The Experts below are selected from a list of 4989 Experts worldwide ranked by ideXlab platform
Mathieu Salzmann - One of the best experts on this subject based on the ideXlab platform.
-
efficient Dense Subspace clustering
Workshop on Applications of Computer Vision, 2014Co-Authors: Mathieu SalzmannAbstract:In this paper, we tackle the problem of clustering data points drawn from a union of linear (or affine) Subspaces. To this end, we introduce an efficient Subspace clustering algorithm that estimates Dense connections between the points lying in the same Subspace. In particular, instead of following the standard compressive sensing approach, we formulate Subspace clustering as a Frobenius norm minimization problem, which inherently yields Denser con- nections between the data points. While in the noise-free case we rely on the self-expressiveness of the observations, in the presence of noise we simultaneously learn a clean dictionary to represent the data. Our formulation lets us address the Subspace clustering problem efficiently. More specifically, the solution can be obtained in closed-form for outlier-free observations, and by performing a series of linear operations in the presence of outliers. Interestingly, we show that our Frobenius norm formulation shares the same solution as the popular nuclear norm minimization approach when the data is free of any noise, or, in the case of corrupted data, when a clean dictionary is learned. Our experimental evaluation on motion segmentation and face clustering demonstrates the benefits of our algorithm in terms of clustering accuracy and efficiency.
-
WACV - Efficient Dense Subspace clustering
IEEE Winter Conference on Applications of Computer Vision, 2014Co-Authors: Mathieu SalzmannAbstract:In this paper, we tackle the problem of clustering data points drawn from a union of linear (or affine) Subspaces. To this end, we introduce an efficient Subspace clustering algorithm that estimates Dense connections between the points lying in the same Subspace. In particular, instead of following the standard compressive sensing approach, we formulate Subspace clustering as a Frobenius norm minimization problem, which inherently yields Denser con- nections between the data points. While in the noise-free case we rely on the self-expressiveness of the observations, in the presence of noise we simultaneously learn a clean dictionary to represent the data. Our formulation lets us address the Subspace clustering problem efficiently. More specifically, the solution can be obtained in closed-form for outlier-free observations, and by performing a series of linear operations in the presence of outliers. Interestingly, we show that our Frobenius norm formulation shares the same solution as the popular nuclear norm minimization approach when the data is free of any noise, or, in the case of corrupted data, when a clean dictionary is learned. Our experimental evaluation on motion segmentation and face clustering demonstrates the benefits of our algorithm in terms of clustering accuracy and efficiency.
Vladimir V. Tkachuk - One of the best experts on this subject based on the ideXlab platform.
-
For every space X, either CpCp(X) or CpCpCp(X) is ψ-separable
Topology and its Applications, 2020Co-Authors: Vladimir V. TkachukAbstract:Abstract We establish that, for any Tychonoff space X, at least one of the function spaces C p C p ( X ) and C p C p C p ( X ) must have a Dense Subspace of countable pseudocharacter. If GCH holds, then at least one of the spaces C p ( X ) and C p C p ( X ) has a Dense Subspace of countable pseudocharacter. We also prove that all iterated function spaces C p , n ( K ) have a uniformly Dense Subspace of countable pseudocharacter whenever K is a Corson compact space. Our results solve several published open questions.
-
If K is Gul'ko compact, then every iterated function space Cp,n(K) has a uniformly Dense Subspace of countable pseudocharacter
Journal of Mathematical Analysis and Applications, 2019Co-Authors: J. Aguilar-velázquez, Vladimir V. TkachukAbstract:Abstract We establish that C p ( X ) has a Dense Subspace of countable i-weight if and only if d ( C p ( X ) ) ⩽ c . It is also proved that the space C p ( K ) has a Dense F σ -discrete Subspace whenever K is Corson compact. If both spaces X and C p ( X ) are Lindelof Σ, then for any natural n ⩾ 2 , the iterated function space C p , n ( X ) has a uniformly Dense Subspace of countable pseudocharacter. In the case of a Gul'ko compact space K, there is a uniformly Dense Subspace of countable pseudocharacter in C p , n ( K ) for any n ∈ N . This is a new result even for C p ( K ) given that K is Eberlein compact.
-
Many Eberlein–Grothendieck spaces have no non-trivial convergent sequences
European Journal of Mathematics, 2017Co-Authors: Vladimir V. TkachukAbstract:We establish that a monolithic compact space X is not scattered if and only if Open image in new window has a Dense subset without non-trivial convergent sequences. Besides, for any cardinal \(\kappa \geqslant \mathfrak {c}\), the space \(\mathbb {R}^\kappa \) has a Dense Subspace without non-trivial convergent sequences. If X is an uncountable \(\sigma \)-compact space of countable weight, then any Dense set Open image in new window has a Dense Subspace without non-trivial convergent sequences. We also prove that for any countably compact sequential space X, if Open image in new window has a Dense k-Subspace, then X is scattered.
