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| Авторизация |
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| Elden L. — Numerical Linear Algebra and Applications in Data Mining |
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| Предметный указатель |
1-norm 14
1-norm, matrix 16
2-norm 16 59
3-mode array 91
Absolute error 15
Adjacency matrix 147
Aitken extrapolation 146
Algebra, multi-linear 91
All-orthogonalitv 95
Array,  -mode 91
Array, -way 91
Backward error 7
Backward error analysis 25
Band width 28
Basis 17
Basis vector 12
Bidiagonal matrix 82 186
Bidiagonalization, Golub — Kahan 86
Bidiagonalization, Householder 82
Bidiagonalization, Lanczos 82 86
Bilinear form 162
Bulge 185
Cancellation 9 78
Centroid 102 108 133
Characteristic equation 172
Cholesky decomposition 24
Clustering 133 151
Column pivoting 73
Column-stochastic matrix 140
Complete orthogonal decomposition 73
Compressed column storage 190
Compressed row storage 189
computer games 7
Computer graphics 7
Concept vector 102 133
Condition number 24 66
Core tensor 96 160
Cosine distance measure 15 126
Data compression 61 100
Decomposition, Schur 187
Dense matrix 40 169
Dependent variable 77
Distance measure, cosine 15
Distance, Euclidean 14
Document weighting 126 151
Eigenfaces 159
Eigenvalue 139
Eigenvalue, perturbation 170 172
Eigenvector 139
Eigenvector, perturbation 171 173
Equality constraint 69
Error, absolute 15
Error, backward 7
Error, floating point arithmetic 7
Error, forward 7
Error, relative 15
Euclidean distance 14
Euclidean vector norm 14
Explanatory variable 77
Floating point operation 6
Floating point standard 6
FLOP 6 43
Flop count, matrix decomposition 71
Forward error 7
Frobenius norm 16 62
Gauss transformation 21
Gaussian elimination 21
Gilbert — Johnson — Keerthi algorithm 7
Givens rotation 38
Golub — Kahan bidiagonalization 86
GSVD 69
Handwritten digit recognition 4
Handwritten digits 91
Hessenberg matrix 54 187
HOSVD 94 160
Householder bidiagonalization 82
Householder transformation 40 82 186 187
IEEE, double precision 7
IEEE, floating point standard 6
IEEE, single precision 7
Ill-conditioned matrix 25
Implicit Q theorem 184
Implicit shift 184
INDEX 124
Index, inverted 124
Information retrieval 2 123 190
Inlink 137
Inner product 14 92
Internet 5 137 153
Inverse document frequency 126
Inverse iteration 176 186 189
Inverse matrix 18
inverted index 124
Irreducible matrix 141
Iteration, inverse 186
K-means algorithm 101 102
k-means algorithm, spherical 102
Kahan matrix 75
Karhunen — Loewe expansion 56
Krylov subspace 89
Lanczos bidiagonalization 82 86
LAPACK 12 71 169 180
Least squares method 32
Least squares problem 49 64
Least squares problem, equality constraint 69
Least squares problem, linear 32
Least squares solution, by QR decomposition 49
Least squares solution, by SVD 66
Least squares solution, minimum norm 68
Least squares, prediction 77
Linear independence 17
Linear operator 3
Linear system, over-determined 31 49 64
Linear system, perturbation theory 24
Linear system, under-determined 68
Link farm 143
Link graph 5 139
Low-rank approximation 61 88 129 133
LSI 124
Manifold 117
Markov chain 140
MATLAB 169
Matrix norm 15
Matrix norm, 1-norm 16
Matrix norm, 2-norm 16 59
Matrix norm, Frobenius 16 62
Matrix norm, max-norm 16
Matrix rank 18
Matrix, adjacency 147
Matrix, bidiagonal 82 186
Matrix, column-stochastic 140
Matrix, decomposition, flop count 71
Matrix, dense 29 40 169
Matrix, Givens 38
Matrix, Hessenberg 54 187
Matrix, Householder 40
Matrix, ill-conditioned 25
Matrix, inverse 18
