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Topic: Eigenspace

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	Analysis of the system
		When performing an eigenvector analysis, it is essential to normalize the input data to correct for variations which the eigenspace should not model; this is the reason, for example, for the alignment stage, which prevents the eigenvectors from attempting to model rotations of the head.
		We also found that if the input head from the tracking system was significantly brighter than the head models in the eigenspace, the reconstructions were severely deformed, probably because the reconstruction coefficients were being increased beyond their statistically valid range.
		The experiments performed with the tracking system while modifying the modular eigenspace masks (Chapter 6) indicate that more work is needed to stabilize the image being used as input to the reconstruction pipeline.
	xenia.media.mit.edu /~kbrussel/Eigenheads/node14.html (463 words)

	Eigenvalue, eigenvector and eigenspace - Wikipedia, the free encyclopedia
		An eigenspace is a space consisting of all eigenvectors which have the same eigenvalue.
		The geometric multiplicity of an eigenvalue is the dimension of the associated eigenspace.
		The vector space on which the matrix acts is always the direct sum of the generalized eigenspaces (i.e., is spanned by them and they are independent).
	en.wikipedia.org /wiki/Eigenvalue,_eigenvector,_and_eigenspace (4142 words)

	Weak Eigenspace Hunters
		It should be noted that weak eigenspaces can also be introduced, and accusations of chaos warfare have been made for many millennia.
		Weak eigenspace hunters are educated and employed across civilised space, but the most well-known education or programming institutions are all located within the Negentropy Alliance for obvious cultural reasons, despite the efforts that have been spent on creating chaos-free complex systems in the Alliance.
		Eigenspace hunters of various kinds (and complexity management consultancy, software and skill) has been a large part of Negentropic export since the end of the Version War.
	www.orionsarm.com /topics/Weak_Eigenspace_Hunters.html (552 words)

	Section 1 (Site not responding. Last check: 2007-10-19)
		and this is also a basis for the eigenspace corresponding to the eigenvalue
		The roots of this equation are given by the quadratic formula as
		Because eigenvectors corresponding to distinct eigenvalues must be linearly independent and we have three didtinct eigenvalues, we are guaranteed to find a basis of eigenvectors for
	www-math.cudenver.edu /~rrosterm/lins05_6sol/node1.html (475 words)

	Eigentaste Applications Library (Site not responding. Last check: 2007-10-19)
		Eigenspace: a class that generates a complete clustering based on user ratings and application parameters.
		More on how eigenspace handles rating objects will be discussed in the Eigenspace section.
		Eigenspace also provides some high level statistical procedures for determining the mean and variance of ratings for each rating element within each user cluster.
	www.zytek.com /gordon/tutorial.html (365 words)

	Detection, recognition and coding of complex objects using probabilistic eigenspace analysis - Patent 5710833 (Site not responding. Last check: 2007-10-19)
		Such eigenspace decompositions, while potentially more powerful than standard detection techniques such as template matching or normalized correlation, still present a formidable computational burden if estimation techniques are to be applied to the high-dimensional space of the imagery.
		The approach of the present invention is based on density estimation, and utilizes an eigenspace decomposition to reduce a high-dimensional image space to a computationally manageable subspace.
		The eigenspace density estimation technique of the present invention is not limited to textured or detailed objects such as faces.
	www.freepatentsonline.com /5710833.html (6018 words)

	Chu-Yin Chang's PhD Thesis Abstract (Site not responding. Last check: 2007-10-19)
		In addition, the online performance of eigenspace methods degrades in the presence of occlusion and background noise in an image.
		In the first part of this work, a computationally efficient algorithm for the eigenspace decomposition of correlated images is presented.
		The second part of this work presents a solution to the pose detection problem, based on eigenspace methods, for cases where occlusion and background noise are present in an image.
	www.engr.colostate.edu /~aam/students/chang_abstract.html (286 words)

