randomFourierTrans: Random Fourier transformation
In kernDeepStackNet: Kernel Deep Stacking Networks
Description
Usage
Arguments
Details
Value
Note
Author(s)
References
See Also
Examples
Description
Calculates the random Fourier transformation using a Gaussian kernel, given the original data.
Usage
1
randomFourierTrans(X, Dim, sigma, seedW=NULL)
Arguments
X
Original data design matrix. All factors have to be encoded, e.g. dummy coding.
Dim
Specifies the dimension of the random Fourier transformation (integer scalar).
sigma
Variance of the Gaussian kernel (positive numeric scalar).
seedW
Random seed for drawing from the multivariate normal distribution (integer scalar).
Details
First a random weight matrix is drawn from the multivariate normal distribution. Then the Data is linear transformed. The linear transformed data is mapped nonlinear by applying cosinus and sinus functions. The matrix multiplaction t(Z) Z approximates the Gaussian radial basis function kernel matrix. The dimension of t(Z) Z is always n x n. The higher the dimension argument Dim, the more accurate the results.
Value
Numeric transformed data matrix with dimension 2*Dim x n.
Note
This function is not intended to be called directly by the user. Should only be used by experienced users, who want to customize the model. It is called in the estimation process of the kernel deep stacking network, e. g. fitKDSN.
Author(s)
Thomas Welchowski welchow@imbie.meb.uni-bonn.de
References
Po-Seng Huang and Li Deng and Mark Hasegawa-Johnson and Xiaodong He, (2013),
Random Features for kernel deep convex network,
Proceedings IEEE International Conference on Acoustics, Speech, and
Signal Processing (ICASSP)
See Also
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
# Generate data matrix
X <- data.frame(rnorm(100), rnorm(100), rnorm(100), rnorm(100), rnorm(100),
factor(sample(c("a", "b", "c", "d", "e"), 100, replace=TRUE)))
X <- model.matrix(object=~., data=X)
# Exclude intercept
X <- X[, -1]
# Apply a random Fourier transformation of lower dimension
rft <- randomFourierTrans(X=X, Dim=2, sigma=1, seedW=0)
# Transformed data
rft$Z
# Used weight matrix
rft$rW
Example output
1 2 3 4 5 6
[1,] -0.6768542 0.06518136 0.37574669 -0.4966198 0.2116745 -0.6957784
[2,] 0.3492194 -0.02217395 -0.07460965 -0.3223374 -0.1042314 -0.1078658
[3,] 0.2046176 0.70409615 -0.59901121 -0.5033575 -0.6746806 -0.1260650
[4,] -0.6148543 -0.70675902 -0.70315958 -0.6293636 -0.6993825 -0.6988311
7 8 9 10 11 12
[1,] 0.69105856 -0.7033352 0.2280896 -0.58519755 0.4369952 0.1196931
[2,] 0.70157574 0.1506943 0.6763112 -0.01823611 -0.1861371 0.6951943
[3,] -0.14979343 0.0729352 -0.6693094 -0.39691791 0.5559094 -0.6969028
[4,] -0.08826933 -0.6908627 0.2064054 -0.70687159 -0.6821678 0.1292472
13 14 15 16 17 18
[1,] 0.70695623 -0.007774136 -0.1264757 0.5794750 -0.31703790 -0.1131224
[2,] 0.42375915 -0.289303651 -0.3219197 -0.5014517 -0.02369032 0.3715694
