added lab 4

Assignments/.gitignore

@@ -1,5 +0,0 @@
-node_modules
-.venv
-.vscode
-Assignment III
-tmp/

Lab 4/given/Data_Analytics2025Fall_Lab4_code.R

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+##########################################
+### Principal Component Analysis (PCA) ###
+##########################################
+
+## load libraries
+library(ggplot2)
+library(ggfortify)
+library(GGally)
+library(e1071)
+library(class)
+library(psych)
+library(readr)
+
+## set working directory so that files can be referenced without the full path
+setwd("/home/ion606/Desktop/Data Analytics/Lab 4")
+
+## read dataset
+wine <- read_csv("wine.data", col_names = FALSE)
+
+## set column names
+names(wine) <- c("Type","Alcohol","Malic acid","Ash","Alcalinity of ash","Magnesium","Total phenols","Flavanoids","Nonflavanoid Phenols","Proanthocyanins","Color Intensity","Hue","Od280/od315 of diluted wines","Proline")
+
+## inspect data frame
+head(wine)
+
+## change the data type of the "Type" column from character to factor
+####
+# Factors look like regular strings (characters) but with factors R knows 
+# that the column is a categorical variable with finite possible values
+# e.g. "Type" in the Wine dataset can only be 1, 2, or 3
+####
+
+wine$Type <- as.factor(wine$Type)
+
+
+## visualize variables
+pairs.panels(wine[,-1],gap = 0,bg = c("red", "yellow", "blue")[wine$Type],pch=21)
+
+ggpairs(wine, ggplot2::aes(colour = Type))
+
+###