	Eigenvalue, eigenvector and eigenspace (Site not responding. Last check: 2007-10-19)
		In mathematics, the eigenvalues, eigenvectors, and eigenspaces of a transformation
		For instance, an eigenvector of a rotation is a vector located within the axis around which the rotation is performed.
		However, the associated eigenspace is the axis usually called the x axis, spanned by the unit vector, so the geometric multiplicity is only 1.
	www.punweb.com /article/Eigenstate (4079 words)

	BioMed Central \| Full text \| Hubs of knowledge: using the functional link structure in Biozon to mine for biologically ...
		The fourth eigenspace emphasizes protein CRK-associated substrate (docid: 1036799), which is a breast cancer anti-estrogen resistance protein, and its encoding DNA sequences and interactions.
		The principal eigenspace of the sparse models emphasizes protein Autoimmune regulator (docid: 947655), protein Autoimmune regulator (docid: 943600) and Ribonuclease P protein subunit RPP1 (docid: 640274) along with the nucleic acid sequences that encode these proteins.
		However, each eigenspace is centered on a different subset of objects and the high scoring documents in each one form a different subgraph with a different structure.
	www.biomedcentral.com /1471-2105/7/71 (13435 words)

	Dimensionality of Illumination Manifolds in Eigenspace - Nayar, Murase (ResearchIndex) (Site not responding. Last check: 2007-10-19)
		Dimensionality of Illumination Manifolds in Eigenspace - Nayar, Murase (ResearchIndex)
		Given that the eigenspaces we use are linear subspaces, the class of linear reflectance functions [15] 16] is of particular interest to...
		8 the Dimensionality of Illumination Manifolds in Eigenspace - Nayar, Murase - 1994
	citeseer.lcs.mit.edu /nayar94dimensionality.html (598 words)

	Details of the modular eigenspace algorithm
		We have implemented the above formula; that is, the sum of the projections of an input vector onto the modular eigenspace is divided by the sum of the contributions of the masks.
		However, we found that when the modular eigenspaces were not orthogonal, the reconstructions sometimes had errors including large variations in the head shape (Figure 6.3).
		We are considering techniques to reduce the modular eigenspace reconstruction error by interpolating nonlinearly among the modular eigenspaces' projections.
	xenia.media.mit.edu /~kbrussel/Eigenheads/node11.html (658 words)

	Parametric eigenspace technique (Site not responding. Last check: 2007-10-19)
		I presume which angle(direction) the image is taken a shot from.
		Then I compress its data by using eigenspace technique in advance.
		I compress it into several or dozen data by using eigenspace technique,which is one of statistic techniques.
	www.robot.mach.mie-u.ac.jp /english/research/eparametric/eparametric.html (60 words)

	Eigenspace Distance Measures on 3D Warped Faces
		A colour eigenspace of these normalized mug-shots is constructed and the mean face and the first 4 eigenfaces are shown in Figure 6.
		The training set of faces is mapped into this eigenspace and the distribution of the coefficients and residuals is modeled as a Gaussian density.
		The maximum likelihood estimate for the probability of a data point fitting this model is computed using this Gaussian.
	vismod.media.mit.edu /tech-reports/TR-401/node6.html (493 words)

	CS510: Eigenspace Assignment (Site not responding. Last check: 2007-10-19)
		For your third assignment, you will implement an eigenspace matching system, as per section 10.4 of Trucco and Verri and your notes.
		The simplest is to take the euclidean distance of the two images in eigenspace, but you may also experiment with angle (i.e.
		To do this assignment, you may borrow the singular value decomposition code found in Numerical Recipes in C. Your assignment must be written in C or C++; it cannot be written in MATLAB, Maple, or any other language.
	www.cs.colostate.edu /~cs510/Labs/Eigenspace.html (297 words)