[3,] 0.01459093 -0.707064044 0.6957039 0.4052267 0.63204982 -0.6979995
[4,] 0.56606376 -0.645215776 -0.6295774 0.4985441 -0.70670982 -0.6016113
19 20 21 22 23 24
[1,] -0.3757473 -0.2962527 0.4892643 0.6900373 0.6576961 0.70474686
[2,] -0.2075915 0.6924681 -0.6726804 0.3516366 -0.5774959 0.70643452
[3,] -0.5990108 -0.6420548 0.5105100 -0.1544296 -0.2596841 -0.05772235
[4,] -0.6759481 -0.1431358 0.2179474 -0.6134751 -0.4080423 0.03082639
25 26 27 28 29 30
[1,] -0.5496335 0.5746423 0.5398372 0.70364977 0.6280840 0.1995324
[2,] 0.5224096 -0.4557251 0.1004139 -0.60804340 -0.1753904 0.1723662
[3,] -0.4448629 -0.4120513 0.4567011 0.06983557 0.3248238 0.6783707
[4,] -0.4765377 -0.5406613 0.6999408 0.36094768 0.6850096 -0.6857769
31 32 33 34 35 36
[1,] 0.4751279 -0.70419908 -0.5039069 -0.5734239 -0.6513926 0.70414129
[2,] -0.5875164 -0.66287988 -0.6731966 -0.3763735 0.6919277 0.25444629
[3,] 0.5236922 0.06405978 -0.4960624 -0.4137452 0.2751140 0.06469196
[4,] 0.3934774 0.24615091 0.2163479 -0.5986176 0.1457262 0.65974017
37 38 39 40 41 42
[1,] -0.45774705 -0.43030499 -0.37941222 -0.6893329 -0.3836145 0.6302268
[2,] -0.04395341 0.70617646 0.70516899 0.6005624 0.6854794 -0.6862402
[3,] 0.53895050 0.56110393 -0.59669621 -0.1575439 -0.5940033 0.3206465
[4,] 0.70573940 0.03626023 -0.05231343 -0.3732624 -0.1735455 -0.1705120
43 44 45 46 47 48
[1,] 0.4481718 -0.06688803 0.5574169 -0.1554992 -0.6764785 -0.05420061
[2,] -0.1452655 0.40735823 -0.6293407 0.5301814 -0.6829140 -0.46689791
[3,] -0.5469388 -0.70393607 -0.4350706 0.6897971 0.2058564 0.70502645
[4,] 0.6920245 -0.57797861 -0.3223822 0.4678757 -0.1833808 0.53104269
49 50 51 52 53 54
[1,] 0.09509576 0.5890203 -0.1564418 0.6729081 0.5586952 0.70533602
[2,] -0.64477294 -0.5864054 0.6556075 0.4252111 0.2795350 0.67464677
[3,] -0.70068309 0.3912226 -0.6895839 -0.2172434 0.4334278 0.05001101
[4,] -0.29028926 -0.3951313 0.2649128 0.5649739 -0.6495076 0.21178228
55 56 57 58 59 60
[1,] -0.6941409 0.6357694 -0.6139404 -0.4672658 -0.5822574 -0.6103480
[2,] -0.0601951 -0.7070251 -0.5515105 -0.6866633 0.4552573 -0.3945281
[3,] -0.1347902 -0.3095114 0.3508236 0.5307190 -0.4012186 0.3570368
[4,] 0.7045400 0.0107501 -0.4425338 -0.1688004 -0.5410553 0.5868113
61 62 63 64 65 66
[1,] -0.3817181 0.442195604 0.6886047 -0.3552308 0.3422321 0.4317433
[2,] 0.6064485 0.707064316 -0.6824990 -0.2361022 -0.5375347 0.5686151
[3,] 0.5952237 0.551781703 -0.1606972 -0.6114009 0.6187707 0.5599979
[4,] 0.3636209 -0.007749402 -0.1849190 0.6665251 0.4594088 -0.4203294
67 68 69 70 71 72
[1,] 0.3545455 0.02092007 -0.49166916 0.2158926 -0.5574443 -0.3517345
[2,] 0.1894578 0.48020264 0.01964352 -0.5935104 -0.2428423 0.6445356
[3,] 0.6117986 0.70679725 0.50819429 0.6733427 0.4350354 0.6134190
[4,] 0.6812531 0.51904279 0.70683388 0.3843767 0.6640991 0.2908159
73 74 75 76 77 78
[1,] -0.5703013 0.5049933 0.6743196 0.1960560 0.707105544 0.6949206
[2,] -0.1333144 -0.4403271 0.2697302 -0.5959668 -0.695531388 0.6585525
