the NBI categories. These vectors were preprocessed as in Example D, creating one hundred 8x8 source matrices. The matrices were submitted to PROXSCAL with specifications: sources- 100, objects- 8, dimension- 7, model- weighted, initial configuration- simplex, conditionality- unconditional, transformations- numerical, rate of convergence- 0.0, number of iterations- 500, and minimum stress- 0.00001.
  • the seven dimensional source space output was partially labeled by bridge material — an application of dye-dropping — and analyzed using the following function
  • a bridge was determined to be steel (concrete) if g p (A x , x) > g p (A 2 , x)
  • Example F Network dimensionality for a 4 -node network
  • This example demonstrates the use of stress/energy minima to determine network dimensionality from partial network output data.
  • Dimensionality in this example, means the number of nodes in a network.
  • a four-node network was constructed as follows: generator nodes 1 to 3 were defined by the sine functions, sin(2x), sin( 2x + -f ) , and sin( 2x + -y-) ; node 4 was the sum of nodes 1 through 3. The output of node 4 was sampled at 32 equal intervals between 0 and 2 ⁇ .
  • the data from node 4 was preprocessed in the manner of Example D: the if- th entry of the source matrix for node 4 was defined to be the absolute value of the difference between the /-th and/ ' -th samples of the node 4 time series.
  • a second, reference, source matrix was defined using the same preprocessing technique, now applied to thirty two equal interval samples of the function sin(x) for 0 ⁇ x ⁇ 2 ⁇ .
  • the resulting 2, 32 x 32 source matrices were input to PROXSCAL with technical specification: sources- 2, objects- 32, dimension- 1 to 6, model- weighted, initial configuration- simplex, conditionality- conditional, transformations- numerical, rate of convergence- 0.0, number of iterations- 500, and minimum stress- 0.0.
  • the dimension specification had a range of values, 1 to 6.
  • the dimension resulting in the lowest stress/energy is the dimensionality of the underlying network.
  • Table 2, FIG. 10, shows dimension and corresponding stress/energy values from the analysis by the tool 100 of the 4-node network. The stress/energy minimum is achieved in dimension 4, hence the tool 100 has correctly determined network dimensionality.
  • Similar experiments were run with more sophisticated dynamical systems and networks. Each of these experiments resulted in the successful determination of system degrees of freedom or dimensionality. These experiments included the determination of the dimensionality of a linear feedback shift register. These devices generate pseudo-random bit streams and are designed to conceal their dimensionality.
  • the illustrated embodiment of the present invention provides a method and apparatus for classifying input data.
  • Input data are received and formed into one or more matrices.
  • the matrices are processed using IDMDS to produce a stress/energy value, a rate or change of stress/energy value, a source space and a common space.
  • An output or back end process uses analytical or visual methods to inte ⁇ ret the source space and the common space.
  • the technique in accordance with the present invention therefore avoids limitations associated with statistical pattern recognition techniques, which are limited to detecting only the expected statistical pattern, and syntactical pattern recognition techniques, which cannot perceive beyond the expected structures.
  • the tool in accordance with the present invention is not limited to the fixed structure of neural pattern recognizers.
  • the technique in accordance with the present invention locates patterns in data without interference from preconceptions of models or users about the data.
  • the pattern recognition method in accordance with the present invention uses energy minimization to allow data to self-organize, causing structure to emerge. Furthermore, the technique in accordance with the present invention determines the dimension of dynamical systems from partial data streams measured on those systems through calculation of stress/energy or rate of change of stress/energy across dimensions.
  • PROXSCAL may be replaced by other IDMDS routines which are commercially available or are proprietary. It is therefore intended in the appended claims to cover all such changes and modifications which fall within the true spirit and scope of the invention.
  • MakeDissMissVal "MakeDissMissVal[R, form,metric,mv,prnt] creates (no. of columns) source dissimilarity matrices from matrix R with possible missing values.
  • R is assumed to have the form: objects-by-categori ⁇ s.
  • Hybrid: :usage "Hybrid[L] creates hybrid dissimilarity matrices from list of data vectors L.”
  • outmat Flatten[Map[Sym[Augment[#] ]&, M] , 1]; Print ["Number of objects: ", Length[outmat[ [1] ] ] ] ; outmat
  • Lp: :usage "Lp[C,p] calulates Minkowski distance with exponent p on sets C of configurations of points.”
  • Mathematica code for step 2 of the invention processing.
  • VMat::usage "VMat[W] computes the p.s.d. V matrix from the weight matrix W.”
  • TMat::usage "TMat[A] defines the T matrix which normalizes common space Z.”
  • Diagonal: :usage "Diagonal[M] creates a diagonal matrix from main diagonal of M.
  • UnDiagonal: :usage "UnDiagonal[M] turns diagonal matrix into a vector.”
  • Begin[ " * Private * "] IDMDSALS[prox_, proxwts_, dim_, epsilon_, iterations_, seed_] : Module[
  • ⁇ XO, ZO, AO ⁇ InitialConfig[numscs, numobj, dim]; Print [ “Number of sources: “, numscs]; Print[ “Number of objects: “, numobj];
  • Z0norm ZO .TO
  • A0norm Map[Inverse[TO] . #&, Ma fDiagonalMatrix, AO] ] ;
  • XO Map[Z0norm . #&, AOnorm] ;
  • V VMat[proxwts] ;
  • Vp PseudoInverse[V] ;
  • tempstress Stress [prox, proxwts, XO] ;
  • stresslist ⁇ tempstress ⁇ ;
  • Aconstrain Map[Inverse[Diagonal [Zt . V . Zconstrain] ] . #&, Map[Diagonal, Map[Zt . #&, numobj * Xupdate] ] ] ;
  • T TMat [Map[UnDiagonal, Aconstrain] ] ;
  • Print ["The common space coordinates are: “, ZOnorm // atrixForm] ; Print ["The source space coordinates are: “, Map[MatrixForm, Chop[Aconstrain] ]] ; ⁇ ZOnorm, Chop[Aconstrain] ⁇
  • BeginPackage["DistanceMatrix * "] DistanceMatrix : : usage "DistanceMatrix[ config] produces- a distance matrix from configuration matrix config.
  • DiagMatNorm: :usage "DiagMatNorm[A] normalizes the list of weight vectors A.” Begi [" * Private * "]
  • NormalizeG: :usage "NormalizeG[A] gives matrix which normalizes the common space given the list of weight vectors A.” Begin[ " * Private * "]
  • norm Table[norm[k], ⁇ k, Length[A[ [1] ] ] ⁇ ] ; N[DiagonalMatrix[norm] ]
  • BMatrix[delta, DM] is part of the Guttman transform. " Begin[ " * Private * "]
  • GuttmanTransform : : usage "The GuttmanTransform[B, X] updates the configuration X through multiplication by the BMatrix B.” Begin[ " * Private * "]
  • AGWStress :: usage "The AGWStress[dissimilarity, distance] is the loss function for multidimensional scaling. " Begin[ " * Private * "]
  • NormStress :: usage "NormStress[dissimilarity] normalizes the stress loss function. Begin[ " * Private * "]
  • SVDConstrain[configs] imposes constraints on the list of configurations configs.
  • start startlist start configurations.
  • Stress difference record ", stressdiffrecord] ;