-
Properties of function spaces reflected by uniformly Dense Subspaces
Topology and its Applications, 2003Co-Authors: Vladimir V. TkachukAbstract:Abstract A set A⊂Cp(X) is uniformly Dense in Cp(X) if, for any f∈Cp(X) and any e>0, there is g∈A such that |g(x)−f(x)| P , if a uniformly Dense Subspace of Cp(X) has P then the whole Cp(X) has P . This is true, in particular, for P ∈{ Lindelof Σ-property, tightness ⩽κ, network weight ⩽κ, Frechet–Urysohn property}. If Cp(X) has a uniformly Dense σ-compact Subspace then X is compact. We give an example of a compact space X such that ψ(Cp(X))>ω while Cp(X) has a uniformly Dense Subspace of countable pseudocharacter.
I V Skrypnik - One of the best experts on this subject based on the ideXlab platform.
-
a new topological degree theory for Densely defined quasibounded s perturbations of multivalued maximal monotone operators in reflexive banach spaces
Abstract and Applied Analysis, 2005Co-Authors: Athanassios G. Kartsatos, I V SkrypnikAbstract:Let X be an infinite-dimensional real reflexive Banach space with dual space X ∗ and G ⊂ X open and bounded. Assume that X and X ∗ are locally uniformly convex. Let T : X ⊃ D ( T ) → 2 X ∗ be maximal monotone and C : X ⊃ D ( C ) → X ∗ quasibounded and of type ( S ˜ + ) . Assume that L ⊂ D ( C ) , where L is a Dense Subspace of X , and 0 ∈ T ( 0 ) . A new topological degree theory is introduced for the sum T + C . Browder's degree theory has thus been extended to Densely defined perturbations of maximal monotone operators while results of Browder and Hess have been extended to various classes of single-valued Densely defined generalized pseudomonotone perturbations C . Although the main results are of theoretical nature, possible applications of the new degree theory are given for several other theoretical problems in nonlinear functional analysis.
-
ranges of Densely defined generalized pseudomonotone perturbations of maximal monotone operators
Journal of Differential Equations, 2003Co-Authors: Z. Guan, Athanassios G. Kartsatos, I V SkrypnikAbstract:Abstract Let X be a real reflexive Banach space and A : X→2 X ∗ be maximal monotone. Let B : X→2 X ∗ be quasibounded, finitely continuous and generalized pseudomonotone with X′⊂D(B), where X′ is a Dense Subspace of X such that X′∩D(A)≠∅. Let S⊂X ∗ . Conditions are given under which S⊂ R(A+B) and int S⊂int R(A+B) . Results of Browder concerning everywhere defined continuous and bounded operators B are improved. Extensions of this theory are also given using the degree theory of the last two authors concerning Densely defined perturbations of nonlinear maximal monotone operators which satisfy a generalized (S+)-condition. Applications of this extended theory are given involving nonlinear parabolic problems on cylindrical domains.
Jung-hyun Bae - One of the best experts on this subject based on the ideXlab platform.
-
Eigenvalues of quasibounded maximal monotone operators
Journal of Inequalities and Applications, 2014Co-Authors: In-sook Kim, Jung-hyun BaeAbstract:Let X be a real reflexive separable Banach space with dual space X ∗ and let L be a Dense Subspace of X. We study a nonlinear eigenvalue problem of the type
-
eigenvalue results for pseudomonotone perturbations of maximal monotone operators
Open Mathematics, 2013Co-Authors: In-sook Kim, Jung-hyun BaeAbstract:Let X be an infinite-dimensional real reflexive Banach space such that X and its dual X* are locally uniformly convex. Suppose that T: X⊃D(T) → 2X* is a maximal monotone multi-valued operator and C: X⊃D(C) → X* is a generalized pseudomonotone quasibounded operator with L ⊂ D(C), where L is a Dense Subspace of X. Applying a recent degree theory of Kartsatos and Skrypnik, we establish the existence of an eigensolution to the nonlinear inclusion 0 ∈ Tx + λCx, with a regularization method by means of the duality operator. Moreover, possible branches of eigensolutions to the above inclusion are discussed. Furthermore, we give a surjectivity result about the operator λT + C when λ is not an eigenvalue for the pair (T, C), T being single-valued and Densely defined.
José Bonet - One of the best experts on this subject based on the ideXlab platform.
-
Every Separable Complex Fréchet Space with a Continuous Norm is Isomorphic to a Space of Holomorphic Functions
Canadian Mathematical Bulletin, 2020Co-Authors: José BonetAbstract:Extending a result of Mashreghi and Ransford, we prove that every complex separable infinite dimensional Frechet space with a continuous norm is isomorphic to a space continuously included in a space of holomorphic functions on the unit disc or the complex plane, which contains the polynomials as a Dense Subspace. As a consequence examples of nuclear Frechet spaces of holomorphic functions without the bounded approximation exist.
-
NONCOMPLETE MACKEY TOPOLOGIES ON BANACH SPACES
Bulletin of the Australian Mathematical Society, 2010Co-Authors: José Bonet, Bernardo CascalesAbstract:Answering a question of W. Arendt and M. Kunze in the negative, we construct a Banach space X and a norm closed weak* Dense Subspace Y of the dual X′ of X such that X , endowed with the Mackey topology μ ( X , Y ) of the dual pair 〈 X , Y 〉, is not complete.