Dimension Reduction, Lusebrink Left Radiomics PCA
2026-07-22
Load libraries
#list all the packages we will need
packages <- c(
"tidyverse", # data wrangling + ggplot2
"corrplot", # correlation matrices
"ggcorrplot", # ggplot2-style correlation matrices
"scales", # axis formatting
"knitr", # table rendering
"kableExtra", # styled tables
"DT", # interactive tables
"RColorBrewer", # colour palettes
"patchwork", # combine ggplots
"glue", # string interpolation
"plotly" # hover ggplots
)
#check what's installed
installed <- rownames(installed.packages())
#find what needs to be installed
to_install <- setdiff(packages, installed)
#install missing packages
if (length(to_install) > 0) {
message("Installing missing packages: ", paste(to_install, collapse = ", "))
install.packages(to_install, repos = "https://cloud.r-project.org")
} else {
message("All packages already installed.")
}
#load all packages
invisible(lapply(packages, library, character.only = TRUE))
#clean up env
rm(packages, installed, to_install)Set file paths
#set main data directory
DATA_DIR <- "/Users/oviya/Desktop/100um/lusebrink_left_features_allclasses_allimages_250um.csv"
df <- read_csv(DATA_DIR, show_col_types = FALSE)
#dim(df)
#names(df)
# assign a unique ID to each voxel
df <- df |>
mutate(voxel_id = row_number(), .before = 1)
# compact data summary
cat("Number of voxels:", nrow(df), "\n")## Number of voxels: 107879cat("Number of columns:", ncol(df), "\n")## Number of columns: 284names(df)[1:15]## [1] "voxel_id"
## [2] "x"
## [3] "y"
## [4] "z"
## [5] "y_global"
## [6] "original_glrlm_GrayLevelNonUniformity"
## [7] "original_glrlm_GrayLevelNonUniformityNormalized"
## [8] "original_glrlm_GrayLevelVariance"
## [9] "original_glrlm_HighGrayLevelRunEmphasis"
## [10] "original_glrlm_LongRunEmphasis"
## [11] "original_glrlm_LongRunHighGrayLevelEmphasis"
## [12] "original_glrlm_LongRunLowGrayLevelEmphasis"
## [13] "original_glrlm_LowGrayLevelRunEmphasis"
## [14] "original_glrlm_RunEntropy"
## [15] "original_glrlm_RunLengthNonUniformity"Separate metadata and radiomic features
# Save voxel location information separately
voxel_metadata <- df |>
select(voxel_id, x, y, z, y_global)
# Keep only radiomic features for preprocessing/PCA
feature_df <- df |>
select(-voxel_id, -x, -y, -z, -y_global)
cat("Number of voxels:", nrow(feature_df), "\n")## Number of voxels: 107879cat("Radiomic features:", ncol(feature_df), "\n")## Radiomic features: 279Troubleshoot missing/invalid values
# Check each radiomic feature for missing or infinite values
value_qc <- tibble(
feature = names(feature_df),
n_missing = sapply(feature_df, function(x) sum(is.na(x))),
n_infinite = sapply(feature_df, function(x) sum(is.infinite(x))),
n_nonfinite = sapply(feature_df, function(x) sum(!is.finite(x)))
) |>
mutate(
percent_nonfinite = 100 * n_nonfinite / nrow(feature_df)
)
# Only keep features that actually have a problem
problem_features <- value_qc |>
filter(n_nonfinite > 0) |>
arrange(desc(n_nonfinite))
cat("Radiomic features checked:", nrow(value_qc), "\n")## Radiomic features checked: 279cat("Features with missing/invalid values:", nrow(problem_features), "\n")## Features with missing/invalid values: 3problem_features## # A tibble: 3 × 5
## feature n_missing n_infinite n_nonfinite percent_nonfinite
## <chr> <int> <int> <int> <dbl>
## 1 original_glcm_JointAverage 742 0 742 0.688
## 2 logSigma0p5_glcm_JointAver… 742 0 742 0.688
## 3 logSigma1p0_glcm_JointAver… 742 0 742 0.688Removing Joint Average, zero variance features
#extra step since PCA will fail with na values
feature_df_pca <- feature_df |>
select(-all_of(problem_features$feature))
sum(!is.finite(as.matrix(feature_df_pca)))## [1] 0#AT 276 radiomic features NOW for lusebrink left# Calculate standard deviation of each feature
feature_sd <- sapply(feature_df_pca, sd)
# Find features that do not vary across voxels
zero_variance_features <- names(feature_sd)[
!is.finite(feature_sd) | feature_sd == 0
]
cat("Zero-variance features:", length(zero_variance_features), "\n")## Zero-variance features: 3zero_variance_features## [1] "original_glcm_MCC" "logSigma0p5_glcm_MCC" "logSigma1p0_glcm_MCC"sapply(
feature_df_pca[, zero_variance_features],
function(x) c(
min = min(x),
max = max(x),
unique_values = length(unique(x))
)
)## original_glcm_MCC logSigma0p5_glcm_MCC logSigma1p0_glcm_MCC
## min 0 0 0
## max 0 0 0
## unique_values 1 1 1#removing
feature_df_pca <- feature_df_pca |>
select(-all_of(zero_variance_features))
cat("Radiomic features remaining for PCA:", ncol(feature_df_pca), "\n")## Radiomic features remaining for PCA: 273#AT 274 radiomic features NOW for lusebrink leftZ-score
# Z-score every radiomic feature
feature_z <- sapply(
feature_df_pca,
function(x) (x - mean(x)) / sd(x)
)
cat("Voxels:", nrow(feature_z), "\n")## Voxels: 107879cat("Z-scored radiomic features:", ncol(feature_z), "\n")## Z-scored radiomic features: 273cat(
"Largest absolute mean:",
max(abs(colMeans(feature_z))),
"\n"
)## Largest absolute mean: 4.564971e-14cat(
"Smallest SD:",
min(apply(feature_z, 2, sd)),
"\n"
)## Smallest SD: 1cat(
"Largest SD:",
max(apply(feature_z, 2, sd)),
"\n"
)## Largest SD: 1head(feature_z)## original_glrlm_GrayLevelNonUniformity
## [1,] -2.560047
## [2,] -2.539655
## [3,] -2.503422
## [4,] -2.505534
## [5,] -2.422106
## [6,] -2.233076
## original_glrlm_GrayLevelNonUniformityNormalized
## [1,] 6.451088
## [2,] 3.122198
## [3,] 2.868279
## [4,] 4.179760
## [5,] 2.852392
## [6,] 2.465889
## original_glrlm_GrayLevelVariance original_glrlm_HighGrayLevelRunEmphasis
## [1,] -0.9734832 -1.347461
## [2,] -1.1900422 -1.261090
## [3,] -1.0480431 -1.203407
## [4,] -1.0067566 -1.220955
## [5,] -1.0833657 -1.145167
## [6,] -1.2290636 -1.186123
## original_glrlm_LongRunEmphasis original_glrlm_LongRunHighGrayLevelEmphasis
## [1,] 3.9903123 -1.184403
## [2,] 3.3243167 -1.124860
## [3,] 2.7584666 -1.103078
## [4,] 4.0097722 -1.062337
## [5,] 0.7011627 -1.080458
## [6,] 0.4934581 -1.137705
## original_glrlm_LongRunLowGrayLevelEmphasis
## [1,] 0.7623620
## [2,] 0.5455086
## [3,] 0.4655579
## [4,] 0.5838678
## [5,] 0.2082965
## [6,] 0.2031703
## original_glrlm_LowGrayLevelRunEmphasis original_glrlm_RunEntropy
## [1,] 0.4204312 -4.579641
## [2,] 0.2599864 -2.776094
## [3,] 0.2138956 -2.796025
## [4,] 0.2462174 -3.368615
## [5,] 0.1531713 -3.040376
## [6,] 0.1598882 -3.017110
## original_glrlm_RunLengthNonUniformity
## [1,] -3.733618
## [2,] -3.549743
## [3,] -3.498736
## [4,] -3.600400
## [5,] -3.405246
## [6,] -3.198915
## original_glrlm_RunLengthNonUniformityNormalized
## [1,] -4.1172759
## [2,] -2.2525621
## [3,] -1.8224574
## [4,] -2.7504829
## [5,] -0.5350303
## [6,] 0.2437575
## original_glrlm_RunPercentage original_glrlm_RunVariance
## [1,] -3.8957740 2.0514299
## [2,] -2.6320693 3.2155809
## [3,] -2.1889512 2.7692745
## [4,] -3.1490384 3.7296980
## [5,] -0.5247994 -0.2758418
## [6,] 0.1130138 -0.1570502
## original_glrlm_ShortRunEmphasis
## [1,] -5.3963910
## [2,] -2.6727414
## [3,] -2.1424110
## [4,] -3.3132986