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Abstract

Cette invention concerne un appareil d'analyse/classification de données qui va effectuer une étape de prétraitement, une étape de minimisation de puissance ainsi qu'une étape de traitement ultérieur afin d'analyser/classifier des données
PCT/US1998/027374 1997-12-29 1998-12-23 Minimisation de puissance applicable a la classification, a la reconnaissance de diagrammes, a la fusion des donnees de capteurs, a la compression de donnees, a la reconstruction de reseaux et au traitement de signaux WO1999034316A2 (fr)

Priority Applications (11)

Application Number Priority Date Filing Date Title
US09/581,949 US6993186B1 (en) 1997-12-29 1998-12-23 Energy minimization for classification, pattern recognition, sensor fusion, data compression, network reconstruction and signal processing
EP98966467A EP1064613A4 (fr) 1997-12-29 1998-12-23 Minimisation de puissance applicable a la classification, a la reconnaissance de diagrammes, a la fusion des donnees de capteurs, a la compression de donnees, a la reconstruction de reseaux et au traitement de signaux
CA002315814A CA2315814A1 (fr) 1997-12-29 1998-12-23 Minimisation de puissance applicable a la classification, a la reconnaissance de diagrammes, a la fusion des donnees de capteurs, a la compression de donnees, a la reconstruction de reseaux et au traitement de signaux
AU23070/99A AU2307099A (en) 1997-12-29 1998-12-23 Energy minimization for classification, pattern recognition, sensor fusion, datacompression, network reconstruction and signal processing
AU38645/99A AU3864599A (en) 1998-12-23 1999-04-21 Energy minimization for data merging and fusion
PCT/US1999/008768 WO2000039705A1 (fr) 1998-12-23 1999-04-21 Minimisation d'energie pour la fusion de donnees
US09/885,342 US6968342B2 (en) 1997-12-29 2001-06-19 Energy minimization for data merging and fusion
US11/096,126 US7174048B2 (en) 1997-12-29 2005-03-31 Energy minimization for classification, pattern recognition, sensor fusion, data compression, network reconstruction and signal processing
US11/097,783 US7702155B2 (en) 1997-12-29 2005-04-01 Energy minimization for classification, pattern recognition, sensor fusion, data compression, network reconstruction and signal processing
US11/097,733 US7272262B2 (en) 1997-12-29 2005-04-01 Energy minimization for classification, pattern recognition, sensor fusion, data compression, network reconstruction and signal processing
US12/757,561 US7912290B2 (en) 1997-12-29 2010-04-09 Energy minimization for classification, pattern recognition, sensor fusion, data compression, network reconstruction and signal processing

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US09581949 A-371-Of-International 1998-12-23
PCT/US1999/008768 Continuation-In-Part WO2000039705A1 (fr) 1997-12-29 1999-04-21 Minimisation d'energie pour la fusion de donnees
US11/097,783 Division US7702155B2 (en) 1997-12-29 2005-04-01 Energy minimization for classification, pattern recognition, sensor fusion, data compression, network reconstruction and signal processing
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US6993186B1 (en) 1997-12-29 2006-01-31 Glickman Jeff B Energy minimization for classification, pattern recognition, sensor fusion, data compression, network reconstruction and signal processing
AU3864599A (en) * 1998-12-23 2000-07-31 Jeff B. Glickman Energy minimization for data merging and fusion
CA2436400A1 (fr) 2002-07-30 2004-01-30 Abel G. Wolman Geometrisation servant a la reconnaissance des formes, l'analyse des donnees, la fusion des donnees et la prise de decisions a plusieurs criteres
US7557805B2 (en) 2003-04-01 2009-07-07 Battelle Memorial Institute Dynamic visualization of data streams
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US5422961A (en) * 1992-04-03 1995-06-06 At&T Corp. Apparatus and method for improving recognition of patterns by prototype transformation
US5602938A (en) * 1994-05-20 1997-02-11 Nippon Telegraph And Telephone Corporation Method of generating dictionary for pattern recognition and pattern recognition method using the same
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