Results 1  10
of
2,345
Coordinate subspace arrangements and monomial ideals
, 1998
"... We relate the (co)homological properties of real coordinate subspace arrangements and of monomial ideals. ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
We relate the (co)homological properties of real coordinate subspace arrangements and of monomial ideals.
The homotopy type of the complement of a coordinate subspace arrangement
, 2007
"... The homotopy type of the complement of a complex coordinate subspace arrangement is studied by fathoming out the connection between its topological and combinatorial structures. A family of arrangements for which the complement is homotopy equivalent to a wedge of spheres is described. One consequ ..."
Abstract

Cited by 31 (4 self)
 Add to MetaCart
The homotopy type of the complement of a complex coordinate subspace arrangement is studied by fathoming out the connection between its topological and combinatorial structures. A family of arrangements for which the complement is homotopy equivalent to a wedge of spheres is described. One
The Ring Structure On The Cohomology Of Coordinate Subspace Arrangements
, 1999
"... Every simplicial complex 2 [n] on the vertex set [n] = f1; : : : ; ng denes a real resp. complex arrangement of coordinate subspaces in R n resp. C n via the correspondence 3 7! spanfe i : i 2 g: The linear structure of the cohomology of the complement of such an arrangement is explicitl ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Every simplicial complex 2 [n] on the vertex set [n] = f1; : : : ; ng denes a real resp. complex arrangement of coordinate subspaces in R n resp. C n via the correspondence 3 7! spanfe i : i 2 g: The linear structure of the cohomology of the complement of such an arrangement
The homotopy type of the complement of the codimensiontwo coordinate subspace arrangement
 Russian Math. Surveys
"... A complex coordinate subspace of C n is given by Lσ = {(z1,..., zn) ∈ C n  zi1 = · · · = zi k = 0} where σ = {i1,..., ik} is a subset of [m]. For each simplicial complex K on the set [m] we associate the complex coordinate subspace arrangement CA(K) = {Lσ  σ ̸ ∈ K} and its complement U(K) = ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
A complex coordinate subspace of C n is given by Lσ = {(z1,..., zn) ∈ C n  zi1 = · · · = zi k = 0} where σ = {i1,..., ik} is a subset of [m]. For each simplicial complex K on the set [m] we associate the complex coordinate subspace arrangement CA(K) = {Lσ  σ ̸ ∈ K} and its complement U(K) =
Torus actions, equivariant momentangle complexes and coordinate subspace arrangements
, 2003
"... We show that the cohomology algebra of the complement of a coordinate subspace arrangement in the mdimensional complex space is isomorphic to the cohomology algebra of the Stanley–Reisner face ring of a certain simplicial complex on m vertices. (The face ring is regarded as a module over the polyno ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
We show that the cohomology algebra of the complement of a coordinate subspace arrangement in the mdimensional complex space is isomorphic to the cohomology algebra of the Stanley–Reisner face ring of a certain simplicial complex on m vertices. (The face ring is regarded as a module over
Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
, 1997
"... We develop a face recognition algorithm which is insensitive to gross variation in lighting direction and facial expression. Taking a pattern classification approach, we consider each pixel in an image as a coordinate in a highdimensional space. We take advantage of the observation that the images ..."
Abstract

Cited by 2310 (17 self)
 Add to MetaCart
We develop a face recognition algorithm which is insensitive to gross variation in lighting direction and facial expression. Taking a pattern classification approach, we consider each pixel in an image as a coordinate in a highdimensional space. We take advantage of the observation that the images
Acquiring linear subspaces for face recognition under variable lighting
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2005
"... Previous work has demonstrated that the image variation of many objects (human faces in particular) under variable lighting can be effectively modeled by low dimensional linear spaces, even when there are multiple light sources and shadowing. Basis images spanning this space are usually obtained in ..."
Abstract

Cited by 317 (2 self)
 Add to MetaCart
PCA is used to estimate a subspace. Finally, images rendered from a 3D model under diffuse lighting based on spherical harmonics are directly used as basis images. In this paper, we show how to arrange physical lighting so that the acquired images of each object can be directly used as the basis
Highresolution intersubject averaging and a coordinate system for the cortical surface
 Hum. Brain Mapp
, 1999
"... Abstract: The neurons of the human cerebral cortex are arranged in a highly folded sheet, with the majority of the cortical surface area buried in folds. Cortical maps are typically arranged with a topography oriented parallel to the cortical surface. Despite this unambiguous sheetlike geometry, the ..."
Abstract

Cited by 339 (44 self)
 Add to MetaCart
Abstract: The neurons of the human cerebral cortex are arranged in a highly folded sheet, with the majority of the cortical surface area buried in folds. Cortical maps are typically arranged with a topography oriented parallel to the cortical surface. Despite this unambiguous sheetlike geometry
Wonderful Models Of Subspace Arrangements
 Selecta Math. (N.S
, 1995
"... this paper we describe, for any given finite family of subspaces of a vector space or for linear subspaces in affine or projective space, a smooth model, proper over the given space, in which the complement of these subspaces is unchanged but the family of subspaces is replaced by a divisor with nor ..."
Abstract

Cited by 119 (6 self)
 Add to MetaCart
this paper we describe, for any given finite family of subspaces of a vector space or for linear subspaces in affine or projective space, a smooth model, proper over the given space, in which the complement of these subspaces is unchanged but the family of subspaces is replaced by a divisor
Principal manifolds and nonlinear dimensionality reduction via tangent space alignment
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 2004
"... Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and nonlinear dimension reduction. Based on a set of unorganized ..."
Abstract

Cited by 261 (15 self)
 Add to MetaCart
data points sampled with noise from the manifold, we represent the local geometry of the manifold using tangent spaces learned by fitting an affine subspace in a neighborhood of each data point. Those tangent spaces are aligned to give the internal global coordinates of the data points with respect
Results 1  10
of
2,345