## [5,] -1.3115096
## [6,] -0.4051717
## original_glrlm_ShortRunHighGrayLevelEmphasis
## [1,] -1.400483
## [2,] -1.280935
## [3,] -1.214460
## [4,] -1.245689
## [5,] -1.168250
## [6,] -1.194819
## original_glrlm_ShortRunLowGrayLevelEmphasis
## [1,] 0.3068558
## [2,] 0.1935473
## [3,] 0.1556469
## [4,] 0.1668380
## [5,] 0.1303209
## [6,] 0.1504791
## logSigma0p5_glrlm_GrayLevelNonUniformity
## [1,] -2.476228
## [2,] -2.504767
## [3,] -2.423868
## [4,] -2.391330
## [5,] -2.328886
## [6,] -2.345865
## logSigma0p5_glrlm_GrayLevelNonUniformityNormalized
## [1,] 2.0132779
## [2,] 0.1761409
## [3,] 0.5602681
## [4,] 1.4240068
## [5,] 0.7709692
## [6,] -0.1000714
## logSigma0p5_glrlm_GrayLevelVariance
## [1,] -0.9711660
## [2,] -0.5744730
## [3,] -0.7282570
## [4,] -0.9713863
## [5,] -0.7328698
## [6,] -0.3393020
## logSigma0p5_glrlm_HighGrayLevelRunEmphasis
## [1,] -0.4813450
## [2,] -0.5966887
## [3,] -0.4023485
## [4,] -0.2418087
## [5,] -0.8941178
## [6,] -0.6228711
## logSigma0p5_glrlm_LongRunEmphasis
## [1,] -0.9627644
## [2,] -1.8311554
## [3,] -0.9961641
## [4,] -0.7496140
## [5,] -1.5210162
## [6,] -1.7025044
## logSigma0p5_glrlm_LongRunHighGrayLevelEmphasis
## [1,] -0.5706888
## [2,] -0.8606667
## [3,] -0.4994477
## [4,] -0.3261276
## [5,] -1.0516023
## [6,] -0.8798651
## logSigma0p5_glrlm_LongRunLowGrayLevelEmphasis
## [1,] -0.3206913
## [2,] -0.2924976
## [3,] -0.3237623
## [4,] -0.3525173
## [5,] -0.1936313
## [6,] -0.2541006
## logSigma0p5_glrlm_LowGrayLevelRunEmphasis logSigma0p5_glrlm_RunEntropy
## [1,] -0.2856468 -3.2287197
## [2,] -0.2185732 -1.4577650
## [3,] -0.2852642 -1.8822694
## [4,] -0.3316148 -2.7457222
## [5,] -0.1293798 -1.9306524
## [6,] -0.1899757 -0.9321961
## logSigma0p5_glrlm_RunLengthNonUniformity
## [1,] -3.558218
## [2,] -3.308367
## [3,] -3.326385
## [4,] -3.431305
## [5,] -3.220728
## [6,] -3.013239
## logSigma0p5_glrlm_RunLengthNonUniformityNormalized
## [1,] 0.7084739
## [2,] 2.1495774
## [3,] 0.7981139
## [4,] 0.4665914
## [5,] 1.8382587
## [6,] 2.0013867
## logSigma0p5_glrlm_RunPercentage logSigma0p5_glrlm_RunVariance
## [1,] 0.8846379 -1.146343
## [2,] 2.1063747 -1.846247
## [3,] 0.9513738 -1.189879
## [4,] 0.6510721 -1.028868
## [5,] 1.7922159 -1.695048
## [6,] 1.9664250 -1.774275
## logSigma0p5_glrlm_ShortRunEmphasis
## [1,] 0.6954175
## [2,] 2.0050264
## [3,] 0.7457861
## [4,] 0.3739678
## [5,] 1.5373083
## [6,] 1.8110115
## logSigma0p5_glrlm_ShortRunHighGrayLevelEmphasis
## [1,] -0.4746000
## [2,] -0.5181904
## [3,] -0.3953883
## [4,] -0.2454720
## [5,] -0.8463850
## [6,] -0.5461545
## logSigma0p5_glrlm_ShortRunLowGrayLevelEmphasis
## [1,] -0.2781811
## [2,] -0.1982677
## [3,] -0.2765771
## [4,] -0.3285068
## [5,] -0.1138033
## [6,] -0.1735659
## logSigma1p0_glrlm_GrayLevelNonUniformity
## [1,] -1.936913
## [2,] -1.935010
## [3,] -1.810824
## [4,] -1.924444
## [5,] -1.675267
## [6,] -1.594931
## logSigma1p0_glrlm_GrayLevelNonUniformityNormalized
## [1,] 3.374158
## [2,] 1.940656
## [3,] 2.197938
## [4,] 1.997633
## [5,] 2.497588
## [6,] 1.655282
## logSigma1p0_glrlm_GrayLevelVariance
## [1,] -1.0731543
## [2,] -1.0108268
## [3,] -1.0242205
## [4,] -1.0169141
## [5,] -0.9737861
## [6,] -0.9497710
## logSigma1p0_glrlm_HighGrayLevelRunEmphasis
## [1,] -0.8381467
## [2,] -0.7774815
## [3,] -0.7745604
## [4,] -0.7850321
## [5,] -0.7250684
## [6,] -0.7107874
## logSigma1p0_glrlm_LongRunEmphasis
## [1,] 0.961902300
## [2,] 1.388663502
## [3,] 0.901385518
## [4,] 0.475017192
## [5,] 0.670801812
## [6,] -0.009291596
## logSigma1p0_glrlm_LongRunHighGrayLevelEmphasis
## [1,] -0.6233443
## [2,] -0.4864947
## [3,] -0.5710819
## [4,] -0.6506417
## [5,] -0.5415666
## [6,] -0.6434554
## logSigma1p0_glrlm_LongRunLowGrayLevelEmphasis
## [1,] -0.1452950
## [2,] -0.1494013
## [3,] -0.1644280
## [4,] -0.1752655
## [5,] -0.1889095
## [6,] -0.2125669
## logSigma1p0_glrlm_LowGrayLevelRunEmphasis logSigma1p0_glrlm_RunEntropy
## [1,] -0.2004882 -3.505266
## [2,] -0.2210493 -2.263817
## [3,] -0.2228827 -2.536062
## [4,] -0.2186908 -2.716442
## [5,] -0.2370311 -2.570427
## [6,] -0.2405137 -2.482514
## logSigma1p0_glrlm_RunLengthNonUniformity
## [1,] -3.133224
## [2,] -3.073869
## [3,] -2.990668
## [4,] -3.009486
## [5,] -2.955597
## [6,] -2.727825
## logSigma1p0_glrlm_RunLengthNonUniformityNormalized
## [1,] -0.495007802
## [2,] -1.495790017
## [3,] -0.827776363
## [4,] -0.231419867
## [5,] -0.871217163
## [6,] 0.007794696
## logSigma1p0_glrlm_RunPercentage logSigma1p0_glrlm_RunVariance
## [1,] -0.68358633 1.3971287
## [2,] -1.44860380 1.5196156
## [3,] -0.88654939 1.1672654
## [4,] -0.32839799 0.6835954
## [5,] -0.92714251 0.5418202
## [6,] -0.03552473 -0.0858389
## logSigma1p0_glrlm_ShortRunEmphasis
## [1,] -0.5213469
## [2,] -1.3916788
## [3,] -0.7510268
## [4,] -0.3240169
## [5,] -1.1541857
## [6,] -0.1434742
## logSigma1p0_glrlm_ShortRunHighGrayLevelEmphasis
## [1,] -0.8642768
## [2,] -0.8379145
## [3,] -0.8097238
## [4,] -0.8022174
## [5,] -0.7798812
## [6,] -0.7226172
## logSigma1p0_glrlm_ShortRunLowGrayLevelEmphasis
## [1,] -0.2096594
## [2,] -0.2430348
## [3,] -0.2371425
## [4,] -0.2275611
## [5,] -0.2557635
## [6,] -0.2481459
## original_firstorder_10Percentile original_firstorder_90Percentile
## [1,] -0.9408148 -2.014974
## [2,] -0.8704143 -1.772873
## [3,] -0.8698660 -1.756351
## [4,] -0.8709622 -1.759327
## [5,] -0.8693178 -1.663791
## [6,] -0.8671250 -1.666101
## original_firstorder_Energy original_firstorder_Entropy
## [1,] -3.025923 -5.209861
## [2,] -2.929134 -3.485606
## [3,] -2.901986 -3.450025
## [4,] -2.949386 -3.267750
## [5,] -2.869192 -2.889052
## [6,] -2.780289 -3.108544
## original_firstorder_InterquartileRange original_firstorder_Kurtosis
## [1,] -2.3165178 2.8121464
## [2,] -1.5272368 -0.3941607
## [3,] -1.1594968 -0.2915026
## [4,] -1.3298399 -0.1724087
## [5,] -0.9736844 -1.3673699
## [6,] -1.3526745 -0.9435086
## original_firstorder_Maximum original_firstorder_MeanAbsoluteDeviation
## [1,] -2.073915 -2.076724
## [2,] -2.216722 -1.959361
## [3,] -2.073915 -1.760643
## [4,] -2.073915 -1.754683
## [5,] -2.216722 -1.407357
## [6,] -2.216722 -1.765717
## original_firstorder_Mean original_firstorder_Median
## [1,] -1.492334 -1.476912
## [2,] -1.388392 -1.356388
## [3,] -1.346214 -1.346387
## [4,] -1.366439 -1.346387
## [5,] -1.260626 -1.157330
## [6,] -1.292188 -1.331150
## original_firstorder_Minimum original_firstorder_Range
## [1,] -0.5689751 -2.213642
## [2,] -0.5689751 -2.430631
## [3,] -0.5689751 -2.213642
## [4,] -0.5689751 -2.213642
## [5,] -0.5689751 -2.430631
## [6,] -0.5689751 -2.430631
## original_firstorder_RobustMeanAbsoluteDeviation
## [1,] -2.459543
## [2,] -2.058451
## [3,] -1.807197
## [4,] -1.998777
## [5,] -1.034711
## [6,] -1.365568
## original_firstorder_RootMeanSquared original_firstorder_Skewness
## [1,] -1.515682 3.0253155
## [2,] -1.413556 0.2933370
## [3,] -1.369660 0.4704974
## [4,] -1.389241 0.7066534
## [5,] -1.283118 -1.2501573
## [6,] -1.316997 -0.6805505
## original_firstorder_TotalEnergy original_firstorder_Uniformity
