Utilisation de R pour générer et tracer des valeurs propres
Aug 17 2020
J'ai les données suivantes:
data <- structure(list(V1 = c(0.94651, 0.5383, 0.96285, 0.91922, 0.46489,
0.77343, 0.90285, 1.0069, 0.4285, -0.016644, 0.73531, -0.010766,
0.72106, 0.71081, -0.086889, 0.37988, 0.32897, 0.52904, -0.0084557,
0.10109), V2 = c(-0.56207, -0.31966, -0.57178, -0.54587, -0.27607,
-0.45929, -0.53615, -0.59794, -0.25446, 0.0098841, -0.43665,
0.006393, -0.42819, -0.4221, 0.051598, -0.22559, -0.19535, -0.31416,
0.0050213, -0.060033), V3 = c(0.8266, 0.085098, 0.81386, 0.94114,
-0.094576, 0.15722, 0.41302, 0.54406, -0.070067, -0.37905, 0.72315,
0.037326, 0.72163, 0.84899, 0.024539, 0.073047, 0.12855, 0.19081,
0.037335, -0.025786), V4 = c(0.085098, 0.77217, 0.087477, 0.095301,
-0.11338, 0.029254, 0.055516, 0.013586, -0.07974, -0.058024,
0.042291, 0.23548, 0.067229, 0.057507, 0.035961, 0.11495, 0.069248,
0.03216, -0.064853, 0.044449), V5 = c(0.81386, 0.087477, 0.80893,
0.92834, -0.042251, 0.23575, 0.46973, 0.58175, -0.012993, -0.30251,
0.73196, 0.053843, 0.74423, 0.85489, 0.044913, 0.13302, 0.16572,
0.22198, 0.076549, 0.017349), V6 = c(0.94114, 0.095301, 0.92834,
1.0931, -0.082746, 0.18189, 0.4852, 0.62751, -0.085199, -0.4134,
0.8921, 0.047127, 0.89089, 1.0642, 0.042064, 0.080492, 0.14708,
0.21112, 0.042478, -0.028438), V7 = c(-0.094576, -0.11338, -0.042251,
-0.082746, 0.80368, 0.6199, 0.53577, 0.43571, 0.52259, 0.72283,
0.14265, 0.12527, 0.15794, 0.10972, 0.27052, 0.35122, 0.24159,
0.1599, 0.28239, 0.32291), V8 = c(0.15722, 0.029254, 0.23575,
0.18189, 0.6199, 1.045, 0.81547, 0.65866, 0.71941, 0.82931, 0.32166,
0.1449, 0.43432, 0.30115, 0.19978, 0.78488, 0.46836, 0.40675,
0.49992, 0.5234), V9 = c(0.41302, 0.055516, 0.46973, 0.4852,
0.53577, 0.81547, 0.88555, 0.7562, 0.51057, 0.47113, 0.54481,
0.15711, 0.61531, 0.59215, 0.26507, 0.59573, 0.48186, 0.39617,
0.38826, 0.37683), V10 = c(0.54406, 0.013586, 0.58175, 0.62751,
0.43571, 0.65866, 0.7562, 0.78475, 0.39652, 0.27494, 0.61592,
0.1222, 0.66145, 0.66101, 0.16319, 0.40111, 0.31974, 0.34904,
0.28275, 0.25133), V11 = c(-0.070067, -0.07974, -0.012993, -0.085199,
0.52259, 0.71941, 0.51057, 0.39652, 1.0164, 0.69192, 0.12521,
0.15234, 0.18136, 0.066519, 0.074701, 0.50289, 0.29894, 0.25127,
0.67174, 0.3459), V12 = c(-0.37905, -0.058024, -0.30251, -0.4134,
0.72283, 0.82931, 0.47113, 0.27494, 0.69192, 1.1506, -0.1139,
0.14507, -0.027262, -0.2119, 0.16865, 0.60408, 0.30354, 0.21503,
0.40543, 0.55259), V13 = c(0.72315, 0.042291, 0.73196, 0.8921,
0.14265, 0.32166, 0.54481, 0.61592, 0.12521, -0.1139, 1.5481,
0.2868, 1.5331, 1.604, 0.32047, 0.29921, 0.30592, 0.49005, 0.391,
0.17689), V14 = c(0.037326, 0.23548, 0.053843, 0.047127, 0.12527,
0.1449, 0.15711, 0.1222, 0.15234, 0.14507, 0.2868, 0.76717, 0.36333,
0.21414, 0.33952, 0.35815, 0.24875, 0.35865, 0.4172, 0.28988),
V15 = c(0.72163, 0.067229, 0.74423, 0.89089, 0.15794, 0.43432,
