Create a projection matrix using projection pursuit optimization (PPO).
Arguments
- X
An n by d numeric matrix (preferable) or data frame.
- y
A response vector of length n.
- model
Model for projection pursuit (for details see
PPO).- split
One of three criteria, 'gini': gini impurity index (classification), 'entropy': information gain (classification, default) or 'mse': mean square error (regression).
- weights
A vector of length same as
datathat are positive weights. (default NULL)- dimProj
Number of variables to be projected,
dimProj=min(ceiling(n^0.4),ceiling(ncol(X)*2/3)) (default) or dimProj="Rand": random from 1 to ncol(X).- numProj
The number of projection directions, when
dimProj="Rand" defaultnumProj= sample(ceiling(ncol(X)/3),1) otherwise defaultnumProj=ceiling(ncol(X)/dimProj).- catLabel
A category labels of class
listin predictors. (default NULL, for details see Examples ofODT)- ...
Used to handle superfluous arguments passed in using paramList.
Value
A random matrix to use in running ODT.
Variable: Variables to be projected.
Number: Number of projections.
Coefficient: Coefficients of the projection matrix.
Examples
set.seed(220828)
X <- matrix(rnorm(1000), 100, 10)
y <- (rnorm(100) > 0) + 0
(RotMat <- RotMatPPO(X, y))
#> Variable Number Coefficient
#> [1,] 7 1 1.00000000
#> [2,] 3 2 1.00000000
#> [3,] 2 3 1.00000000
#> [4,] 10 4 1.00000000
#> [5,] 8 5 -0.63747080
#> [6,] 7 5 -0.33498954
#> [7,] 6 5 0.40102900
#> [8,] 4 5 0.44271368
#> [9,] 10 5 -0.35297779
#> [10,] 2 6 -0.22464801
#> [11,] 1 6 0.70400011
#> [12,] 5 6 0.16604464
#> [13,] 3 6 -0.04357413
#> [14,] 9 6 0.65149643
#> [15,] 1 7 0.62001403
#> [16,] 9 7 0.26056728
#> [17,] 8 7 -0.12300744
#> [18,] 4 7 0.40539513
#> [19,] 6 7 0.60680413
(RotMat <- RotMatPPO(X, y, dimProj = "Rand"))
#> Variable Number Coefficient
#> [1,] 9 1 1.00000000
#> [2,] 3 2 1.00000000
#> [3,] 8 3 1.00000000
#> [4,] 1 4 1.00000000
#> [5,] 1 1 0.41034620
#> [6,] 2 1 -0.05702688
#> [7,] 3 1 -0.20189258
#> [8,] 4 1 0.24738638
#> [9,] 5 1 0.18941654
#> [10,] 6 1 0.33597211
#> [11,] 7 1 -0.19232749
#> [12,] 8 1 -0.11345253
#> [13,] 9 1 0.36297960
#> [14,] 10 1 -0.62931064
(RotMat <- RotMatPPO(X, y, dimProj = 6, numProj = 4))
#> Variable Number Coefficient
#> [1,] 8 1 1.0000000
#> [2,] 1 2 1.0000000
#> [3,] 2 3 1.0000000
#> [4,] 6 4 1.0000000
#> [5,] 5 5 0.7524546
#> [6,] 2 5 -0.2513190
#> [7,] 4 5 0.6088110
#> [8,] 1 6 0.8235489
#> [9,] 8 6 -0.5672452
#> [10,] 6 7 0.8527041
#> [11,] 3 7 -0.5223943
#> [12,] 10 8 -0.8067687
#> [13,] 9 8 0.4836435
#> [14,] 7 8 -0.3394308
#> [15,] 6 9 0.5429000
#> [16,] 1 9 0.3816742
#> [17,] 10 9 -0.6710470
#> [18,] 5 9 0.3305759
# classification
data(seeds)
(PP <- RotMatPPO(seeds[, 1:7], seeds[, 8], model = "Log", split = "entropy"))
#> Variable Number Coefficient
#> [1,] 7 1 1.00000000
#> [2,] 6 2 1.00000000
#> [3,] 5 3 1.00000000
#> [4,] 7 4 0.80070860
#> [5,] 2 4 -0.57197028
#> [6,] 6 4 0.09180371
#> [7,] 5 4 -0.15260345
#> [8,] 3 5 -0.99266473
#> [9,] 1 5 -0.01373195
#> [10,] 4 5 -0.12011731
#> [11,] 3 6 -0.92259750
#> [12,] 7 6 0.22777345
#> [13,] 2 6 -0.23433424
#> [14,] 5 6 0.20498921