## [1,] -3.025923 8.433786
## [2,] -2.929134 4.947658
## [3,] -2.901986 4.643742
## [4,] -2.949386 4.164541
## [5,] -2.869192 2.969153
## [6,] -2.780289 3.608712
## original_firstorder_Variance original_glcm_Autocorrelation
## [1,] -1.394617 -1.414728
## [2,] -1.519219 -1.340612
## [3,] -1.421524 -1.305952
## [4,] -1.379325 -1.320435
## [5,] -1.375783 -1.179114
## [6,] -1.513649 -1.229755
## original_glcm_ClusterProminence original_glcm_ClusterShade
## [1,] -0.7238924 0.04276802
## [2,] -0.7269473 -0.07451384
## [3,] -0.7076056 -0.01733243
## [4,] -0.7002823 0.02772991
## [5,] -0.6760608 -0.24124993
## [6,] -0.6911256 -0.06892947
## original_glcm_ClusterTendency original_glcm_Contrast
## [1,] -1.375028 -1.385804
## [2,] -1.342527 -1.605312
## [3,] -1.229611 -1.315042
## [4,] -1.195316 -1.250844
## [5,] -1.000628 -1.840380
## [6,] -1.094501 -1.863720
## original_glcm_Correlation original_glcm_DifferenceAverage
## [1,] -2.407723 -1.805200
## [2,] -1.544024 -1.945708
## [3,] -1.297948 -1.420653
## [4,] -1.222551 -1.336137
## [5,] 1.547766 -2.547673
## [6,] 1.226682 -2.603876
## original_glcm_DifferenceEntropy original_glcm_DifferenceVariance
## [1,] -3.982775 -1.199863
## [2,] -3.511642 -1.721408
## [3,] -2.515392 -1.432090
## [4,] -2.331605 -1.340303
## [5,] -4.035804 -1.906958
## [6,] -3.855229 -1.846356
## original_glcm_Id original_glcm_Idm original_glcm_Idmn original_glcm_Idn
## [1,] 3.037838 2.935769 1.412529 1.892249
## [2,] 2.455702 2.380759 1.641083 2.009221
## [3,] 1.505657 1.361014 1.336560 1.434761
## [4,] 1.447580 1.306999 1.269399 1.346835
## [5,] 3.985691 3.995268 1.889761 2.692458
## [6,] 3.986745 4.135659 1.914657 2.755587
## original_glcm_Imc1 original_glcm_Imc2 original_glcm_InverseVariance
## [1,] -1.815524 -0.70343273 -0.02009731
## [2,] -1.170595 -0.07066675 1.06750803
## [3,] -1.131774 0.10425478 0.29461367
## [4,] -1.471696 0.30564082 0.19010758
## [5,] -2.072966 0.76085459 1.54883087
## [6,] -1.317764 0.50941812 2.69802563
## original_glcm_JointEnergy original_glcm_JointEntropy
## [1,] 7.933110 -5.176124
## [2,] 3.603452 -3.630895
## [3,] 3.077546 -3.338156
## [4,] 3.111050 -3.410323
## [5,] 3.064322 -3.462083
## [6,] 2.294896 -2.880679
## original_glcm_MaximumProbability original_glcm_SumAverage
## [1,] 7.050276 -1.604093
## [2,] 4.147653 -1.484730
## [3,] 3.431260 -1.430269
## [4,] 3.874153 -1.453575
## [5,] 2.134343 -1.250780
## [6,] 2.523894 -1.322852
## original_glcm_SumEntropy original_glcm_SumSquares
## [1,] -4.592340 -1.444601
## [2,] -3.225862 -1.471366
## [3,] -2.959597 -1.310127
## [4,] -2.976572 -1.266942
## [5,] -2.472662 -1.252124
## [6,] -2.116427 -1.333539
## original_glszm_GrayLevelNonUniformity
## [1,] -3.041318
## [2,] -3.244218
## [3,] -2.863780
## [4,] -3.244218
## [5,] -2.863780
## [6,] -2.863780
## original_glszm_GrayLevelNonUniformityNormalized
## [1,] 8.425394
## [2,] 3.951811
## [3,] 4.129522
## [4,] 3.951811
## [5,] 4.129522
## [6,] 4.129522
## original_glszm_GrayLevelVariance original_glszm_HighGrayLevelZoneEmphasis
## [1,] -1.331478 -1.433549
## [2,] -1.709975 -1.401894
## [3,] -1.579775 -1.342916
## [4,] -1.476541 -1.324759
## [5,] -1.729775 -1.368335
## [6,] -1.729775 -1.368335
## original_glszm_LargeAreaEmphasis
## [1,] -1.1624613
## [2,] -1.1270006
## [3,] -1.1590137
## [4,] -1.1565512
## [5,] -1.1503948
## [6,] -0.9435408
## original_glszm_LargeAreaHighGrayLevelEmphasis
## [1,] -1.0861602
## [2,] -1.0682996
## [3,] -1.0770239
## [4,] -1.0796204
## [5,] -1.0539643
## [6,] -0.9870661
## original_glszm_LargeAreaLowGrayLevelEmphasis
## [1,] -0.5270258
## [2,] -0.5134439
## [3,] -0.5480042
## [4,] -0.5368656
## [5,] -0.5796727
## [6,] -0.3838326
## original_glszm_LowGrayLevelZoneEmphasis
## [1,] 0.7341834
## [2,] 0.5978199
## [3,] 0.5202497
## [4,] 0.5177911
## [5,] 0.5355742
## [6,] 0.5355742
## original_glszm_SizeZoneNonUniformity
## [1,] -2.007295
## [2,] -1.979227
## [3,] -1.786258
## [4,] -1.698545
## [5,] -1.847657
## [6,] -2.031855
## original_glszm_SizeZoneNonUniformityNormalized
## [1,] 2.3643044
## [2,] 0.7566926
## [3,] 1.3614077
## [4,] 2.7413984
## [5,] 0.9815226
## [6,] -0.1581328
## original_glszm_SmallAreaEmphasis
## [1,] 0.90345391
## [2,] 0.75841640
## [3,] 1.29223269
## [4,] 2.00158863
## [5,] 0.07352176
## [6,] -1.31883117
## original_glszm_SmallAreaHighGrayLevelEmphasis
## [1,] -1.1807568
## [2,] -1.2173364
## [3,] -1.0544127
## [4,] -0.8854108
## [5,] -1.3698028
## [6,] -1.5353828
## original_glszm_SmallAreaLowGrayLevelEmphasis original_glszm_ZoneEntropy
## [1,] 0.7650348 -6.118086
## [2,] 0.6344809 -4.711145
## [3,] 0.6239996 -4.152791
## [4,] 0.6884609 -5.539248
## [5,] 0.5528108 -4.877380
## [6,] 0.2913006 -4.152791
## original_glszm_ZonePercentage original_glszm_ZoneVariance
## [1,] 1.9474647 -1.114329
## [2,] 1.7727344 -1.083094
## [3,] 2.1097140 -1.091055
## [4,] 2.2314004 -1.074743
## [5,] 1.7203153 -1.124624
## [6,] 0.5726139 -1.035106
## original_ngtdm_Busyness original_ngtdm_Coarseness
## [1,] -0.3582365 14.391187
## [2,] -0.5477449 8.675964
## [3,] -0.4589173 7.817936
## [4,] -0.5308272 10.053452
## [5,] -0.8446298 14.523524
## [6,] -0.4229481 9.264893
## original_ngtdm_Complexity original_ngtdm_Contrast original_ngtdm_Strength
## [1,] -1.552642 6.2754620 1.08840943
## [2,] -1.489925 0.2499783 0.01338156
## [3,] -1.440177 1.1803216 0.13526070
## [4,] -1.433508 1.6326766 0.44736405
## [5,] -1.568371 0.1043929 0.77931474
## [6,] -1.575030 -0.5452118 0.22407598
## original_gldm_DependenceEntropy original_gldm_DependenceNonUniformity
## [1,] -7.064811 -3.422023
## [2,] -5.857913 -3.165494
## [3,] -5.416368 -3.092739
## [4,] -6.348426 -3.140030
## [5,] -6.347031 -2.647156
## [6,] -5.423752 -2.170156
## original_gldm_DependenceNonUniformityNormalized
## [1,] 3.034640
## [2,] 2.619357
## [3,] 2.608479
## [4,] 3.374433
## [5,] 4.853461
## [6,] 5.238890
## original_gldm_DependenceVariance original_gldm_GrayLevelNonUniformity
## [1,] -1.578013 -2.294939
## [2,] -1.641594 -2.248076
## [3,] -1.619155 -2.207907
## [4,] -1.523394 -2.396476
## [5,] -1.585958 -2.335554
## [6,] -1.739161 -2.006361
## original_gldm_GrayLevelVariance original_gldm_HighGrayLevelEmphasis
## [1,] -1.297727 -1.404072
## [2,] -1.481861 -1.352919
## [3,] -1.359454 -1.318041
## [4,] -1.307410 -1.333122
## [5,] -1.300767 -1.235314
## [6,] -1.423183 -1.268279
## original_gldm_LargeDependenceEmphasis
## [1,] -1.626174
## [2,] -1.677201
## [3,] -1.742809
## [4,] -1.715472
## [5,] -1.401651
## [6,] -1.290464
## original_gldm_LargeDependenceHighGrayLevelEmphasis
## [1,] -1.419469
## [2,] -1.410817
## [3,] -1.423076
## [4,] -1.429302
## [5,] -1.258558
## [6,] -1.250983
## original_gldm_LargeDependenceLowGrayLevelEmphasis
## [1,] -0.2100587
## [2,] -0.2991447
## [3,] -0.3475380
## [4,] -0.3002039
## [5,] -0.2925792
## [6,] -0.1954794
## original_gldm_LowGrayLevelEmphasis original_gldm_SmallDependenceEmphasis
## [1,] 0.9874801 1.7167585
## [2,] 0.8206878 1.5869862
## [3,] 0.7659767 2.0730281
## [4,] 0.8129318 2.5052665
## [5,] 