0.61531, 0.66145, 0.18136, -0.027262, 1.5331, 0.36333, 1.6139,
1.5989, 0.3219, 0.41679, 0.37344, 0.59587, 0.493, 0.24522
), V16 = c(0.84899, 0.057507, 0.85489, 1.0642, 0.10972, 0.30115,
0.59215, 0.66101, 0.066519, -0.2119, 1.604, 0.21414, 1.5989,
1.8191, 0.2722, 0.25619, 0.28694, 0.40081, 0.29757, 0.12688
), V17 = c(0.024539, 0.035961, 0.044913, 0.042064, 0.27052,
0.19978, 0.26507, 0.16319, 0.074701, 0.16865, 0.32047, 0.33952,
0.3219, 0.2722, 0.92673, 0.42773, 0.41275, 0.47912, 0.37034,
0.35505), V18 = c(0.073047, 0.11495, 0.13302, 0.080492, 0.35122,
0.78488, 0.59573, 0.40111, 0.50289, 0.60408, 0.29921, 0.35815,
0.41679, 0.25619, 0.42773, 1.0542, 0.61743, 0.57759, 0.67009,
0.67155), V19 = c(0.12855, 0.069248, 0.16572, 0.14708, 0.24159,
0.46836, 0.48186, 0.31974, 0.29894, 0.30354, 0.30592, 0.24875,
0.37344, 0.28694, 0.41275, 0.61743, 0.51219, 0.46494, 0.47372,
0.39662), V20 = c(0.19081, 0.03216, 0.22198, 0.21112, 0.1599,
0.40675, 0.39617, 0.34904, 0.25127, 0.21503, 0.49005, 0.35865,
0.59587, 0.40081, 0.47912, 0.57759, 0.46494, 0.79956, 0.50647,
0.40812), V21 = c(0.037335, -0.064853, 0.076549, 0.042478,
0.28239, 0.49992, 0.38826, 0.28275, 0.67174, 0.40543, 0.391,
0.4172, 0.493, 0.29757, 0.37034, 0.67009, 0.47372, 0.50647,
1.4825, 0.40309), V22 = c(-0.025786, 0.044449, 0.017349,
-0.028438, 0.32291, 0.5234, 0.37683, 0.25133, 0.3459, 0.55259,
0.17689, 0.28988, 0.24522, 0.12688, 0.35505, 0.67155, 0.39662,
0.40812, 0.40309, 0.59524), V23 = c(0.25527, -0.017435, 0.24472,
0.19172, -0.08942, 0.019515, 0.023886, 0.085312, -0.1077,
-0.25759, -0.0056936, -0.16772, 0.00016361, 0.032313, -0.29165,
-0.055895, -0.061876, 0.011813, -0.18098, -0.14357), V24 = c(-0.017435,
0.86281, -0.01802, -0.013843, -0.20764, -0.034841, -0.011684,
-0.054282, -0.05775, -0.079061, 0.039397, 0.48237, 0.04116,
0.017332, 0.033632, 0.044072, 0.019504, -0.027936, 0.057321,
0.0088914), V25 = c(0.24472, -0.01802, 0.23612, 0.18369,
-0.069095, 0.042049, 0.039087, 0.092742, -0.091879, -0.22268,
-0.0020998, -0.1605, 0.0058407, 0.032342, -0.27061, -0.025945,
-0.034951, 0.03467, -0.16788, -0.11148), V26 = c(0.19172,
-0.013843, 0.18369, 0.14561, -0.074105, 0.012767, 0.019197,
0.063111, -0.08197, -0.19216, -0.0014697, -0.12429, 0.0022122,
0.025654, -0.21522, -0.039968, -0.042864, 0.0073339, -0.13347,
-0.10308), V27 = c(-0.08942, -0.20764, -0.069095, -0.074105,
0.91404, 0.34296, 0.1169, 0.18089, 0.39112, 0.51196, 0.071998,
0.039649, 0.060645, 0.014709, 0.40831, 0.13309, 0.10797,
0.27916, 0.1567, 0.2165), V28 = c(0.019515, -0.034841, 0.042049,
0.012767, 0.34296, 0.40838, 0.26292, 0.19653, 0.22056, 0.42274,
0.063293, -0.0042594, 0.089042, 0.026711, 0.16124, 0.43457,
0.39117, 0.39529, 0.076837, 0.425), V29 = c(0.023886, -0.011684,
0.039087, 0.019197, 0.1169, 0.26292, 0.29695, 0.15903, 0.129,
0.27237, 0.055221, 0.037713, 0.071066, 0.02503, 0.074612,
0.39081, 0.53542, 0.40199, 0.061141, 0.40689), V30 = c(0.085312,