	Recognizing Human Behavior Using Universal Eigenspace (Site not responding. Last check: 2007-10-19)
		An efficient application of eigenspace technique to recognize human behaviors is described.
		A number of different posture sets from some selected behaviors create universal eigenspace and different sets of unknown postures are recognized from it.
		A new approach of producing eigenspace is described and the robustness of the method is effectively proved in the experiment.
	csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/proceedings/&toc=comp/proceedings/icpr/2002/1695/01/1695toc.xml&DOI=10.1109/ICPR.2002.1044694 (204 words)

	Apathy :wq
		The eigenspace associated with the eigenvalue c of a matrix A is the null space of A - c*I.
		Modular eigenspaces are used to decorrelate eigenfeatures (eyes, nose, and mouth) from the rest of the head data.
		More mathymaticians sock it out over eigenspace, mainly trying to figure out why their eigenvectors are sticking out of their eigenvalues.
	apathy.pitas.com /eigenspace.html (775 words)

	Identifying the face by EigenSpace decomposition.
		This is the idea behind the EigenSpace coding made popular by Turk and Pentland [TP91].
		To construct an eigenspace, we begin with a database of images, as for example shown in figure 8.
		The principal components of the covariance matrix form an orthogonal basis set, which are the axis of the EigenSpace as shown in figure 9.
	www-prima.inrialpes.fr /ECVNet/IRS95/node15.html (753 words)

	Relative Perturbation Theory: II. Eigenspace and Singular Subspace Variations
		Eigenspace and Singular Subspace Variations: SIAM Journal on Matrix Analysis and Applications Vol.
		These bounds may be bad news for invariant subspaces corresponding to clustered eigenvalues or clustered singular values of much smaller magnitudes than the norms of matrices under considerations.
		In this paper, we consider how eigenspaces of a Hermitian matrix A change when it is perturbed to $\widetilde A=D^AD$ and how singular spaces of a (nonsquare) matrix B change when it is perturbed to $\widetilde B=D_1^BD_2$, where D, D1, and D2 are nonsingular.
	epubs.siam.org /sam-bin/dbq/article/29850 (212 words)

	[No title]
		p(v)=(6-v)(-1-v)-(3)(-4)=v^2-5v+6=(v-2)(v-3) ==> eigenvalues are {2,3} A-2I = 4 -4 ==> eigenspace of v=2 3 -3 is Span{(1,1)'} A-3I = 3 -4 ==> eigenspace of v=3 3 -4 is Span{(4,3)'} g.
		A-1I = 0 1 1 ==> eigenspace of v=1 0 1 1 is Span{(1,0,0)',(0,1,-1)'} 0 0 0 A-2I = -1 1 1 ==> eigenspace of v=2 0 0 1 is Span{(1,1,0)'} 0 0 -1 i.
		A-0I = 4 -5 1 ==> eigenspace of v=0 1 0 -1 is Span{(1,1,1)'} 0 1 -1 A-1I = 3 -5 1 ==> eigenspace of v=1 1 -1 -1 is Span{(3,2,1)'} 0 1 -2 A-2I = 2 -5 1 ==> eigenspace of v=2 1 -2 -1 is Span{(7,3,1)'} 0 1 -3 k.
	www.math.wustl.edu /~victor/classes/ma309/s09.txt (1273 words)

	Identifying the face by EigenSpace decomposition.
		This is the idea behind the EigenSpace coding made popular by Turk and Pentland [TP91].
		To construct an eigenspace, we begin with a database of images, as for example shown in figure 8.
		The principal components of the covariance matrix form an orthogonal basis set, which are the axis of the EigenSpace as shown in figure 9.
	homepages.inf.ed.ac.uk /rbf/CVonline/LOCAL_COPIES/ECVNET/CROWLEY2/node15.html (753 words)

	Institutionen för datavetenskap - Numerical Linear Algebra Group - Matrix Equations, Canonical Forms and Eigenspace ...
		in control theory, ask for eigenspaces of a matrix or matrix pair associated with the eigenvalues in a given domain $\Gamma$ of the complex plane.
		The error bounds are based on estimates of condition numbers for eigenvalues and eigenspaces.
		A related and challenging problem is the clustering of computed eigenvalues in groups of close eigenvalues, where, ideally, each group corresponds to a multiple eigenvalue.
	www.cs.umu.se /research/nla/regular_pairs (221 words)