[3,] -0.4180388 -0.4949564 0.2128218 -0.6793836 -0.001322944 0.1307110
[4,] 0.6944259 -0.5532739 -0.6536403 -0.3805570 0.127420909 0.2575047
79 80 81 82 83 84
[1,] -0.4059327 -0.69964604 -0.5844763 0.02187418 -0.6446698 -0.1139828
[2,] 0.4896442 -0.70380678 0.6231884 -0.57440364 0.5258785 0.5088547
[3,] -0.5789807 0.10244712 -0.3979793 -0.70676836 -0.2905183 0.6978595
[4,] 0.5101457 -0.06823504 0.3341202 0.41238387 0.4727069 0.4909856
85 86 87 88 89 90
[1,] -0.2795250 0.6081966 0.4727968 0.5580410 -0.3897197 -0.70600778
[2,] 0.4408189 0.6592868 -0.4448786 -0.6805647 -0.6395227 0.65487346
[3,] -0.6495120 0.3606895 0.5257977 0.4342697 -0.5900157 0.03940832
[4,] -0.5528821 0.2556186 -0.5496208 0.1919159 -0.3016797 0.26672223
91 92 93 94 95 96
[1,] -0.12821076 0.6503966 0.3944287 -0.3011872 -0.707104290 0.6372164
[2,] 0.04561059 0.5251767 0.2210298 -0.2876970 -0.638930719 -0.4017070
[3,] -0.69538622 -0.2774603 -0.5868782 0.6397549 -0.001876917 -0.3065212
[4,] 0.70563424 0.4734865 -0.6716739 0.6459338 -0.302931570 0.5819205
97 98 99 100
[1,] 0.5534907 -0.1474283 0.6057833 0.2896121
[2,] -0.5238570 0.4906468 0.6735207 -0.4852095
[3,] 0.4400546 -0.6915670 0.3647281 0.6450774
[4,] 0.4749461 -0.5091814 0.2153366 -0.5143654
[,1] [,2]
[1,] 1.262954285 -0.3262334
[2,] 1.329799263 1.2724293
[3,] 0.414641434 -1.5399500
[4,] -0.928567035 -0.2947204
[5,] -0.005767173 2.4046534
[6,] 0.763593461 -0.7990092
[7,] -1.147657009 -0.2894616
[8,] -0.299215118 -0.4115108
[9,] 0.252223448 -0.8919211
kernDeepStackNet documentation built on May 2, 2019, 8:16 a.m.
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Description Usage Arguments Details Value Note Author(s) References See Also Examples
Description
Calculates the random Fourier transformation using a Gaussian kernel, given the original data.
Usage
1 | randomFourierTrans(X, Dim, sigma, seedW=NULL)
|
Arguments
X |
Original data design matrix. All factors have to be encoded, e.g. dummy coding. |
Dim |
Specifies the dimension of the random Fourier transformation (integer scalar). |
sigma |
Variance of the Gaussian kernel (positive numeric scalar). |
seedW |
Random seed for drawing from the multivariate normal distribution (integer scalar). |
Details
First a random weight matrix is drawn from the multivariate normal distribution. Then the Data is linear transformed. The linear transformed data is mapped nonlinear by applying cosinus and sinus functions. The matrix multiplaction t(Z) Z approximates the Gaussian radial basis function kernel matrix. The dimension of t(Z) Z is always n x n. The higher the dimension argument Dim, the more accurate the results.
Value
Numeric transformed data matrix with dimension 2*Dim x n.
Note
This function is not intended to be called directly by the user. Should only be used by experienced users, who want to customize the model. It is called in the estimation process of the kernel deep stacking network, e. g. fitKDSN.