Matrix, irreducible 141
Matrix, nilpotent 190
Matrix, nonsingular 18
Matrix, null-space 59
Matrix, orthogonal 36
Matrix, permutation 21 73
Matrix, range 59
Matrix, rectangular 21
Matrix, reducible 141
Matrix, reflection 40
Matrix, rotation 38
Matrix, sparse 3 126 189
| Matrix, square 21
Matrix, term-document 2 125 151
Matrix, term-sentence 151
Matrix, transition 140
Matrix, tridiagonal 178
Max-norm 14
Maximum norm matrix 16
Medline 123
MODE 91
Multi-linear algebra 91
Multiplication,  -mode 92
Multiplication, tensor-matrix 92
Mutual reinforcement 152
n-way array 91
Nilpotent matrix 190
Noise removal 61
Nonsingular matrix 18
Norm, matrix 15
Norm, matrix, Frobenius 16 62
Norm, operator 15
Norm, tensor 92
Norm, vector 15
Norm, vector, Euclidean 14
Normal equations 32 52
NULL-SPACE 59
Numerical rank 61 73
Operator norm 15
Orthogonal matrix 36
Orthogonal similarity transformation 169 177
Orthogonal vectors 15 36
Orthonormal basis 36
Orthonormal vectors 36
Outer product 14
Outlinks 137
Over-determined system 30 31 49 64
p-Norm 14
Page rank 151
Parser, text 125
Partial least squares 89
Partial pivoting 21 29
Pattern recognition 4
PCA 63 159
Permutation matrix 21 73
Perron — Frobenius theorem 141
Personalization vector 143
Perturbation, eigenvalue 170 172
Perturbation, eigenvector 171 173
Plane rotation 38
PLS 89
Power method 139 144 174
PRECISION 127
Prediction 77
Principal component analysis 63 159
Principal components 56
Principal components regression 80
Pseudoinverse 68
QR algorithm 169
QR decomposition 46
QR decomposition, column pivoting 73 155
QR decomposition, thin 47
QR decomposition, updating 52
Query 3 123 137
Quotient SVD 70
Random walk 140
RANGE 59
Rank 18
Rank, numerical 61 73
Recall 127
Rectangular matrix 21
Reduced rank model 78
Reducible matrix 141
Reflection matrix 40
Relative error 7 15
Reorthogonalization 90
Residual eigenvalue 176
Residual vector 32
Rotation, Givens 38
Rotation, plane 38
Rounding error 7
Saliency score 152
saxpy 12 13
Scalar product 92
Schur decomposition 171 187
Search engine 5
Shift, implicit 184
Shift, Wilkinson 181
Similarity transformation 169
Similarity transformation, orthogonal 169 177
Singular image 110
Singular value 56
Singular value decomposition 3 4 55 94
Singular value, -mode 95
Singular value, tensor 95
Singular vector 56
Slice (of a tensor) 93
Sparse matrix 126 189
Spherical k-means algorithm 102
Square matrix 21
Stemming 124 151
Stop word 124 151
Strongly connected 141
Summarization text 151
SVD 4 55 94
SVD, computation 186
SVD, expansion 57
SVD, generalized 69
SVD, outer product form 57
SVD, quotient 70
SVD, tensor 94 160
SVD, thin 57
SVD, truncated 61
Tangent distance 118
Tangent planes 118
Teleportation 142 154
Tensor 9 91
Tensor, core 96 160
Tensor, SVD 94 160
Tensor, unfolding 93
TensorFaces 159
Term 124 151
Term frequency 126
Term weighting 126 151
Term-document matrix 2 125 151
Term-sentence matrix 151
Text parser 125
Text summarization 151
Theorem, Perron — Frobenius 141
Trace 17 92
Training set 91
Transformation, Householder 82 186 187
Transformation, similarity 169
Transition matrix 140
Triangle inequality 15
Tridiagonal matrix 178
Truncated SVD 61
Truncated SVD solution 80
Tucker model 94
Under-determined system 68
Unfolding 93
Unit roundoff 7
Variable, dependent 77
Variable, explanatory 77
Vector norm 15
Vector space model 124 151
Vector, basis 12
Vector, concept 133
Web search engine 123 137
Weighting, document 126 151
Weighting, term 126 151
Wilkinson shift 181
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