Lab 4/lab4_pca.R

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+has_pkg <- function(pkg) requireNamespace(pkg, quietly = TRUE)
+
+has_ggplot2 <- has_pkg("ggplot2")
+has_GGally  <- has_pkg("GGally")
+has_e1071   <- has_pkg("e1071")
+has_class   <- has_pkg("class")
+has_psych   <- has_pkg("psych")
+has_readr   <- has_pkg("readr")
+
+# WHY IS THIS HERE YOU MIGHT ASK???? WELL LET ME TELL YOU I SPENT TWO HOURS ON STUPID PACKAGE IMPORTS
+# OOOOOOHHH PSYCH IS IN A DIFFERENT REPO??? OH IT ISN'T??? I have a fever of 103 I DO NOT CARE
+if (has_ggplot2) { library(ggplot2) } else { warning("ggplot2 not available; plots will be skipped") }
+if (has_GGally)  { library(GGally)  } else { message("GGally not available; skipping ggpairs plot") }
+if (has_e1071)   { library(e1071)   }
+if (has_class)   { library(class)   } else { stop("class package not available for kNN") }
+if (!has_psych)  { message("psych not available; skipping pairs.panels plot") }
+if (has_readr)   { library(readr)   }
+library(grid)        # unit() for arrows in plots
+suppressWarnings(RNGkind(sample.kind = "Rounding"))
+
+# set a reproducible seed
+set.seed(4600)
+
+# 178 rows
+# col 1 is class label (1,2,3)
+# other 13 columns continuous predictors
+
+possible_paths <- c(
+  "wine.data",
+  "./wine.data",
+  "../wine.data",
+  "DAN/wine.data",
+  "./DAN/wine.data"
+)
+data_path <- NA
+for (p in possible_paths) { if (file.exists(p)) { data_path <- p; break } }
+if (is.na(data_path)) stop("could not find wine.data; place this script in the DAN folder or given/ and re-run")
+
+if (has_readr) {
+  wine <- readr::read_csv(
+    file = data_path,
+    col_names = FALSE,
+    show_col_types = FALSE,
+    progress = FALSE
+  )
+} else {
+  wine <- read.csv(file = data_path, header = FALSE)
+}
+
+colnames(wine) <- c(
+  "Type",
+  "Alcohol",
+  "Malic_acid",
+  "Ash",
+  "Alcalinity_of_ash",
+  "Magnesium",
+  "Total_phenols",
+  "Flavanoids",
+  "Nonflavanoid_phenols",
+  "Proanthocyanins",
+  "Color_intensity",
+  "Hue",
+  "OD280_OD315",
+  "Proline"
+)
+
+wine$Type <- as.factor(wine$Type)
+
+# put here from when I accidentally read in the wrong file repeatedly
+# left because it makes it more, "robust"
+stopifnot(nrow(wine) == 178, ncol(wine) == 14)
+print(summary(wine$Type))
+
+# exploratory plots (because I went down a rabbit hole and by god I'm using it)
+
+if (has_psych) {
+  # pairs panel (psych) – colors by class
+  psych::pairs.panels(
+    wine[,-1],
+    gap = 0,
+    bg = c("red","gold","royalblue")[wine$Type],
+    pch = 21,
+    main = "wine (uci) – scatterplot matrix by class"
+  )
+}
+
+if (has_GGally && has_ggplot2) {
+  # ggpairs for nice matrix <3
+  GGally::ggpairs(wine, ggplot2::aes(colour = Type), columns = 2:ncol(wine))
+}
+
+# split into train/test BEFORE!!!!!!!!!!!!!!!!!!!!!! any preprocessing to avoid leakage
+
+set.seed(4600)
+n <- nrow(wine)
+train_idx <- sample.int(n, size = floor(0.7 * n))
+wine_train <- wine[train_idx, , drop = FALSE]
+wine_test  <- wine[-train_idx, , drop = FALSE]
+
+X_train <- wine_train[, -1]
+y_train <- wine_train$Type
+X_test  <- wine_test[, -1]
+y_test  <- wine_test$Type
+
+# yes
+if (any(sapply(X_train, function(x) var(x, na.rm = TRUE) == 0))) {
+  warning("one or more predictors have zero variance in the training set; scale() would fail")
+}
+if (anyNA(X_train) | anyNA(X_test)) {
+  stop("found NA values in predictors; handle missingness before PCA")
+}
+