0.6195871 0.8659032
## [6,] 0.6490473 -0.1555866
## original_gldm_SmallDependenceHighGrayLevelEmphasis
## [1,] -0.7627582
## [2,] -0.7868709
## [3,] -0.5995942
## [4,] -0.4515461
## [5,] -0.9601035
## [6,] -1.1618620
## original_gldm_SmallDependenceLowGrayLevelEmphasis
## [1,] 1.4058732
## [2,] 1.1976387
## [3,] 1.2596459
## [4,] 1.3682758
## [5,] 0.9343297
## [6,] 0.5126795
## logSigma0p5_firstorder_10Percentile logSigma0p5_firstorder_90Percentile
## [1,] 0.04049022 -0.6516502
## [2,] -0.36323741 -0.7294122
## [3,] -0.11733416 -0.5244329
## [4,] 0.36293323 -0.5116257
## [5,] -0.69394855 -1.0141267
## [6,] -0.59081877 -0.6337010
## logSigma0p5_firstorder_Energy logSigma0p5_firstorder_Entropy
## [1,] -1.182923 -1.3402856
## [2,] -1.132549 -0.8015463
## [3,] -1.155260 -1.2009304
## [4,] -1.187258 -2.0689084
## [5,] -1.070791 -1.1977266
## [6,] -1.060556 -0.3005629
## logSigma0p5_firstorder_InterquartileRange logSigma0p5_firstorder_Kurtosis
## [1,] -0.7011394 -1.3490739
## [2,] -0.2711237 -1.0083476
## [3,] -0.1734865 -1.2936397
## [4,] -0.2339081 -1.4994632
## [5,] -0.5944298 -0.9186914
## [6,] 0.1154460 -1.0848708
## logSigma0p5_firstorder_Maximum
## [1,] -1.2113675
## [2,] -1.1225728
## [3,] -1.1225728
## [4,] -1.1225728
## [5,] -1.5264618
## [6,] -0.9030344
## logSigma0p5_firstorder_MeanAbsoluteDeviation logSigma0p5_firstorder_Mean
## [1,] -0.61016709 -0.37817526
## [2,] -0.23894792 -0.58624375
## [3,] -0.28048926 -0.30294289
## [4,] -0.73672653 -0.08991954
## [5,] -0.50973500 -0.97785876
## [6,] 0.05005424 -0.65535469
## logSigma0p5_firstorder_Median logSigma0p5_firstorder_Minimum
## [1,] -0.38212999 0.5766352
## [2,] -0.68586964 -0.0294031
## [3,] -0.18272453 0.3808436
## [4,] 0.02775344 0.9036080
## [5,] -0.85731923 -0.1749970
## [6,] -0.70724225 -0.1749970
## logSigma0p5_firstorder_Range
## [1,] -1.5431027
## [2,] -0.9642382
## [3,] -1.3031594
## [4,] -1.7350360
## [5,] -1.1996190
## [6,] -0.6506333
## logSigma0p5_firstorder_RobustMeanAbsoluteDeviation
## [1,] -0.3658755
## [2,] -0.3785706
## [3,] -0.1766443
## [4,] -0.6496464
## [5,] -0.5907562
## [6,] 0.1789038
## logSigma0p5_firstorder_RootMeanSquared logSigma0p5_firstorder_Skewness
## [1,] -1.1097862 0.06817717
## [2,] -0.6358681 -0.12122118
## [3,] -0.9998419 -0.30753952
## [4,] -1.4162813 -0.26958501
## [5,] -0.1736850 0.29499927
## [6,] -0.3821549 0.16254665
## logSigma0p5_firstorder_TotalEnergy logSigma0p5_firstorder_Uniformity
## [1,] -1.182923 0.9760976
## [2,] -1.132549 0.6759736
## [3,] -1.155260 1.0422974
## [4,] -1.187258 2.1187951
## [5,] -1.070791 1.0704626
## [6,] -1.060556 0.2523519
## logSigma0p5_firstorder_Variance logSigma0p5_glcm_Autocorrelation
## [1,] -0.7255627 0.1746908
## [2,] -0.4300489 0.0557303
## [3,] -0.5343386 0.2803233
## [4,] -0.8300997 0.4542127
## [5,] -0.5753588 -0.3412804
## [6,] -0.1818485 -0.0194317
## logSigma0p5_glcm_ClusterProminence logSigma0p5_glcm_ClusterShade
## [1,] -0.5088320 0.26682398
## [2,] -0.4226448 0.09053653
## [3,] -0.4205371 0.12309670
## [4,] -0.4997205 0.19732788
## [5,] -0.4149395 -0.05261232
## [6,] -0.2095275 -0.16141993
## logSigma0p5_glcm_ClusterTendency logSigma0p5_glcm_Contrast
## [1,] -0.81759190 -0.5738645
## [2,] -0.46767357 -0.4749432
## [3,] -0.40770963 -0.6385973
## [4,] -0.71514815 -0.7162965
## [5,] -0.40776476 -0.3194456
## [6,] 0.07182651 -0.3624850
## logSigma0p5_glcm_Correlation logSigma0p5_glcm_DifferenceAverage
## [1,] -1.07186587 -0.332232278
## [2,] -0.09548323 -0.159975094
## [3,] 0.44611539 -0.524011496
## [4,] -0.39934323 -0.733344718
## [5,] -0.16360146 -0.008389076
## [6,] 0.87814697 -0.049730748
## logSigma0p5_glcm_DifferenceEntropy logSigma0p5_glcm_DifferenceVariance
## [1,] -1.8714358 -1.2795449
## [2,] -1.4113002 -1.1270936
## [3,] -0.8844938 -0.8689450
## [4,] -1.2477748 -0.8918188
## [5,] -1.5198118 -0.7846942
## [6,] -1.0173759 -0.8449802
## logSigma0p5_glcm_Id logSigma0p5_glcm_Idm logSigma0p5_glcm_Idmn
## [1,] -0.2906757 -0.3271286 0.5727578
## [2,] -0.4728820 -0.5561430 0.4696924
## [3,] 0.3191408 0.2242377 0.6395747
## [4,] 0.8011547 0.7313334 0.7206540
## [5,] -0.3464866 -0.4958217 0.3091109
## [6,] -0.4390926 -0.5366889 0.3538611
## logSigma0p5_glcm_Idn logSigma0p5_glcm_Imc1 logSigma0p5_glcm_Imc2
## [1,] 0.283472719 -3.324688 0.8655158
## [2,] 0.099082592 -2.657257 0.8773488
## [3,] 0.499353237 -2.287979 0.7740012
## [4,] 0.732819545 -2.034977 0.4970694
## [5,] -0.048858029 -2.693271 0.7563776
## [6,] -0.008886277 -2.431019 0.9066245
## logSigma0p5_glcm_InverseVariance logSigma0p5_glcm_JointEnergy
## [1,] 0.44371868 3.049718
## [2,] -0.13508047 1.743550
## [3,] -0.15691036 1.534498
## [4,] 0.07721263 2.317248
## [5,] -1.08011820 2.839947
## [6,] -0.49369829 1.128861
## logSigma0p5_glcm_JointEntropy logSigma0p5_glcm_MaximumProbability
## [1,] -3.066602 2.228603
## [2,] -2.211738 1.908338
## [3,] -2.093922 1.443953
## [4,] -2.604674 2.091346
## [5,] -2.605034 2.917173
## [6,] -1.574318 1.485834
## logSigma0p5_glcm_SumAverage logSigma0p5_glcm_SumEntropy
## [1,] 0.31359024 -3.172474
## [2,] 0.18785243 -2.020037
## [3,] 0.39815305 -1.718866
## [4,] 0.56765876 -2.307433
## [5,] -0.21681097 -2.432194
## [6,] 0.09392347 -1.139407
## logSigma0p5_glcm_SumSquares logSigma0p5_glszm_GrayLevelNonUniformity
## [1,] -0.799111585 -2.579089
## [2,] -0.480690019 -2.579089
## [3,] -0.455165734 -2.579089
## [4,] -0.733449577 -2.579089
## [5,] -0.403892588 -2.177097
## [6,] 0.003807291 -2.277595
## logSigma0p5_glszm_GrayLevelNonUniformityNormalized
## [1,] 1.1629786
## [2,] 0.2037943
## [3,] 0.6234374
## [4,] 1.8823664
## [5,] 0.9498261
## [6,] -0.2158486
## logSigma0p5_glszm_GrayLevelVariance
## [1,] -0.84819485
## [2,] -0.43304339
## [3,] -0.64978191
## [4,] -1.03134993
## [5,] -0.90539068
## [6,] -0.01285113
## logSigma0p5_glszm_HighGrayLevelZoneEmphasis
## [1,] 0.35161896
## [2,] 0.03360461
## [3,] 0.18733004
## [4,] 0.52863923
## [5,] -0.48011047
## [6,] 0.03593968
## logSigma0p5_glszm_LargeAreaEmphasis
## [1,] -1.0369682
## [2,] -1.0126476
## [3,] -0.9803600
## [4,] -0.9539428
## [5,] -0.9832952
## [6,] -0.9869643
## logSigma0p5_glszm_LargeAreaHighGrayLevelEmphasis
## [1,] -0.9351084
## [2,] -0.9140185
## [3,] -0.8696387
## [4,] -0.8368011
## [5,] -0.8978101
## [6,] -0.8921620
## logSigma0p5_glszm_LargeAreaLowGrayLevelEmphasis
## [1,] -0.8265772
## [2,] -0.8114818
## [3,] -0.8007072
## [4,] -0.7909433
## [5,] -0.7862206
## [6,] -0.7938920
## logSigma0p5_glszm_LowGrayLevelZoneEmphasis
## [1,] -0.4670430
## [2,] -0.3525449
## [3,] -0.4138981
## [4,] -0.5140769
## [5,] -0.1977950
## [6,] -0.3183807
## logSigma0p5_glszm_SizeZoneNonUniformity
## [1,] -0.60441557
## [2,] -0.21291060
## [3,] -0.58039137
## [4,] -0.86067330
## [5,] -0.56170587
## [6,] 0.07359976
## logSigma0p5_glszm_SizeZoneNonUniformityNormalized
## [1,] 3.612703
## [2,] 4.280009
## [3,] 2.965661
## [4,] 2.631923
## [5,] 2.434153
## [6,] 3.670217
## logSigma0p5_glszm_SmallAreaEmphasis
## [1,] 2.4945468
## [2,] 2.6229259
## [3,] 1.5823800
## [4,] 0.7310241
## [5,] 1.9430236