(PP <- RotMatPPO(seeds[, 1:7], seeds[, 8], model = "PPR", split = "entropy"))
#> Variable Number Coefficient
#> [1,] 3 1 1.000000000
#> [2,] 1 2 1.000000000
#> [3,] 2 3 1.000000000
#> [4,] 3 4 -0.988281570
#> [5,] 6 4 0.008187774
#> [6,] 1 4 0.048662943
#> [7,] 2 4 -0.144445205
#> [8,] 5 5 -0.291498857
#> [9,] 7 5 0.548547148
#> [10,] 4 5 -0.783660924
#> [11,] 3 6 -0.848820653
#> [12,] 4 6 -0.442538941
#> [13,] 7 6 0.282088117
#> [14,] 5 6 -0.063945909
(PP <- RotMatPPO(seeds[, 1:7], seeds[, 8], model = "LDA", split = "entropy"))
#> Variable Number Coefficient
#> [1,] 6 1 1.00000000
#> [2,] 7 2 1.00000000
#> [3,] 5 3 1.00000000
#> [4,] 5 4 0.84899943
#> [5,] 1 4 0.42679608
#> [6,] 6 4 -0.05823805
#> [7,] 7 4 0.30602845
#> [8,] 2 5 -0.42409016
#> [9,] 3 5 -0.90512230
#> [10,] 4 5 -0.03001925
#> [11,] 3 6 0.92258733
#> [12,] 5 6 0.17607151
#> [13,] 1 6 -0.04931458
#> [14,] 2 6 0.33970504
# regression
data(body_fat)
(PP <- RotMatPPO(body_fat[, 2:15], body_fat[, 1], model = "Log", split = "mse"))
#> Variable Number Coefficient
#> [1,] 12 1 1.0000000000
#> [2,] 8 2 1.0000000000
#> [3,] 9 3 1.0000000000
#> [4,] 14 4 1.0000000000
#> [5,] 5 5 -0.1354890116
#> [6,] 10 5 -0.0229807153
#> [7,] 14 5 0.9318006142
#> [8,] 11 5 -0.0487637387
#> [9,] 12 5 -0.1148845383
#> [10,] 2 5 -0.0924499623
#> [11,] 9 5 -0.2978907099
#> [12,] 7 6 -0.0425456052
#> [13,] 4 6 0.0137041007
#> [14,] 6 6 0.0316612459
#> [15,] 8 6 -0.0108830294
#> [16,] 3 6 0.0107094563
#> [17,] 1 6 -0.9976644991
#> [18,] 13 6 -0.0378424231
#> [19,] 1 7 -0.9668121838
#> [20,] 14 7 0.2391075465
#> [21,] 9 7 -0.0053082782
#> [22,] 5 7 0.0443749634
#> [23,] 12 7 -0.0441831784
#> [24,] 2 7 0.0006183072
#> [25,] 11 7 -0.0644354848
(PP <- RotMatPPO(body_fat[, 2:15], body_fat[, 1], model = "Rand", split = "mse"))
#> Variable Number Coefficient
#> [1,] 12 1 1.0000000
#> [2,] 5 2 1.0000000
#> [3,] 3 3 1.0000000
#> [4,] 4 4 1.0000000
#> [5,] 5 5 0.3779645
#> [6,] 9 5 -0.3779645
#> [7,] 12 5 -0.3779645
#> [8,] 14 5 0.3779645
#> [9,] 1 5 0.3779645
#> [10,] 10 5 0.3779645
#> [11,] 8 5 -0.3779645
#> [12,] 7 6 -0.3779645
#> [13,] 4 6 -0.3779645
#> [14,] 2 6 -0.3779645
#> [15,] 13 6 0.3779645
#> [16,] 11 6 -0.3779645
#> [17,] 3 6 0.3779645
#> [18,] 6 6 0.3779645
#> [19,] 5 7 0.3779645
#> [20,] 9 7 -0.3779645
#> [21,] 12 7 0.3779645
#> [22,] 14 7 -0.3779645
#> [23,] 1 7 -0.3779645
#> [24,] 10 7 0.3779645
#> [25,] 8 7 0.3779645
(PP <- RotMatPPO(body_fat[, 2:15], body_fat[, 1], model = "PPR", split = "mse"))
#> Variable Number Coefficient
#> [1,] 8 1 1.000000000
#> [2,] 10 2 1.000000000
#> [3,] 5 3 1.000000000
#> [4,] 6 4 1.000000000
#> [5,] 7 5 -0.356875669
#> [6,] 6 5 0.037456061
#> [7,] 13 5 -0.186967615
#> [8,] 2 5 -0.027215019
#> [9,] 14 5 0.883994707
#> [10,] 5 5 0.215317575
#> [11,] 10 5 0.087925847
#> [12,] 12 6 -0.045902870
#> [13,] 3 6 0.018505068
#> [14,] 1 6 -0.994007545
#> [15,] 4 6 -0.000279017
#> [16,] 9 6 -0.057642171
#> [17,] 11 6 -0.077971676
#> [18,] 8 6 0.009859475
#> [19,] 1 7 -0.966846911
#> [20,] 14 7 0.235875959
#> [21,] 7 7 -0.010618395
#> [22,] 5 7 0.029799022
#> [23,] 13 7 -0.024434531
#> [24,] 10 7 0.026277615
#> [25,] 11 7 -0.085330484