+# project both train and test using the train-fitted pca
+pca_tr <- prcomp(X_train, center = TRUE, scale. = TRUE)
+
+pve_tr <- (pca_tr$sdev^2) / sum(pca_tr$sdev^2)
+pve_df <- data.frame(
+  PC = paste0("PC", seq_along(pve_tr)),
+  PVE = pve_tr,
+  CumPVE = cumsum(pve_tr)
+)
+
+print("variance explained (training pca):")
+print(pve_df)
+
+# scree plot from training pca
+p_scree <- ggplot(pve_df, aes(x = seq_along(PVE), y = PVE)) +
+  geom_line() + geom_point() +
+  scale_x_continuous(breaks = 1:length(pve_df$PC), labels = pve_df$PC) +
+  labs(title = "scree plot – variance explained by principal components (training pca)",
+       x = "principal component", y = "proportion of variance explained") +
+  theme_minimal()
+
+# cumulative variance plot from training pca
+p_cumvar <- ggplot(pve_df, aes(x = seq_along(CumPVE), y = CumPVE)) +
+  geom_line() + geom_point() +
+  scale_x_continuous(breaks = 1:length(pve_df$PC), labels = pve_df$PC) +
+  labs(title = "cumulative variance explained (training pca)",
+       x = "principal component", y = "cumulative proportion of variance") +
+  theme_minimal()
+
+# ========================================================================================================
+
+# choose number of pcs: default to the smallest k with >= thresh cum variance
+# you can change thresh to 0.90 or 0.99 if you prefer
+
+pc_variance_threshold <- 0.95
+k_pcs <- which(cumsum(pve_tr) >= pc_variance_threshold)[1]
+if (is.na(k_pcs)) k_pcs <- ncol(X_train)  # crashes if fails so...
+cat("chosen number of pcs (threshold =", pc_variance_threshold, "):", k_pcs, "\n")
+
+# project train/test into the pca space
+Z_train_full <- as.data.frame(predict(pca_tr, newdata = X_train))
+Z_test_full  <- as.data.frame(predict(pca_tr, newdata = X_test))
+
+# for downstream modeling
+Z_train <- Z_train_full[, seq_len(k_pcs), drop = FALSE]
+Z_test  <- Z_test_full[,  seq_len(k_pcs), drop = FALSE]
+
+scores_all <- as.data.frame(predict(pca_tr, newdata = wine[,-1]))
+scores_all$Type <- wine$Type
+
+# loadings from training pca
+loadings <- as.data.frame(pca_tr$rotation)
+loadings$Variable <- rownames(loadings)
+top_pc1 <- loadings[order(abs(loadings$PC1), decreasing = TRUE), c("Variable","PC1")][1:5, ]
+top_pc2 <- loadings[order(abs(loadings$PC2), decreasing = TRUE), c("Variable","PC2")][1:5, ]
+print("top contributors to pc1 (training pca):"); print(top_pc1)
+print("top contributors to pc2 (training pca):"); print(top_pc2)
+
+
+# function to make convex hull data for each group
+scores <- scores_all
+hull_df <- do.call(rbind, lapply(split(scores, scores$Type), function(df) {
+  pts <- df[chull(df$PC1, df$PC2), c("PC1","PC2")]
+  pts$Type <- unique(df$Type)
+  pts
+}))
+p_pc12 <- ggplot(scores, aes(PC1, PC2, color = Type)) +
+  geom_point(size = 2, alpha = 0.85) +
+  geom_polygon(data = hull_df, aes(fill = Type, group = Type), color = NA, alpha = 0.15) +
+  guides(fill = "none") +
+  theme_minimal() +
+  labs(title = "pc1 vs pc2 by class (projected with training pca)")
+
+# arrow arrow arrow arrow arrow arrow arrow arrow arrow
+loading_scalefactor <- 3 * max(abs(scores$PC1), abs(scores$PC2)) # heuristic
+load_plot_df <- loadings
+load_plot_df$PC1s <- load_plot_df$PC1 * loading_scalefactor
+load_plot_df$PC2s <- load_plot_df$PC2 * loading_scalefactor
+
+p_biplot <- ggplot(scores, aes(PC1, PC2, color = Type)) +
+  geom_point(size = 2, alpha = 0.85) +
+  geom_segment(
+    data = load_plot_df,