## [6,] 2.4603406
## logSigma0p5_glszm_SmallAreaHighGrayLevelEmphasis
## [1,] 1.9470835
## [2,] 1.4841271
## [3,] 0.8403372
## [4,] 0.7979588
## [5,] 0.3878808
## [6,] 1.5480132
## logSigma0p5_glszm_SmallAreaLowGrayLevelEmphasis
## [1,] -0.04749547
## [2,] 0.17971480
## [3,] -0.03961571
## [4,] -0.32891161
## [5,] 0.27029528
## [6,] 0.14720229
## logSigma0p5_glszm_ZoneEntropy logSigma0p5_glszm_ZonePercentage
## [1,] -3.031713 4.392089
## [2,] -2.249411 3.631769
## [3,] -2.616051 2.556459
## [4,] -3.511560 1.921049
## [5,] -2.728890 2.810623
## [6,] -1.713511 3.091541
## logSigma0p5_glszm_ZoneVariance logSigma0p5_ngtdm_Busyness
## [1,] -1.0189476 -0.9461485
## [2,] -0.9952688 -1.2398085
## [3,] -0.9833078 -1.2375115
## [4,] -0.9802707 -0.7647064
## [5,] -0.9748713 -1.0560442
## [6,] -0.9684596 -1.3147595
## logSigma0p5_ngtdm_Coarseness logSigma0p5_ngtdm_Complexity
## [1,] 13.052499 -0.8460936
## [2,] 12.000393 -0.7089797
## [3,] 11.642194 -0.8460193
## [4,] 6.655412 -0.9396333
## [5,] 7.996930 -0.7467647
## [6,] 11.075685 -0.5755013
## logSigma0p5_ngtdm_Contrast logSigma0p5_ngtdm_Strength
## [1,] 2.6442012 1.4757134
## [2,] 1.2592605 2.9072998
## [3,] 1.4723109 2.3301227
## [4,] 3.0485634 0.3530296
## [5,] 1.4057456 1.4358087
## [6,] 0.4343477 4.4721792
## logSigma0p5_gldm_DependenceEntropy
## [1,] -5.993246
## [2,] -4.335032
## [3,] -4.858742
## [4,] -5.670414
## [5,] -4.714065
## [6,] -3.779364
## logSigma0p5_gldm_DependenceNonUniformity
## [1,] -2.363511
## [2,] -2.219359
## [3,] -2.333089
## [4,] -2.438044
## [5,] -2.201667
## [6,] -1.895016
## logSigma0p5_gldm_DependenceNonUniformityNormalized
## [1,] 5.728712
## [2,] 3.980120
## [3,] 2.702031
## [4,] 2.889370
## [5,] 3.117620
## [6,] 3.268046
## logSigma0p5_gldm_DependenceVariance
## [1,] -1.423462
## [2,] -1.309497
## [3,] -1.244403
## [4,] -1.273289
## [5,] -1.303512
## [6,] -1.282457
## logSigma0p5_gldm_GrayLevelNonUniformity logSigma0p5_gldm_GrayLevelVariance
## [1,] -2.360082 -0.66094616
## [2,] -2.240802 -0.38108298
## [3,] -2.150429 -0.42796356
## [4,] -2.097027 -0.74212918
## [5,] -2.105334 -0.50894390
## [6,] -2.103585 -0.03464992
## logSigma0p5_gldm_HighGrayLevelEmphasis
## [1,] 0.20643902
## [2,] 0.01410757
## [3,] 0.27652238
## [4,] 0.46008011
## [5,] -0.34687820
## [6,] -0.03874614
## logSigma0p5_gldm_LargeDependenceEmphasis
## [1,] -1.675049
## [2,] -1.588624
## [3,] -1.424262
## [4,] -1.359058
## [5,] -1.520564
## [6,] -1.538304
## logSigma0p5_gldm_LargeDependenceHighGrayLevelEmphasis
## [1,] -1.2234788
## [2,] -1.1624655
## [3,] -0.9654705
## [4,] -0.8986138
## [5,] -1.1462179
## [6,] -1.1388192
## logSigma0p5_gldm_LargeDependenceLowGrayLevelEmphasis
## [1,] -0.7271970
## [2,] -0.7025096
## [3,] -0.6797995
## [4,] -0.6687926
## [5,] -0.6664962
## [6,] -0.6792235
## logSigma0p5_gldm_LowGrayLevelEmphasis
## [1,] -0.3833857
## [2,] -0.3157980
## [3,] -0.3851913
## [4,] -0.4381517
## [5,] -0.2028571
## [6,] -0.2751621
## logSigma0p5_gldm_SmallDependenceEmphasis
## [1,] 4.669025
## [2,] 4.310517
## [3,] 2.588399
## [4,] 1.659052
## [5,] 3.154329
## [6,] 3.718507
## logSigma0p5_gldm_SmallDependenceHighGrayLevelEmphasis
## [1,] 3.863058
## [2,] 2.958888
## [3,] 1.806973
## [4,] 1.570464
## [5,] 1.403011
## [6,] 2.669962
## logSigma0p5_gldm_SmallDependenceLowGrayLevelEmphasis
## [1,] 0.51241010
## [2,] 0.69033094
## [3,] 0.25473796
## [4,] -0.07720903
## [5,] 0.67433564
## [6,] 0.57557728
## logSigma1p0_firstorder_10Percentile logSigma1p0_firstorder_90Percentile
## [1,] -0.17411321 -0.8243381
## [2,] -0.13564882 -0.7139759
## [3,] -0.12663168 -0.7033283
## [4,] -0.14466585 -0.7000657
## [5,] -0.01801079 -0.6225664
## [6,] -0.08154657 -0.5654481
## logSigma1p0_firstorder_Energy logSigma1p0_firstorder_Entropy
## [1,] -0.8666076 -1.990067
## [2,] -0.8497408 -1.776760
## [3,] -0.8420813 -1.745674
## [4,] -0.8530705 -1.599917
## [5,] -0.8493681 -2.151389
## [6,] -0.8252414 -1.431336
## logSigma1p0_firstorder_InterquartileRange logSigma1p0_firstorder_Kurtosis
## [1,] -1.351706 -0.5064040
## [2,] -1.365690 -0.1950605
## [3,] -1.325516 -0.2194418
## [4,] -1.189437 -0.5641903
## [5,] -1.430708 1.0717229
## [6,] -1.326193 0.2356137
## logSigma1p0_firstorder_Maximum
## [1,] -1.0687969
## [2,] -0.9748419
## [3,] -0.9748419
## [4,] -0.9748419
## [5,] -0.8362133
## [6,] -0.7749968
## logSigma1p0_firstorder_MeanAbsoluteDeviation logSigma1p0_firstorder_Mean
## [1,] -1.375269 -0.5011797
## [2,] -1.256394 -0.4126302
## [3,] -1.268420 -0.4170676
## [4,] -1.235489 -0.4338701
## [5,] -1.315893 -0.3429109
## [6,] -1.184390 -0.3392545
## logSigma1p0_firstorder_Median logSigma1p0_firstorder_Minimum
## [1,] -0.4611420 0.09551689
## [2,] -0.3753121 0.09551689
## [3,] -0.3874371 0.09551689
## [4,] -0.4091348 0.09551689
## [5,] -0.3135494 0.09551689
## [6,] -0.3135494 0.09551689
## logSigma1p0_firstorder_Range
## [1,] -1.675206
## [2,] -1.537826
## [3,] -1.537826
## [4,] -1.537826
## [5,] -1.335124
## [6,] -1.245614
## logSigma1p0_firstorder_RobustMeanAbsoluteDeviation
## [1,] -1.344053
## [2,] -1.320394
## [3,] -1.298347
## [4,] -1.326554
## [5,] -1.505170
## [6,] -1.242709
## logSigma1p0_firstorder_RootMeanSquared logSigma1p0_firstorder_Skewness
## [1,] -0.00172138 -0.9993230
## [2,] -0.14583214 -1.3577427
## [3,] -0.13919551 -1.1740491
## [4,] -0.10883168 -0.7628381
## [5,] -0.26201007 -1.1894790
## [6,] -0.26163663 -0.6554735
## logSigma1p0_firstorder_TotalEnergy logSigma1p0_firstorder_Uniformity
## [1,] -0.8666076 1.967254
## [2,] -0.8497408 2.129166
## [3,] -0.8420813 1.957578
## [4,] -0.8530705 1.543939
## [5,] -0.8493681 3.354372
## [6,] -0.8252414 1.777384
## logSigma1p0_firstorder_Variance logSigma1p0_glcm_Autocorrelation
## [1,] -0.9825594 -0.9143732
## [2,] -0.9380960 -0.8535464
## [3,] -0.9439750 -0.8583337
## [4,] -0.9315891 -0.8677306
## [5,] -0.9261334 -0.8158723
## [6,] -0.8859624 -0.8161809
## logSigma1p0_glcm_ClusterProminence logSigma1p0_glcm_ClusterShade
## [1,] -0.4843536 0.05860954
## [2,] -0.4817726 0.02816378
## [3,] -0.4823216 0.03862994
## [4,] -0.4821943 0.04736833
## [5,] -0.4838613 0.04299452
## [6,] -0.4779734 0.03944552
## logSigma1p0_glcm_ClusterTendency logSigma1p0_glcm_Contrast
## [1,] -0.9399337 -0.7803485
## [2,] -0.8992662 -0.8682278
## [3,] -0.9012241 -0.7979243
## [4,] -0.8916711 -0.7375501
## [5,] -0.9627971 -1.0109653
## [6,] -0.8712001 -0.8822394
## logSigma1p0_glcm_Correlation logSigma1p0_glcm_DifferenceAverage
## [1,] -3.3381875 -0.8141338
## [2,] -1.5496850 -1.2109264
## [3,] -2.2046281 -0.9896845
## [4,] -2.4296260 -0.8012509
## [5,] -1.5732778 -1.6389815
## [6,] -0.6666584 -1.2830705
## logSigma1p0_glcm_DifferenceEntropy logSigma1p0_glcm_DifferenceVariance
## [1,] -2.2430110 -1.1923257
## [2,] -0.5738460 -0.6146650
## [3,] -0.4218125 -0.5572096
## [4,] -0.4909212 -0.6084912
## [5,] -1.7372688 -1.0841984
## [6,] -0.3964948 -0.4619221
## logSigma1p0_glcm_Id logSigma1p0_glcm_Idm logSigma1p0_glcm_Idmn
## [1,] 0.5466312 0.6997826 0.7880310
## [2,] 1.5785027 1.5307500 0.8781843
## [3,] 