-0.054282, 0.092742, 0.063111, 0.18089, 0.19653, 0.15903,
0.16809, 0.093384, 0.11927, 0.04596, -0.027867, 0.052697,
0.030282, 0.030441, 0.18169, 0.19679, 0.26977, -0.0073689,
0.1654), V31 = c(-0.1077, -0.05775, -0.091879, -0.08197,
0.39112, 0.22056, 0.129, 0.093384, 0.81882, 0.36239, 0.11077,
0.11839, 0.10007, 0.028829, 0.28994, 0.2202, 0.23569, 0.26342,
0.3219, 0.28324), V32 = c(-0.25759, -0.079061, -0.22268,
-0.19216, 0.51196, 0.42274, 0.27237, 0.11927, 0.36239, 0.9133,
0.079302, 0.17579, 0.091098, -0.0070463, 0.54, 0.54119, 0.53789,
0.4253, 0.31003, 0.772), V33 = c(-0.0056936, 0.039397, -0.0020998,
-0.0014697, 0.071998, 0.063293, 0.055221, 0.04596, 0.11077,
0.079302, 0.16478, 0.17777, 0.14017, 0.071905, 0.13318, 0.12564,
0.11937, 0.15937, 0.15798, 0.18798), V34 = c(-0.16772, 0.48237,
-0.1605, -0.12429, 0.039649, -0.0042594, 0.037713, -0.027867,
0.11839, 0.17579, 0.17777, 1.1407, 0.1481, 0.058347, 0.43169,
0.16129, 0.16705, 0.16025, 0.40938, 0.27552), V35 = c(0.00016361,
0.04116, 0.0058407, 0.0022122, 0.060645, 0.089042, 0.071066,
0.052697, 0.10007, 0.091098, 0.14017, 0.1481, 0.14548, 0.061918,
0.10971, 0.15723, 0.13187, 0.17229, 0.13877, 0.175), V36 = c(0.032313,
0.017332, 0.032342, 0.025654, 0.014709, 0.026711, 0.02503,
0.030282, 0.028829, -0.0070463, 0.071905, 0.058347, 0.061918,
0.037792, 0.017188, 0.046331, 0.040203, 0.06882, 0.04331,
0.05934), V37 = c(-0.29165, 0.033632, -0.27061, -0.21522,
0.40831, 0.16124, 0.074612, 0.030441, 0.28994, 0.54, 0.13318,
0.43169, 0.10971, 0.017188, 1.0391, 0.31502, 0.21118, 0.28367,
0.43956, 0.47978), V38 = c(-0.055895, 0.044072, -0.025945,
-0.039968, 0.13309, 0.43457, 0.39081, 0.18169, 0.2202, 0.54119,
0.12564, 0.16129, 0.15723, 0.046331, 0.31502, 0.83371, 0.79387,
0.6541, 0.23566, 0.84715), V39 = c(-0.061876, 0.019504, -0.034951,
-0.042864, 0.10797, 0.39117, 0.53542, 0.19679, 0.23569, 0.53789,
0.11937, 0.16705, 0.13187, 0.040203, 0.21118, 0.79387, 1.1892,
0.79066, 0.21556, 0.89389), V40 = c(0.011813, -0.027936,
0.03467, 0.0073339, 0.27916, 0.39529, 0.40199, 0.26977, 0.26342,
0.4253, 0.15937, 0.16025, 0.17229, 0.06882, 0.28367, 0.6541,
0.79066, 0.85596, 0.20311, 0.68227), V41 = c(-0.18098, 0.057321,
-0.16788, -0.13347, 0.1567, 0.076837, 0.061141, -0.0073689,
0.3219, 0.31003, 0.15798, 0.40938, 0.13877, 0.04331, 0.43956,
0.23566, 0.21556, 0.20311, 0.71678, 0.35077), V42 = c(-0.14357,
0.0088914, -0.11148, -0.10308, 0.2165, 0.425, 0.40689, 0.1654,
0.28324, 0.772, 0.18798, 0.27552, 0.175, 0.05934, 0.47978,
0.84715, 0.89389, 0.68227, 0.35077, 1.233)), class = "data.frame", row.names = c(NA,
-20L))
Mon code est le suivant:
library(MASS)
library(purrr)
library(psy)
eigen_fun <- function() {
sigma1 <- as.matrix((data[,3:22]))
sigma2 <- as.matrix((data[,23:42]))
sample1 <- mvrnorm(n = 250, mu = as_vector(data[,1]), Sigma = sigma1)
sample2 <- mvrnorm(n = 250, mu = as_vector(data[,2]), Sigma = sigma2)
sampCombined <- rbind(sample1, sample2)