+    mapping = aes(x = 0, y = 0, xend = PC1s, yend = PC2s),
+    inherit.aes = FALSE,
+    arrow = arrow(length = unit(0.02, "npc")),
+    color = "black",
+    alpha = 0.8
+  ) +
+  geom_text(
+    data = load_plot_df,
+    mapping = aes(x = PC1s, y = PC2s, label = Variable),
+    inherit.aes = FALSE,
+    hjust = 0,
+    vjust = 0
+  ) +
+  theme_minimal() +
+  labs(title = "pc1 vs pc2 with variable loadings (training pca projection)")
+
+# 1) kNN on original variables with standardization
+# 2) kNN on first 2 principal components only
+
+# helper to create metrics from a confusion matrix (rows=true, cols=pred)
+compute_metrics <- function(cm) {
+  lv <- rownames(cm)
+  if (is.null(lv)) lv <- as.character(1:nrow(cm))
+  TP <- diag(cm)
+  FP <- colSums(cm) - TP
+  FN <- rowSums(cm) - TP
+  precision <- TP / (TP + FP)
+  recall <- TP / (TP + FN)
+  f1 <- 2 * precision * recall / (precision + recall)
+  acc <- sum(TP) / sum(cm)
+  macro_precision <- mean(precision, na.rm = TRUE)
+  macro_recall <- mean(recall, na.rm = TRUE)
+  macro_f1 <- mean(f1, na.rm = TRUE)
+  per_class <- data.frame(
+    class = lv,
+    precision = precision,
+    recall = recall,
+    f1 = f1,
+    row.names = NULL
+  )
+  summary <- data.frame(
+    accuracy = acc,
+    macro_precision = macro_precision,
+    macro_recall = macro_recall,
+    macro_f1 = macro_f1
+  )
+  list(per_class = per_class, summary = summary)
+}
+
+set.seed(4600)
+ks <- seq(1, 15, by = 2)
+Kfolds <- 5
+
+# kNN on original vars
+X_train_scaled <- scale(X_train, center = TRUE, scale = TRUE)
+scale_center <- attr(X_train_scaled, "scaled:center")
+scale_scale <- attr(X_train_scaled, "scaled:scale")
+X_test_scaled <- scale(X_test, center = scale_center, scale = scale_scale)
+
+n_train_orig <- nrow(X_train_scaled)
+folds_orig <- sample(rep(1:Kfolds, length.out = n_train_orig))
+cv_acc_orig <- sapply(ks, function(k) {
+  mean(sapply(1:Kfolds, function(f) {
+    tr <- which(folds_orig != f)
+    va <- which(folds_orig == f)
+    pred_cv <- knn(train = X_train_scaled[tr, , drop = FALSE],
+                   test = X_train_scaled[va, , drop = FALSE],
+                   cl = y_train[tr], k = k)
+    mean(pred_cv == y_train[va])
+  }))
+})
+
+best_k_orig <- ks[which.max(cv_acc_orig)]
+cat("[Original vars] best k:", best_k_orig, "cv acc:", max(cv_acc_orig), "\n")
+
+pred_orig <- knn(train = X_train_scaled, test = X_test_scaled, cl = y_train, k = best_k_orig)
+acc_orig <- mean(pred_orig == y_test)
+cm_orig <- table(truth = y_test, pred = pred_orig)
+
+cat("[Original vars] held-out accuracy:", round(acc_orig, 4), "\n")
+print(cm_orig)
+
+metrics_orig <- compute_metrics(cm_orig)
+print(metrics_orig$summary)
+print(metrics_orig$per_class)
+
+# kNN on first 2 PCs only
+Z2_train <- Z_train_full[, 1:2, drop = FALSE]
+Z2_test  <- Z_test_full[, 1:2, drop = FALSE]
+n_train_2pc <- nrow(Z2_train)
+
+folds_2pc <- sample(rep(1:Kfolds, length.out = n_train_2pc))
+cv_acc_2pc <- sapply(ks, function(k) {
+  mean(sapply(1:Kfolds, function(f) {
+    tr <- which(folds_2pc != f)
+    va <- which(folds_2pc == f)
+    pred_cv <- knn(train = Z2_train[tr, , drop = FALSE],
+                   test = Z2_train[va, , drop = FALSE],
+                   cl = y_train[tr], k = k)
+    mean(pred_cv == y_train[va])
+  }))
+})
+
+best_k_2pc <- ks[which.max(cv_acc_2pc)]
+cat("[First 2 PCs] best k:", best_k_2pc, "cv acc:", max(cv_acc_2pc), "\n")
+