1.0865398 1.1077119 0.8061770
## [4,] 0.6694731 0.7483455 0.7443596
## [5,] 2.5040605 2.3365363 1.0243484
## [6,] 1.7738127 1.6855535 0.8925600
## logSigma1p0_glcm_Idn logSigma1p0_glcm_Imc1 logSigma1p0_glcm_Imc2
## [1,] 0.8121496 0.17733538 -0.9463782
## [2,] 1.2485043 0.49693839 -1.1880841
## [3,] 1.0083147 0.78585391 -0.9044529
## [4,] 0.8038177 0.70947442 -0.6996869
## [5,] 1.7122299 0.71647239 -2.6070884
## [6,] 1.3281283 0.04087937 -0.4122273
## logSigma1p0_glcm_InverseVariance logSigma1p0_glcm_JointEnergy
## [1,] 2.5550291 1.7580809
## [2,] -0.2743633 2.0865535
## [3,] 0.7030634 1.2452170
## [4,] 1.5215659 0.7915671
## [5,] -1.9762859 5.4565247
## [6,] -0.8441992 2.4128732
## logSigma1p0_glcm_JointEntropy logSigma1p0_glcm_MaximumProbability
## [1,] -2.035364 1.142242
## [2,] -1.892021 2.473540
## [3,] -1.551459 1.501693
## [4,] -1.384439 0.486102
## [5,] -2.884021 5.042947
## [6,] -1.772735 3.099251
## logSigma1p0_glcm_SumAverage logSigma1p0_glcm_SumEntropy
## [1,] -0.9029349 -2.302456
## [2,] -0.8093413 -1.943749
## [3,] -0.8161832 -1.761407
## [4,] -0.8305958 -1.660747
## [5,] -0.7515068 -2.787310
## [6,] -0.7542476 -1.701712
## logSigma1p0_glcm_SumSquares logSigma1p0_glszm_GrayLevelNonUniformity
## [1,] -0.9336461 -1.3455362
## [2,] -0.9121144 -1.3455362
## [3,] -0.9029048 -0.6712969
## [4,] -0.8852830 -0.6712969
## [5,] -0.9891760 -0.6712969
## [6,] -0.8900223 -0.7836700
## logSigma1p0_glszm_GrayLevelNonUniformityNormalized
## [1,] 2.958392
## [2,] 1.665177
## [3,] 2.130734
## [4,] 2.130734
## [5,] 2.130734
## [6,] 1.234105
## logSigma1p0_glszm_GrayLevelVariance
## [1,] -1.1937056
## [2,] -1.0936836
## [3,] -1.1296916
## [4,] -1.1296916
## [5,] -1.0748223
## [6,] -0.9984246
## logSigma1p0_glszm_HighGrayLevelZoneEmphasis
## [1,] -0.9899108
## [2,] -0.9184321
## [3,] -0.9060748
## [4,] -0.9060748
## [5,] -0.8755450
## [6,] -0.8190890
## logSigma1p0_glszm_LargeAreaEmphasis
## [1,] -0.8117074
## [2,] -0.7765199
## [3,] -0.8005245
## [4,] -0.8236616
## [5,] -0.7438388
## [6,] -0.7529008
## logSigma1p0_glszm_LargeAreaHighGrayLevelEmphasis
## [1,] -0.7329271
## [2,] -0.7160119
## [3,] -0.7265665
## [4,] -0.7364560
## [5,] -0.7005720
## [6,] -0.7047832
## logSigma1p0_glszm_LargeAreaLowGrayLevelEmphasis
## [1,] -0.1547854
## [2,] -0.1523449
## [3,] -0.1542629
## [4,] -0.1561661
## [5,] -0.1500449
## [6,] -0.1506473
## logSigma1p0_glszm_LowGrayLevelZoneEmphasis
## [1,] -0.01975159
## [2,] -0.06452644
## [3,] -0.07723814
## [4,] -0.07723814
## [5,] -0.09139131
## [6,] -0.11827177
## logSigma1p0_glszm_SizeZoneNonUniformity
## [1,] -0.7156517
## [2,] -0.7156517
## [3,] -0.5870438
## [4,] -0.4584359
## [5,] -0.3298280
## [6,] -0.5013052
## logSigma1p0_glszm_SizeZoneNonUniformityNormalized
## [1,] 1.5237422
## [2,] 0.5648844
## [3,] 0.9100732
## [4,] 1.8305767
## [5,] 2.7510801
## [6,] 0.8845039
## logSigma1p0_glszm_SmallAreaEmphasis
## [1,] -0.9706560
## [2,] 0.2428486
## [3,] 0.9719621
## [4,] 1.0132359
## [5,] 2.0652214
## [6,] 0.7865054
## logSigma1p0_glszm_SmallAreaHighGrayLevelEmphasis
## [1,] -0.9353081
## [2,] -0.4707567
## [3,] -0.2594234
## [4,] -0.2471504
## [5,] 0.0318650
## [6,] -0.1785931
## logSigma1p0_glszm_SmallAreaLowGrayLevelEmphasis
## [1,] -0.224032879
## [2,] -0.043522271
## [3,] 0.101102070
## [4,] 0.109420361
## [5,] 0.391462340
## [6,] -0.002931533
## logSigma1p0_glszm_ZoneEntropy logSigma1p0_glszm_ZonePercentage
## [1,] -2.880805 1.515439
## [2,] -2.267634 1.276645
## [3,] -1.792021 1.737176
## [4,] -1.792021 2.291519
## [5,] -2.382976 1.515439
## [6,] -1.403417 1.352053
## logSigma1p0_glszm_ZoneVariance logSigma1p0_ngtdm_Busyness
## [1,] -0.7965114 0.06080964
## [2,] -0.7420525 -0.29292714
## [3,] -0.7592485 -0.25685882
## [4,] -0.7823772 -0.23442215
## [5,] -0.6551691 -0.30982251
## [6,] -0.6864224 -0.30181485
## logSigma1p0_ngtdm_Coarseness logSigma1p0_ngtdm_Complexity
## [1,] -0.008547759 -0.7773855
## [2,] -0.008524931 -0.7643678
## [3,] -0.008548094 -0.7590027
## [4,] -0.008542473 -0.7532052
## [5,] -0.008533936 -0.7761877
## [6,] -0.008548405 -0.7398146
## logSigma1p0_ngtdm_Contrast logSigma1p0_ngtdm_Strength
## [1,] 0.3946809 -0.7752940
## [2,] -0.5537464 -0.4597743
## [3,] -0.5061574 -0.5693955
## [4,] -0.2961292 -0.5214209
## [5,] -1.0051184 -0.3378473
## [6,] -0.8075426 -0.2016870
## logSigma1p0_gldm_DependenceEntropy
## [1,] -6.687609
## [2,] -5.105869
## [3,] -5.754723
## [4,] -6.353683
## [5,] -5.651590
## [6,] -4.463398
## logSigma1p0_gldm_DependenceNonUniformity
## [1,] -1.414345
## [2,] -1.793538
## [3,] -1.700432
## [4,] -1.671090
## [5,] -1.763518
## [6,] -1.625146
## logSigma1p0_gldm_DependenceNonUniformityNormalized
## [1,] 5.6801159
## [2,] 0.5638024
## [3,] 0.9787930
## [4,] 1.7355130
## [5,] 0.3785693
## [6,] 0.5051462
## logSigma1p0_gldm_DependenceVariance
## [1,] -1.0686296
## [2,] -0.7187601
## [3,] -0.7409530
## [4,] -0.9187277
## [5,] -0.3184542
## [6,] -0.4192857
## logSigma1p0_gldm_GrayLevelNonUniformity logSigma1p0_gldm_GrayLevelVariance
## [1,] -1.570151 -0.9588224
## [2,] -1.374107 -0.9266373
## [3,] -1.355534 -0.9327113
## [4,] -1.496376 -0.9202724
## [5,] -1.081899 -0.9641569
## [6,] -1.177629 -0.8829980
## logSigma1p0_gldm_HighGrayLevelEmphasis
## [1,] -0.9227837
## [2,] -0.8698697
## [3,] -0.8748363
## [4,] -0.8846684
## [5,] -0.8297172
## [6,] -0.8233739
## logSigma1p0_gldm_LargeDependenceEmphasis
## [1,] -1.1293582
## [2,] -0.8219342
## [3,] -0.8999960
## [4,] -1.0369533
## [5,] -0.5333465
## [6,] -0.6563909
## logSigma1p0_gldm_LargeDependenceHighGrayLevelEmphasis
## [1,] -0.8974650
## [2,] -0.7867168
## [3,] -0.8146514
## [4,] -0.8628651
## [5,] -0.6831490
## [6,] -0.7267060
## logSigma1p0_gldm_LargeDependenceLowGrayLevelEmphasis
## [1,] -0.1776673
## [2,] -0.1613465
## [3,] -0.1655525
## [4,] -0.1730498
## [5,] -0.1460158
## [6,] -0.1525607
## logSigma1p0_gldm_LowGrayLevelEmphasis
## [1,] -0.07906168
## [2,] -0.10516709
## [3,] -0.10320519
## [4,] -0.09744371
## [5,] -0.12608660
## [6,] -0.12426129
## logSigma1p0_gldm_SmallDependenceEmphasis
## [1,] 0.8319455
## [2,] 0.6909995
## [3,] 1.3668911
## [4,] 1.7809245
## [5,] 1.4348805
## [6,] 0.8975777
## logSigma1p0_gldm_SmallDependenceHighGrayLevelEmphasis
## [1,] -0.40897862
## [2,] -0.35327091
## [3,] -0.14319991
## [4,] -0.01676697
## [5,] -0.10304812
## [6,] -0.18014459
## logSigma1p0_gldm_SmallDependenceLowGrayLevelEmphasis
## [1,] 0.3167900
## [2,] 0.1770992
## [3,] 0.3746168
## [4,] 0.5052596
## [5,] 0.4019920
## [6,] 0.1510680Outliers
# Find IQR outliers for each radiomic feature
outlier_summary <- lapply(
colnames(feature_z),
function(feature_name) {
x <- feature_z[, feature_name]
q1 <- quantile(x, 0.25)
q3 <- quantile(x, 0.75)
iqr <- q3 - q1
lower <- q1 - 1.5 * iqr
upper <- q3 + 1.5 * iqr
is_outlier <- x < lower | x > upper
data.frame(
feature = feature_name,
n_outliers = sum(is_outlier),
percent_outliers = 100 * mean(is_outlier),
min_z = min(x),
max_z = max(x)
)
}
)
outlier_summary <- bind_rows(outlier_summary)
cat("Features assessed:", nrow(outlier_summary), "\n")## Features assessed: 273cat(