covCombined <- cov(sampCombined)
covCombinedPCA <- prcomp(sampCombined)
eigenvalues <- covCombinedPCA$sdev^2
eigenvalues
}
mat <- replicate(50, eigen_fun())
colMeans(mat)
scree.plot(mat, title = "Scree Plot", type = "E", use = "complete.obs", simu = "F")
Je commence par générer 250 échantillons aléatoires à partir de la distribution normale N (\ mu_1, \ Sigma_1) et 250 échantillons à partir de la distribution normale N (\ mu_2, \ Sigma_2). Je calcule ensuite la matrice de covariance de l'échantillon de ces 500 échantillons aléatoires, puis je trouve les valeurs propres de la matrice de covariance de l'échantillon.
Je répète ensuite cette partie pour avoir un total de 50 vecteurs de valeurs propres mat.
Je calcule ensuite le vecteur moyen des valeurs propres sur les 50 répétitions en utilisant colMeans(mat).
Enfin, je veux afficher les 50 vecteurs de valeurs propres et leur vecteur moyen dans un tracé de valeurs propres ou de scree. En dépit d'être un novice, en regardant cette intrigue, il me semble que quelque chose ne va pas? Ai-je fait quelque chose de mal?
ÉDITER:
Après la mise à jour de mon Mac, les packages RStudio semblaient devenir confus et cesser de fonctionner. Après avoir mis à jour certains packages, j'obtiens maintenant l'erreur suivante:
data <- read.csv("data.csv", header = FALSE)
set.seed(1);
eigen_fun <- function() {
sigma1 <- as.matrix((data[,3:22]))
sigma2 <- as.matrix((data[,23:42]))
sample1 <- mvrnorm(n = 250, mu = as_vector(data[,1]), Sigma = sigma1)
sample2 <- mvrnorm(n = 250, mu = as_vector(data[,2]), Sigma = sigma2)
sampCombined <- rbind(sample1, sample2);
covCombined <- cov(sampCombined);
covCombinedPCA <- prcomp(sampCombined);
eigenvalues <- covCombinedPCA$sdev^2;
}
mat <- replicate(50, eigen_fun())
colMeans(mat)
scree.plot(mat, title = "Scree Plot", type = "E", use = "complete.obs", simu = "F");
Error in scree.plot(mat, title = "Scree Plot", type = "E", use = "complete.obs", : unused arguments (type = "E", use = "complete.obs", simu = "F")
Réponses
1 Edo Aug 17 2020 at 20:56
J'essaie toujours de comprendre votre sortie attendue ... Je modifierai au cas où.
Est-ce l'un de ces deux?
Ici, vous avez toutes les 50 lignes toutes ensemble.
library(ggplot2)
library(tidyr)
library(dplyr)
as.data.frame(mat) %>%
mutate(id = row_number()) %>%
pivot_longer(starts_with("V")) %>%
ggplot(aes(x = id, y = value, colour = name, group = name)) +
geom_hline(aes(yintercept = ave(value, name)), linetype = 3) +
geom_path(show.legend = FALSE) +
geom_point(show.legend = FALSE) +
theme_classic()
Ici, vous avez un graphique pour chaque ligne.
as.data.frame(mat) %>%
mutate(id = row_number()) %>%
pivot_longer(starts_with("V")) %>%
ggplot(aes(x = id, y = value, colour = name, group = name)) +
geom_hline(aes(yintercept = ave(value, name)), linetype = 3) +
geom_path(show.legend = FALSE) +
geom_point(show.legend = FALSE) +
theme_classic() +
facet_wrap("name")