+pred_2pc <- knn(train = Z2_train, test = Z2_test, cl = y_train, k = best_k_2pc)
+acc_2pc <- mean(pred_2pc == y_test)
+cm_2pc <- table(truth = y_test, pred = pred_2pc)
+
+cat("[First 2 PCs] held-out accuracy:", round(acc_2pc, 4), "\n")
+print(cm_2pc)
+
+metrics_2pc <- compute_metrics(cm_2pc)
+print(metrics_2pc$summary)
+print(metrics_2pc$per_class)
+
+# ===========================================================================================
+outputs_dir <- "outputs"
+if (!dir.exists(outputs_dir)) dir.create(outputs_dir, recursive = TRUE, showWarnings = FALSE)
+
+# plots
+if (exists("p_pc12") && inherits(p_pc12, "ggplot")) ggsave(filename = file.path(outputs_dir, "pc12_scatter.png"), plot = p_pc12, width = 8, height = 6, dpi = 300)
+if (exists("p_biplot") && inherits(p_biplot, "ggplot")) ggsave(filename = file.path(outputs_dir, "pc12_biplot.png"),  plot = p_biplot, width = 8, height = 6, dpi = 300)
+if (exists("p_scree") && inherits(p_scree, "ggplot")) ggsave(filename = file.path(outputs_dir, "pca_scree.png"),    plot = p_scree, width = 8, height = 6, dpi = 300)
+if (exists("p_cumvar") && inherits(p_cumvar, "ggplot")) ggsave(filename = file.path(outputs_dir, "pca_cumvar.png"),   plot = p_cumvar, width = 8, height = 6, dpi = 300)
+
+# top contributors/vars to PC1 and PC2
+write.csv(top_pc1, file = file.path(outputs_dir, "top_contributors_pc1.csv"), row.names = FALSE)
+write.csv(top_pc2, file = file.path(outputs_dir, "top_contributors_pc2.csv"), row.names = FALSE)
+
+# confusion matrices as wide CSV and pretty text
+write.csv(as.matrix(cm_orig), file = file.path(outputs_dir, "confusion_original_wide.csv"))
+writeLines(capture.output(cm_orig), con = file.path(outputs_dir, "confusion_original.txt"))
+
+write.csv(as.matrix(cm_2pc), file = file.path(outputs_dir, "confusion_2pc_wide.csv"))
+writeLines(capture.output(cm_2pc), con = file.path(outputs_dir, "confusion_2pc.txt"))
+
+# metrics
+write.csv(metrics_orig$per_class, file = file.path(outputs_dir, "metrics_original_per_class.csv"), row.names = FALSE)
+write.csv(metrics_orig$summary,   file = file.path(outputs_dir, "metrics_original_summary.csv"), row.names = FALSE)
+write.csv(metrics_2pc$per_class,  file = file.path(outputs_dir, "metrics_2pc_per_class.csv"), row.names = FALSE)
+write.csv(metrics_2pc$summary,    file = file.path(outputs_dir, "metrics_2pc_summary.csv"), row.names = FALSE)
+
+# summary
+metrics_compare <- data.frame(
+  model = c("original_variables", "first_2_pcs"),
+  accuracy = c(metrics_orig$summary$accuracy, metrics_2pc$summary$accuracy),
+  macro_precision = c(metrics_orig$summary$macro_precision, metrics_2pc$summary$macro_precision),
+  macro_recall = c(metrics_orig$summary$macro_recall, metrics_2pc$summary$macro_recall),
+  macro_f1 = c(metrics_orig$summary$macro_f1, metrics_2pc$summary$macro_f1)
+)
+write.csv(metrics_compare, file = file.path(outputs_dir, "metrics_comparison.csv"), row.names = FALSE)
+
+# The below was made with help from ChatGPT because the psych package is confusing
+if (!interactive() && has_ggplot2) {
+  pdf("Rplots_pca_fixed.pdf", width = 8, height = 6)
+  if (has_psych) {
+    psych::pairs.panels(
+      wine[,-1],
+      gap = 0,
+      bg = c("red","gold","royalblue")[wine$Type],
+      pch = 21,
+      main = "wine (uci) – scatterplot matrix by class"
+    )
+  }
+
+  if (exists("p_scree") && inherits(p_scree, "ggplot")) print(p_scree)
+  if (exists("p_pc12") && inherits(p_pc12, "ggplot")) print(p_pc12)
+  dev.off()
+}