	Machine Vision Group
		In this algorithm an eigenspace is formed for every gesture in the vocabulary.
		By projecting the samples of a gesture into the corresponding eigenspace the manifolds are formed.
		Therefore, the set of clusters in an eigenspace is approximated by a sequence of gaussian distributions representing the spatial and temporal variations of hand in the corresponding gesture.
	www.compapp.dcu.ie /~ashamaie/mvg/graphm.html (241 words)

	Diagonalization
		since the eigenspace for this eigenvalue is one-dimensional.
		The eigenspaces of each eigenvalue have orthogonal bases.
		The dimension of an eigenspace corresponds to the multiplicity of the eigenvalue.
	distance-ed.math.tamu.edu /Math640/chapter5/node8.html (764 words)

	Eigenspace (Site not responding. Last check: 2007-10-19)
		Eigenspace is the Wall-Magazine of Physics Society, Department of Physics, IIT Kanpur.
		In the year 2001, Physics Society came out with an idea of keeping the students abreast with current affairs and technological trends by starting a Wall Magazine.
		Eigenspace is an effort to induce writing abilities among the students and to provide a platform to express their views and ideas on the latest advances in the area of Physics and Technology.
	www.iitk.ac.in /phy/New01/eigenspace (72 words)

	U.S. Pregrant 20020095287 - Method of determining an eigenspace for representing a plurality of training speakers (Site not responding. Last check: 2007-10-19)
		For each speaker a combined model is then displayed in a high-dimensional model space by concatenation of the model parameters of the models of the individual training speakers to a respective coherent super vector.
		Subsequently, a transformation is carried out while the model space dimension is reduced to obtain eigenspace basis vectors (Ee), which transformation utilizes a reduction criterion based on the variability of the vectors to be transformed.
		Then the high-dimensional model space is first in a first step reduced to a speaker subspace by a change of basis, in which speaker subspace all the training speakers are represented.
	cxp.paterra.com /uspregrant20020095287.html (203 words)

	BU CLA CS 835: Seminar in Image and Video Computing --- Class commentary on articles
		Neat proof show that the closer projects are in eigenspace, the more highly correlated are the images Note that comparison is made to manifold not original image projections.
		The object is then represented in both universal eigenspace - which is determined by the set of all objects of interest, and its own eigenspace.
		It does this by creating two separate eigenspaces: one formed from the set of average representation of objects (the "universal" space) to distinguish between objects, and one formed from the different appearances of a single object under the range of orientation and lighting created at training time (the "object" space).
	cs-www.bu.edu /faculty/sclaroff/courses/cs835/commentary/eigen.html (3397 words)

	Amazon.com: eigenspace (Site not responding. Last check: 2007-10-19)
		Eigenspaces of Graphs (Encyclopedia of Mathematics and its Applications) by Dragos Cvetkovic, Peter Rowlinson, and Slobodan Simic (Hardcover - Nov 17, 2004)
		Eigenspace techniques for active flutter suppression (NASA contractor report) by William L Garrard (Unknown Binding - 1987)
		is the projection onto the eigenspace generated by the i-th eigenfunction.
	www.amazon.com /s?ie=UTF8&keywords=eigenspace&tag=robbsbiologybook&index=blended&link_code=qs&page=1 (819 words)

	Eigenspace Update Algorithm
		During the past few years several interesting applications of eigenspace representation of the images have been proposed.
		More important is the fact that incremental updating of eigenspace representations will open up new and interesting research applications in vision such as active recognition and learning.
		The main objective of this paper is to put these in perspective and discuss a new updating scheme for low numerical rank matrices that can be shown to be numerically stable and fast.
	vision.ece.ucsb.edu /projects/incsvd (390 words)

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