"Median % outliers per feature:",
median(outlier_summary$percent_outliers),
"\n"
)## Median % outliers per feature: 2.474068cat(
"Maximum % outliers in a feature:",
max(outlier_summary$percent_outliers),
"\n"
)## Maximum % outliers in a feature: 20.07156outlier_summary |>
arrange(desc(percent_outliers)) |>
slice_head(n = 10)## feature n_outliers
## 1 logSigma1p0_glcm_ClusterShade 21653
## 2 logSigma0p5_glcm_ClusterShade 15291
## 3 logSigma1p0_glrlm_LowGrayLevelRunEmphasis 13992
## 4 logSigma1p0_glrlm_ShortRunLowGrayLevelEmphasis 13965
## 5 logSigma1p0_gldm_LargeDependenceLowGrayLevelEmphasis 13632
## 6 logSigma1p0_glrlm_LongRunLowGrayLevelEmphasis 13626
## 7 logSigma1p0_glcm_ClusterProminence 12888
## 8 logSigma1p0_glszm_LargeAreaLowGrayLevelEmphasis 12549
## 9 original_glcm_ClusterShade 12530
## 10 logSigma1p0_gldm_LowGrayLevelEmphasis 12220
## percent_outliers min_z max_z
## 1 20.07156 -12.2563159 13.42948
## 2 14.17421 -18.4560890 14.96087
## 3 12.97009 -0.4153115 13.88723
## 4 12.94506 -0.4527320 14.49125
## 5 12.63638 -0.1906242 39.98686
## 6 12.63082 -0.3441881 23.31752
## 7 11.94672 -0.4851412 12.97924
## 8 11.63248 -0.1602284 83.29698
## 9 11.61486 -15.0182195 16.38647
## 10 11.32751 -0.3663328 22.22302#PCA
# Run PCA on the Z-scored radiomic features
pca <- prcomp(
feature_z,
center = FALSE,
scale. = FALSE
)
summary(pca)## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 7.5295 6.9408 5.6212 5.0060 3.7678 2.84662 2.77848
## Proportion of Variance 0.2077 0.1765 0.1157 0.0918 0.0520 0.02968 0.02828
## Cumulative Proportion 0.2077 0.3841 0.4999 0.5917 0.6437 0.67335 0.70163
## PC8 PC9 PC10 PC11 PC12 PC13 PC14
## Standard deviation 2.42231 2.28014 2.16779 1.99114 1.84209 1.68982 1.58286
## Proportion of Variance 0.02149 0.01904 0.01721 0.01452 0.01243 0.01046 0.00918
## Cumulative Proportion 0.72312 0.74217 0.75938 0.77390 0.78633 0.79679 0.80597
## PC15 PC16 PC17 PC18 PC19 PC20 PC21
## Standard deviation 1.56343 1.55377 1.51598 1.46539 1.38079 1.3111 1.29165
## Proportion of Variance 0.00895 0.00884 0.00842 0.00787 0.00698 0.0063 0.00611
## Cumulative Proportion 0.81492 0.82377 0.83219 0.84005 0.84704 0.8533 0.85944
## PC22 PC23 PC24 PC25 PC26 PC27 PC28
## Standard deviation 1.24570 1.21614 1.20073 1.16749 1.14215 1.09819 1.09039
## Proportion of Variance 0.00568 0.00542 0.00528 0.00499 0.00478 0.00442 0.00436
## Cumulative Proportion 0.86513 0.87054 0.87583 0.88082 0.88560 0.89001 0.89437
## PC29 PC30 PC31 PC32 PC33 PC34 PC35
## Standard deviation 1.07804 1.04659 1.03847 1.01450 1.00618 0.99662 0.95663
## Proportion of Variance 0.00426 0.00401 0.00395 0.00377 0.00371 0.00364 0.00335
## Cumulative Proportion 0.89863 0.90264 0.90659 0.91036 0.91407 0.91771 0.92106
## PC36 PC37 PC38 PC39 PC40 PC41 PC42
## Standard deviation 0.93063 0.91427 0.89127 0.87563 0.84914 0.83826 0.79569
## Proportion of Variance 0.00317 0.00306 0.00291 0.00281 0.00264 0.00257 0.00232
## Cumulative Proportion 0.92423 0.92729 0.93020 0.93301 0.93565 0.93823 0.94055
## PC43 PC44 PC45 PC46 PC47 PC48 PC49
## Standard deviation 0.7929 0.78002 0.75842 0.73263 0.71256 0.70518 0.67591
## Proportion of Variance 0.0023 0.00223 0.00211 0.00197 0.00186 0.00182 0.00167
## Cumulative Proportion 0.9428 0.94508 0.94718 0.94915 0.95101 0.95283 0.95450
## PC50 PC51 PC52 PC53 PC54 PC55 PC56
## Standard deviation 0.67035 0.63685 0.62465 0.61525 0.5957 0.59093 0.57616
## Proportion of Variance 0.00165 0.00149 0.00143 0.00139 0.0013 0.00128 0.00122
## Cumulative Proportion 0.95615 0.95764 0.95907 0.96045 0.9617 0.96303 0.96425
## PC57 PC58 PC59 PC60 PC61 PC62 PC63
## Standard deviation 0.55519 0.54958 0.53465 0.5235 0.51800 0.51333 0.50476
## Proportion of Variance 0.00113 0.00111 0.00105 0.0010 0.00098 0.00097 0.00093
## Cumulative Proportion 0.96538 0.96648 0.96753 0.9685 0.96952 0.97048 0.97141
## PC64 PC65 PC66 PC67 PC68 PC69 PC70
## Standard deviation 0.4963 0.48924 0.48059 0.46574 0.45957 0.45085 0.44786
## Proportion of Variance 0.0009 0.00088 0.00085 0.00079 0.00077 0.00074 0.00073
## Cumulative Proportion 0.9723 0.97319 0.97404 0.97483 0.97561 0.97635 0.97709
## PC71 PC72 PC73 PC74 PC75 PC76 PC77
## Standard deviation 0.43250 0.42339 0.41729 0.41201 0.4048 0.39957 0.38821
## Proportion of Variance 0.00069 0.00066 0.00064 0.00062 0.0006 0.00058 0.00055
## Cumulative Proportion 0.97777 0.97843 0.97907 0.97969 0.9803 0.98087 0.98143
## PC78 PC79 PC80 PC81 PC82 PC83 PC84
## Standard deviation 0.38595 0.38053 0.3689 0.35997 0.35812 0.35454 0.34942
## Proportion of Variance 0.00055 0.00053 0.0005 0.00047 0.00047 0.00046 0.00045
## Cumulative Proportion 0.98197 0.98250 0.9830 0.98348 0.98394 0.98441 0.98485
## PC85 PC86 PC87 PC88 PC89 PC90 PC91
## Standard deviation 0.34473 0.33767 0.3301 0.32175 0.31932 0.31876 0.31287
## Proportion of Variance 0.00044 0.00042 0.0004 0.00038 0.00037 0.00037 0.00036
## Cumulative Proportion 0.98529 0.98571 0.9861 0.98648 0.98686 0.98723 0.98759
## PC92 PC93 PC94 PC95 PC96 PC97 PC98
## Standard deviation 0.30687 0.30350 0.30064 0.29384 0.29185 0.2853 0.2842
## Proportion of Variance 0.00034 0.00034 0.00033 0.00032 0.00031 0.0003 0.0003
## Cumulative Proportion 0.98793 0.98827 0.98860 0.98892 0.98923 0.9895 0.9898
## PC99 PC100 PC101 PC102 PC103 PC104 PC105
## Standard deviation 0.28284 0.27986 0.27548 0.27431 0.27104 0.26305 0.25930
## Proportion of Variance 0.00029 0.00029 0.00028 0.00028 0.00027 0.00025 0.00025
## Cumulative Proportion 0.99012 0.99040 0.99068 0.99096 0.99123 0.99148 0.99173
## PC106 PC107 PC108 PC109 PC110 PC111 PC112
## Standard deviation 0.25557 0.25387 0.24915 0.24557 0.23943 0.23843 0.23678
## Proportion of Variance 0.00024 0.00024 0.00023 0.00022 0.00021 0.00021 0.00021
## Cumulative Proportion 0.99197 0.99220 0.99243 0.99265 0.99286 0.99307 0.99327
## PC113 PC114 PC115 PC116 PC117 PC118 PC119
## Standard deviation 0.2346 0.23044 0.22681 0.22291 0.21996 0.21784 0.21618
## Proportion of Variance 0.0002 0.00019 0.00019 0.00018 0.00018 0.00017 0.00017
## Cumulative Proportion 0.9935 0.99367 0.99386 0.99404 0.99422 0.99439 0.99456
## PC120 PC121 PC122 PC123 PC124 PC125 PC126
## Standard deviation 0.21148 0.20954 0.20671 0.19862 0.19687 0.19498 0.19373
## Proportion of Variance 0.00016 0.00016 0.00016 0.00014 0.00014 0.00014 0.00014
## Cumulative Proportion 0.99473 0.99489 0.99504 0.99519 0.99533 0.99547 0.99561
## PC127 PC128 PC129 PC130 PC131 PC132 PC133
## Standard deviation 0.18561 0.18489 0.18347 0.18268 0.17668 0.17436 0.17214
## Proportion of Variance 0.00013 0.00013 0.00012 0.00012 0.00011 0.00011 0.00011
## Cumulative Proportion 0.99573 0.99586 0.99598 0.99610 0.99622 0.99633 0.99644
## PC134 PC135 PC136 PC137 PC138 PC139 PC140
## Standard deviation 0.17106 0.1692 0.1665 0.1637 0.1613 0.15955 0.15621
## Proportion of Variance 0.00011 0.0001 0.0001 0.0001 0.0001 0.00009 0.00009
## Cumulative Proportion 0.99655 0.9967 0.9968 0.9969 0.9969 0.99704 0.99713
## PC141 PC142 PC143 PC144 PC145 PC146 PC147
## Standard