Lab 4/outputs/confusion_2pc.txt

@@ -0,0 +1,5 @@
+     pred
+truth  1  2  3
+    1 15  2  0
+    2  1 19  1
+    3  0  1 15

Lab 4/outputs/confusion_2pc_wide.csv

@@ -0,0 +1,4 @@
+"","1","2","3"
+"1",15,2,0
+"2",1,19,1
+"3",0,1,15

Lab 4/outputs/confusion_original.txt

@@ -0,0 +1,5 @@
+     pred
+truth  1  2  3
+    1 17  0  0
+    2  1 18  2
+    3  0  0 16

Lab 4/outputs/confusion_original_wide.csv

@@ -0,0 +1,4 @@
+"","1","2","3"
+"1",17,0,0
+"2",1,18,2
+"3",0,0,16

Lab 4/outputs/metrics_2pc_per_class.csv

@@ -0,0 +1,4 @@
+"class","precision","recall","f1"
+"1",0.9375,0.882352941176471,0.909090909090909
+"2",0.863636363636364,0.904761904761905,0.883720930232558
+"3",0.9375,0.9375,0.9375

Lab 4/outputs/metrics_2pc_summary.csv

@@ -0,0 +1,2 @@
+"accuracy","macro_precision","macro_recall","macro_f1"
+0.907407407407407,0.912878787878788,0.908204948646125,0.910103946441156

Lab 4/outputs/metrics_comparison.csv

@@ -0,0 +1,3 @@
+"model","accuracy","macro_precision","macro_recall","macro_f1"
+"original_variables",0.944444444444444,0.944444444444444,0.952380952380952,0.94522732169791
+"first_2_pcs",0.907407407407407,0.912878787878788,0.908204948646125,0.910103946441156

Lab 4/outputs/metrics_original_per_class.csv

@@ -0,0 +1,4 @@
+"class","precision","recall","f1"
+"1",0.944444444444444,1,0.971428571428571
+"2",1,0.857142857142857,0.923076923076923
+"3",0.888888888888889,1,0.941176470588235

Lab 4/outputs/metrics_original_summary.csv

@@ -0,0 +1,2 @@
+"accuracy","macro_precision","macro_recall","macro_f1"
+0.944444444444444,0.944444444444444,0.952380952380952,0.94522732169791

Lab 4/outputs/top_contributors_pc1.csv

@@ -0,0 +1,6 @@
+"Variable","PC1"
+"Flavanoids",0.430570697054093
+"Total_phenols",0.388556731445086
+"OD280_OD315",0.379238757892512
+"Proanthocyanins",0.318149910146199
+"Nonflavanoid_phenols",-0.292569052362651

Lab 4/outputs/top_contributors_pc2.csv

@@ -0,0 +1,6 @@
+"Variable","PC2"
+"Color_intensity",-0.504116493512561
+"Alcohol",-0.480328824227057
+"Ash",-0.369020648548877
+"Proline",-0.3555672525193
+"Hue",0.300324646690879

Lab 4/wine.data

@@ -0,0 +1,178 @@
+1,14.23,1.71,2.43,15.6,127,2.8,3.06,.28,2.29,5.64,1.04,3.92,1065
+1,13.2,1.78,2.14,11.2,100,2.65,2.76,.26,1.28,4.38,1.05,3.4,1050
+1,13.16,2.36,2.67,18.6,101,2.8,3.24,.3,2.81,5.68,1.03,3.17,1185
+1,14.37,1.95,2.5,16.8,113,3.85,3.49,.24,2.18,7.8,.86,3.45,1480
+1,13.24,2.59,2.87,21,118,2.8,2.69,.39,1.82,4.32,1.04,2.93,735
+1,14.2,1.76,2.45,15.2,112,3.27,3.39,.34,1.97,6.75,1.05,2.85,1450
+1,14.39,1.87,2.45,14.6,96,2.5,2.52,.3,1.98,5.25,1.02,3.58,1290
+1,14.06,2.15,2.61,17.6,121,2.6,2.51,.31,1.25,5.05,1.06,3.58,1295
+1,14.83,1.64,2.17,14,97,2.8,2.98,.29,1.98,5.2,1.08,2.85,1045
+1,13.86,1.35,2.27,16,98,2.98,3.15,.22,1.85,7.22,1.01,3.55,1045
+1,14.1,2.16,2.3,18,105,2.95,3.32,.22,2.38,5.75,1.25,3.17,1510
+1,14.12,1.48,2.32,16.8,95,2.2,2.43,.26,1.57,5,1.17,2.82,1280
+1,13.75,1.73,2.41,16,89,2.6,2.76,.29,1.81,5.6,1.15,2.9,1320
+1,14.75,1.73,2.39,11.4,91,3.1,3.69,.43,2.81,5.4,1.25,2.73,1150
+1,14.38,1.87,2.38,12,102,3.3,3.64,.29,2.96,7.5,1.2,3,1547
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+1,14.3,1.92,2.72,20,120,2.8,3.14,.33,1.97,6.2,1.07,2.65,1280
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Lab 4/wine.names