Author(s)
Thomas Welchowski welchow@imbie.meb.uni-bonn.de
References
Po-Seng Huang and Li Deng and Mark Hasegawa-Johnson and Xiaodong He, (2013), Random Features for kernel deep convex network, Proceedings IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | # Generate data matrix
X <- data.frame(rnorm(100), rnorm(100), rnorm(100), rnorm(100), rnorm(100),
factor(sample(c("a", "b", "c", "d", "e"), 100, replace=TRUE)))
X <- model.matrix(object=~., data=X)
# Exclude intercept
X <- X[, -1]
# Apply a random Fourier transformation of lower dimension
rft <- randomFourierTrans(X=X, Dim=2, sigma=1, seedW=0)
# Transformed data
rft$Z
# Used weight matrix
rft$rW
|
Example output
1 2 3 4 5 6
[1,] -0.6768542 0.06518136 0.37574669 -0.4966198 0.2116745 -0.6957784
[2,] 0.3492194 -0.02217395 -0.07460965 -0.3223374 -0.1042314 -0.1078658
[3,] 0.2046176 0.70409615 -0.59901121 -0.5033575 -0.6746806 -0.1260650
[4,] -0.6148543 -0.70675902 -0.70315958 -0.6293636 -0.6993825 -0.6988311
7 8 9 10 11 12
[1,] 0.69105856 -0.7033352 0.2280896 -0.58519755 0.4369952 0.1196931
[2,] 0.70157574 0.1506943 0.6763112 -0.01823611 -0.1861371 0.6951943
[3,] -0.14979343 0.0729352 -0.6693094 -0.39691791 0.5559094 -0.6969028
[4,] -0.08826933 -0.6908627 0.2064054 -0.70687159 -0.6821678 0.1292472
13 14 15 16 17 18
[1,] 0.70695623 -0.007774136 -0.1264757 0.5794750 -0.31703790 -0.1131224
[2,] 0.42375915 -0.289303651 -0.3219197 -0.5014517 -0.02369032 0.3715694
[3,] 0.01459093 -0.707064044 0.6957039 0.4052267 0.63204982 -0.6979995
[4,] 0.56606376 -0.645215776 -0.6295774 0.4985441 -0.70670982 -0.6016113
19 20 21 22 23 24
[1,] -0.3757473 -0.2962527 0.4892643 0.6900373 0.6576961 0.70474686
[2,] -0.2075915 0.6924681 -0.6726804 0.3516366 -0.5774959 0.70643452
[3,] -0.5990108 -0.6420548 0.5105100 -0.1544296 -0.2596841 -0.05772235
[4,] -0.6759481 -0.1431358 0.2179474 -0.6134751 -0.4080423 0.03082639
25 26 27 28 29 30
[1,] -0.5496335 0.5746423 0.5398372 0.70364977 0.6280840 0.1995324
[2,] 0.5224096 -0.4557251 0.1004139 -0.60804340 -0.1753904 0.1723662
[3,] -0.4448629 -0.4120513 0.4567011 0.06983557 0.3248238 0.6783707
[4,] -0.4765377 -0.5406613 0.6999408 0.36094768 0.6850096 -0.6857769
31 32 33 34 35 36
[1,] 0.4751279 -0.70419908 -0.5039069 -0.5734239 -0.6513926 0.70414129
[2,] -0.5875164 -0.66287988 -0.6731966 -0.3763735 0.6919277 0.25444629
[3,] 0.5236922 0.06405978 -0.4960624 -0.4137452 0.2751140 0.06469196
[4,] 0.3934774 0.24615091 0.2163479 -0.5986176 0.1457262 0.65974017
37 38 39 40 41 42
[1,] -0.45774705 -0.43030499 -0.37941222 -0.6893329 -0.3836145 0.6302268
[2,] -0.04395341 0.70617646 0.70516899 0.6005624 0.6854794 -0.6862402
[3,] 0.53895050 0.56110393 -0.59669621 -0.1575439 -0.5940033 0.3206465
[4,] 0.70573940 0.03626023 -0.05231343 -0.3732624 -0.1735455 -0.1705120
43 44 45 46 47 48
[1,] 0.4481718 -0.06688803 0.5574169 -0.1554992 -0.6764785 -0.05420061
[2,] -0.1452655 0.40735823 -0.6293407 0.5301814 -0.6829140 -0.46689791
[3,] -0.5469388 -0.70393607 -0.4350706 0.6897971 0.2058564 0.70502645