deviation 0.15342 0.15243 0.15159 0.14955 0.14666 0.14456 0.14180
## Proportion of Variance 0.00009 0.00009 0.00008 0.00008 0.00008 0.00008 0.00007
## Cumulative Proportion 0.99721 0.99730 0.99738 0.99746 0.99754 0.99762 0.99769
## PC148 PC149 PC150 PC151 PC152 PC153 PC154
## Standard deviation 0.14064 0.14052 0.13576 0.13536 0.13423 0.13245 0.13073
## Proportion of Variance 0.00007 0.00007 0.00007 0.00007 0.00007 0.00006 0.00006
## Cumulative Proportion 0.99777 0.99784 0.99791 0.99797 0.99804 0.99810 0.99817
## PC155 PC156 PC157 PC158 PC159 PC160 PC161
## Standard deviation 0.12934 0.12639 0.12304 0.12063 0.11836 0.11805 0.11668
## Proportion of Variance 0.00006 0.00006 0.00006 0.00005 0.00005 0.00005 0.00005
## Cumulative Proportion 0.99823 0.99829 0.99834 0.99839 0.99845 0.99850 0.99855
## PC162 PC163 PC164 PC165 PC166 PC167 PC168
## Standard deviation 0.11418 0.11323 0.11219 0.10958 0.10783 0.10712 0.10567
## Proportion of Variance 0.00005 0.00005 0.00005 0.00004 0.00004 0.00004 0.00004
## Cumulative Proportion 0.99859 0.99864 0.99869 0.99873 0.99877 0.99882 0.99886
## PC169 PC170 PC171 PC172 PC173 PC174 PC175
## Standard deviation 0.10369 0.10294 0.10179 0.10083 0.09842 0.09722 0.09670
## Proportion of Variance 0.00004 0.00004 0.00004 0.00004 0.00004 0.00003 0.00003
## Cumulative Proportion 0.99890 0.99894 0.99897 0.99901 0.99905 0.99908 0.99912
## PC176 PC177 PC178 PC179 PC180 PC181 PC182
## Standard deviation 0.09583 0.09404 0.09236 0.09068 0.08983 0.08851 0.08750
## Proportion of Variance 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003
## Cumulative Proportion 0.99915 0.99918 0.99921 0.99924 0.99927 0.99930 0.99933
## PC183 PC184 PC185 PC186 PC187 PC188 PC189
## Standard deviation 0.08585 0.08564 0.08287 0.08240 0.08060 0.07874 0.07834
## Proportion of Variance 0.00003 0.00003 0.00003 0.00002 0.00002 0.00002 0.00002
## Cumulative Proportion 0.99936 0.99938 0.99941 0.99943 0.99946 0.99948 0.99950
## PC190 PC191 PC192 PC193 PC194 PC195 PC196
## Standard deviation 0.07777 0.07661 0.07435 0.07324 0.07167 0.07064 0.06979
## Proportion of Variance 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002
## Cumulative Proportion 0.99952 0.99955 0.99957 0.99959 0.99960 0.99962 0.99964
## PC197 PC198 PC199 PC200 PC201 PC202 PC203
## Standard deviation 0.06954 0.06819 0.06712 0.06471 0.06268 0.06154 0.05975
## Proportion of Variance 0.00002 0.00002 0.00002 0.00002 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99966 0.99967 0.99969 0.99971 0.99972 0.99973 0.99975
## PC204 PC205 PC206 PC207 PC208 PC209 PC210
## Standard deviation 0.05948 0.05765 0.05750 0.05636 0.05385 0.05371 0.05294
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99976 0.99977 0.99979 0.99980 0.99981 0.99982 0.99983
## PC211 PC212 PC213 PC214 PC215 PC216 PC217
## Standard deviation 0.05266 0.05160 0.04890 0.04837 0.04751 0.04564 0.04517
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99984 0.99985 0.99986 0.99987 0.99987 0.99988 0.99989
## PC218 PC219 PC220 PC221 PC222 PC223 PC224
## Standard deviation 0.04409 0.04375 0.04240 0.04119 0.04103 0.03960 0.03936
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99990 0.99990 0.99991 0.99992 0.99992 0.99993 0.99993
## PC225 PC226 PC227 PC228 PC229 PC230 PC231
## Standard deviation 0.03758 0.0357 0.03505 0.03411 0.03394 0.03322 0.03278
## Proportion of Variance 0.00001 0.0000 0.00000 0.00000 0.00000 0.00000 0.00000
## Cumulative Proportion 0.99994 0.9999 0.99995 0.99995 0.99996 0.99996 0.99996
## PC232 PC233 PC234 PC235 PC236 PC237 PC238
## Standard deviation 0.03113 0.0294 0.02924 0.02792 0.02697 0.02618 0.02595
## Proportion of Variance 0.00000 0.0000 0.00000 0.00000 0.00000 0.00000 0.00000
## Cumulative Proportion 0.99997 1.0000 0.99997 0.99998 0.99998 0.99998 0.99998
## PC239 PC240 PC241 PC242 PC243 PC244 PC245
## Standard deviation 0.0254 0.025 0.0238 0.01943 0.01905 0.01874 0.01751
## Proportion of Variance 0.0000 0.000 0.0000 0.00000 0.00000 0.00000 0.00000
## Cumulative Proportion 1.0000 1.000 1.0000 0.99999 0.99999 1.00000 1.00000
## PC246 PC247 PC248 PC249 PC250 PC251
## Standard deviation 0.01724 0.01672 0.01048 0.009813 0.008335 0.006642
## Proportion of Variance 0.00000 0.00000 0.00000 0.000000 0.000000 0.000000
## Cumulative Proportion 1.00000 1.00000 1.00000 1.000000 1.000000 1.000000
## PC252 PC253 PC254 PC255 PC256 PC257
## Standard deviation 0.004366 0.003142 0.002764 0.002526 0.001816 0.001376
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000
## PC258 PC259 PC260 PC261 PC262
## Standard deviation 0.0008922 0.000435 0.0003066 0.0002027 5.364e-05
## Proportion of Variance 0.0000000 0.000000 0.0000000 0.0000000 0.000e+00
## Cumulative Proportion 1.0000000 1.000000 1.0000000 1.0000000 1.000e+00
## PC263 PC264 PC265 PC266 PC267
## Standard deviation 3.121e-05 8.145e-06 1.184e-07 7.786e-08 6.981e-08
## Proportion of Variance 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00
## Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## PC268 PC269 PC270 PC271 PC272
## Standard deviation 6.118e-08 5.232e-08 4.577e-08 4.461e-08 2.895e-08
## Proportion of Variance 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00
## Cumulative Proportion 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
## PC273
## Standard deviation 2.492e-08
## Proportion of Variance 0.000e+00
## Cumulative Proportion 1.000e+00# Variance explained by each principal component (variance/total variance)
variance_explained <- pca$sdev^2 / sum(pca$sdev^2)
# Cumulative variance explained
cumulative_variance <- cumsum(variance_explained)
# Find the first PC where cumulative variance reaches 90%
n_pcs_90 <- which(cumulative_variance >= 0.90)[1]
cat("Total original features:", ncol(feature_z), "\n")## Total original features: 273cat("PCs needed to explain 90% variance:", n_pcs_90, "\n")## PCs needed to explain 90% variance: 30cat(
"Cumulative variance explained:",
round(cumulative_variance[n_pcs_90] * 100, 2),
"%\n"
)## Cumulative variance explained: 90.26 %#???? Second opinion needed on this graph
# Create PCA variance table
pca_variance <- data.frame(
PC = seq_along(variance_explained),
variance_explained = variance_explained,
cumulative_variance = cumulative_variance
)
# Plot cumulative variance explained
ggplot(
pca_variance,
aes(x = PC, y = cumulative_variance)
) +
geom_line() +
geom_point(size = 1) +
geom_hline(
yintercept = 0.90,
linetype = "dashed"
) +
geom_vline(
xintercept = n_pcs_90,
linetype = "dashed"
) +
labs(
title = "PCA cumulative variance — Lüsebrink Left",
x = "Principal component",
y = "Cumulative variance explained"
) +
theme_minimal()
# Create scree plot data
pca_variance <- data.frame(
PC = seq_along(variance_explained),
variance_explained = variance_explained
)
# Scree plot
ggplot(
pca_variance,
aes(x = PC, y = variance_explained)
) +
geom_col(fill = "steelblue") +
geom_line() +
geom_point() +
labs(
title = "Scree Plot — Lüsebrink Left",
x = "Principal Components",
y = "Proportion of Variance Explained"
) +
theme_minimal()