@@ -0,0 +1,100 @@
+1. Title of Database: Wine recognition data
+	Updated Sept 21, 1998 by C.Blake : Added attribute information
+
+2. Sources:
+   (a) Forina, M. et al, PARVUS - An Extendible Package for Data
+       Exploration, Classification and Correlation. Institute of Pharmaceutical
+       and Food Analysis and Technologies, Via Brigata Salerno, 
+       16147 Genoa, Italy.
+
+   (b) Stefan Aeberhard, email: stefan@coral.cs.jcu.edu.au
+   (c) July 1991
+3. Past Usage:
+
+   (1)
+   S. Aeberhard, D. Coomans and O. de Vel,
+   Comparison of Classifiers in High Dimensional Settings,
+   Tech. Rep. no. 92-02, (1992), Dept. of Computer Science and Dept. of
+   Mathematics and Statistics, James Cook University of North Queensland.
+   (Also submitted to Technometrics).
+
+   The data was used with many others for comparing various 
+   classifiers. The classes are separable, though only RDA 
+   has achieved 100% correct classification.
+   (RDA : 100%, QDA 99.4%, LDA 98.9%, 1NN 96.1% (z-transformed data))
+   (All results using the leave-one-out technique)
+
+   In a classification context, this is a well posed problem 
+   with "well behaved" class structures. A good data set 
+   for first testing of a new classifier, but not very 
+   challenging.
+
+   (2) 
+   S. Aeberhard, D. Coomans and O. de Vel,
+   "THE CLASSIFICATION PERFORMANCE OF RDA"
+   Tech. Rep. no. 92-01, (1992), Dept. of Computer Science and Dept. of
+   Mathematics and Statistics, James Cook University of North Queensland.
+   (Also submitted to Journal of Chemometrics).
+
+   Here, the data was used to illustrate the superior performance of
+   the use of a new appreciation function with RDA. 
+
+4. Relevant Information:
+
+   -- These data are the results of a chemical analysis of
+      wines grown in the same region in Italy but derived from three
+      different cultivars.
+      The analysis determined the quantities of 13 constituents
+      found in each of the three types of wines. 
+
+   -- I think that the initial data set had around 30 variables, but 
+      for some reason I only have the 13 dimensional version. 
+      I had a list of what the 30 or so variables were, but a.) 
+      I lost it, and b.), I would not know which 13 variables
+      are included in the set.
+
+   -- The attributes are (dontated by Riccardo Leardi, 
+	riclea@anchem.unige.it )
+ 	1) Alcohol
+ 	2) Malic acid
+ 	3) Ash
+	4) Alcalinity of ash  
+ 	5) Magnesium
+	6) Total phenols
+ 	7) Flavanoids
+ 	8) Nonflavanoid phenols
+ 	9) Proanthocyanins
+	10)Color intensity
+ 	11)Hue
+ 	12)OD280/OD315 of diluted wines
+ 	13)Proline            
+
+5. Number of Instances
+
+      	class 1 59
+	class 2 71
+	class 3 48
+
+6. Number of Attributes 
+	
+	13
+
+7. For Each Attribute:
+
+	All attributes are continuous
+	
+	No statistics available, but suggest to standardise
+	variables for certain uses (e.g. for us with classifiers
+	which are NOT scale invariant)
+
+	NOTE: 1st attribute is class identifier (1-3)
+
+8. Missing Attribute Values:
+
+	None
+
+9. Class Distribution: number of instances per class
+
+      	class 1 59
+	class 2 71
+	class 3 48