[4,] 0.6920245 -0.57797861 -0.3223822 0.4678757 -0.1833808 0.53104269
49 50 51 52 53 54
[1,] 0.09509576 0.5890203 -0.1564418 0.6729081 0.5586952 0.70533602
[2,] -0.64477294 -0.5864054 0.6556075 0.4252111 0.2795350 0.67464677
[3,] -0.70068309 0.3912226 -0.6895839 -0.2172434 0.4334278 0.05001101
[4,] -0.29028926 -0.3951313 0.2649128 0.5649739 -0.6495076 0.21178228
55 56 57 58 59 60
[1,] -0.6941409 0.6357694 -0.6139404 -0.4672658 -0.5822574 -0.6103480
[2,] -0.0601951 -0.7070251 -0.5515105 -0.6866633 0.4552573 -0.3945281
[3,] -0.1347902 -0.3095114 0.3508236 0.5307190 -0.4012186 0.3570368
[4,] 0.7045400 0.0107501 -0.4425338 -0.1688004 -0.5410553 0.5868113
61 62 63 64 65 66
[1,] -0.3817181 0.442195604 0.6886047 -0.3552308 0.3422321 0.4317433
[2,] 0.6064485 0.707064316 -0.6824990 -0.2361022 -0.5375347 0.5686151
[3,] 0.5952237 0.551781703 -0.1606972 -0.6114009 0.6187707 0.5599979
[4,] 0.3636209 -0.007749402 -0.1849190 0.6665251 0.4594088 -0.4203294
67 68 69 70 71 72
[1,] 0.3545455 0.02092007 -0.49166916 0.2158926 -0.5574443 -0.3517345
[2,] 0.1894578 0.48020264 0.01964352 -0.5935104 -0.2428423 0.6445356
[3,] 0.6117986 0.70679725 0.50819429 0.6733427 0.4350354 0.6134190
[4,] 0.6812531 0.51904279 0.70683388 0.3843767 0.6640991 0.2908159
73 74 75 76 77 78
[1,] -0.5703013 0.5049933 0.6743196 0.1960560 0.707105544 0.6949206
[2,] -0.1333144 -0.4403271 0.2697302 -0.5959668 -0.695531388 0.6585525
[3,] -0.4180388 -0.4949564 0.2128218 -0.6793836 -0.001322944 0.1307110
[4,] 0.6944259 -0.5532739 -0.6536403 -0.3805570 0.127420909 0.2575047
79 80 81 82 83 84
[1,] -0.4059327 -0.69964604 -0.5844763 0.02187418 -0.6446698 -0.1139828
[2,] 0.4896442 -0.70380678 0.6231884 -0.57440364 0.5258785 0.5088547
[3,] -0.5789807 0.10244712 -0.3979793 -0.70676836 -0.2905183 0.6978595
[4,] 0.5101457 -0.06823504 0.3341202 0.41238387 0.4727069 0.4909856
85 86 87 88 89 90
[1,] -0.2795250 0.6081966 0.4727968 0.5580410 -0.3897197 -0.70600778
[2,] 0.4408189 0.6592868 -0.4448786 -0.6805647 -0.6395227 0.65487346
[3,] -0.6495120 0.3606895 0.5257977 0.4342697 -0.5900157 0.03940832
[4,] -0.5528821 0.2556186 -0.5496208 0.1919159 -0.3016797 0.26672223
91 92 93 94 95 96
[1,] -0.12821076 0.6503966 0.3944287 -0.3011872 -0.707104290 0.6372164
[2,] 0.04561059 0.5251767 0.2210298 -0.2876970 -0.638930719 -0.4017070
[3,] -0.69538622 -0.2774603 -0.5868782 0.6397549 -0.001876917 -0.3065212
[4,] 0.70563424 0.4734865 -0.6716739 0.6459338 -0.302931570 0.5819205
97 98 99 100
[1,] 0.5534907 -0.1474283 0.6057833 0.2896121
[2,] -0.5238570 0.4906468 0.6735207 -0.4852095
[3,] 0.4400546 -0.6915670 0.3647281 0.6450774
[4,] 0.4749461 -0.5091814 0.2153366 -0.5143654
[,1] [,2]
[1,] 1.262954285 -0.3262334
[2,] 1.329799263 1.2724293
[3,] 0.414641434 -1.5399500
[4,] -0.928567035 -0.2947204
[5,] -0.005767173 2.4046534
[6,] 0.763593461 -0.7990092
[7,] -1.147657009 -0.2894616
[8,] -0.299215118 -0.4115108
[9,] 0.252223448 -0.8919211
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