diff --git a/knn.R b/knn.R
index c068170..4838b28 100644
--- a/knn.R
+++ b/knn.R
@@ -2,13 +2,14 @@
 # https://www.kaggle.com/c/digit-recognizer/data
 # produce submission file with optimal knn model
 
-# Fast Nearest Neighbor Search Algorithms and Applications
-library(FNN)
-
 # load training and test datasets
 train <- read.csv("train.csv", header=TRUE)
 test <- read.csv("test.csv", header=TRUE)
 
+##########################################################
+# Fast Nearest Neighbor Search Algorithms and Applications
+library(FNN)
+
 # drop label columns for use in KNN
 trainCl <- train[, 1]
 train <- train[, -1]
diff --git a/knnPerformance_vs_kAndKernel_10kSet.pdf b/knnPerformance_vs_kAndKernel_10kSet.pdf
new file mode 100644
index 0000000..f614dc0
Binary files /dev/null and b/knnPerformance_vs_kAndKernel_10kSet.pdf differ
diff --git a/numK_10kSet_noZeroVarCols.pdf b/numK_10kSet_noZeroVarCols.pdf
new file mode 100644
index 0000000..23e7cc8
Binary files /dev/null and b/numK_10kSet_noZeroVarCols.pdf differ
diff --git a/optimizeKKNN.R b/optimizeKKNN.R
new file mode 100644
index 0000000..c83e6d8
--- /dev/null
+++ b/optimizeKKNN.R
@@ -0,0 +1,78 @@
+# Kaggle: Digit Recognizer
+# https://www.kaggle.com/c/digit-recognizer/data
+# optimize a knn model using the kknn implementation
+
+# Weighted k-Nearest Neighbors
+library(kknn)
+
+# load the training data
+rawTrainData <- read.csv("train.csv", header=TRUE)
+
+# randomly sample rows of training data
+train <- rawTrainData[sample(nrow(rawTrainData)), ]
+train <- train[1:10000,]
+
+# optimize knn for k and kernel
+# using leave-one-out cross-validation
+kMax <- 15
+kernels <- c("triangular","rectangular","gaussian")
+model_1 <- train.kknn(as.factor(label) ~ ., train, kmax=kMax, kernel=kernels)
+
+# what about removing pixels with near zero variance? not good predictors...
+library(caret)
+badCols <- nearZeroVar(train[,-1])
+print(paste("Fraction of nearZeroVar columns:", round(length(badCols)/length(train),4)))
+train <- train[, -(badCols+1)]
+model_2 <- train.kknn(as.factor(label) ~ ., train, kmax=kMax, kernel=kernels)
+
+# what about centering and scaling (standardizing)?
+# UPDATE: This gives identical results to model_2
+#train <- rawTrainData[sample(nrow(rawTrainData)), ]
+#train <- train[1:1000,]
+#label <- train[, 1]
+#centeredPixels <- apply(train[, -1], 2, scale, center=TRUE, scale=TRUE)
+#train <- data.frame(label, centeredPixels)
+#model_3 <- train.kknn(as.factor(label) ~ ., train, kmax=kMax, kernel=kernels)
+
+#######################################################################
+# plot mis-classification rate per k, per kernel, per data modification
+plot(1:nrow(model_1$MISCLASS), model_1$MISCLASS[,1], type='n', col='blue', ylim=c(0.0,0.105),
+     xlab="Number of Nearest Neighbors", ylab="Fractional Error Rate", main="kNN performance by k and kernel")
+# model_1
+for(kern in kernels) {
+    color=rainbow(length(kernels))[match(kern, kernels)]
+    points(1:nrow(model_1$MISCLASS), model_1$MISCLASS[,kern], type='p', pch=16, col=color)
+    lines(predict(loess(model_1$MISCLASS[,kern] ~ c(1:kMax))), col=color, lwd=2, lty="solid")
+}
+# model_2
+for(kern in kernels) {
+    color=rainbow(length(kernels))[match(kern, kernels)]
+    points(1:nrow(model_2$MISCLASS), model_2$MISCLASS[,kern], type='p', pch=17, col=color)
+    lines(predict(loess(model_2$MISCLASS[,kern] ~ c(1:kMax))), col=color, lwd=2, lty="dotted")
+}
+# model_3
+#for(kern in kernels) {
+#    color=rainbow(length(kernels))[match(kern, kernels)]
+#    points(1:nrow(model_3$MISCLASS), model_3$MISCLASS[,kern], type='p', pch=15, col=color)
+#    lines(predict(loess(model_3$MISCLASS[,kern] ~ c(1:kMax))), col=color, lwd=2, lty="dotted")
+#}
+
+# mark the best values of each set of models
+model_1_best <- model_1$MISCLASS[model_1$best.parameters$k, model_1$best.parameters$kernel]
+model_2_best <- model_2$MISCLASS[model_2$best.parameters$k, model_2$best.parameters$kernel]
+points(model_1$best.parameters$k, model_1_best, pch=16, col="black")
+points(model_2$best.parameters$k, model_2_best, pch=17, col="black")
+
+legend("bottomright", ncol=2, legend=c(kernels, paste(kernels,"(red. data)")),
+       col=rep(rainbow(length(kernels)),2), pch=c(rep(16,3), rep(17,3)),
+       lwd=2, lty=c(rep("solid",3), rep("dotted",3)),
+       bty="n", y.intersp=1.5, inset=0.01, cex=0.8)
+
+
+# print out the best parameters
+print(paste("Best model_1 parameters:", "kernel =", model_1$best.parameters$kernel, ", k =", model_1$best.parameters$k))
+print(model_1$MISCLASS)
+print(paste("Best model_2 parameters:", "kernel =", model_2$best.parameters$kernel, ", k =", model_2$best.parameters$k))
+print(model_2$MISCLASS)
+#print(paste("Best model_3 parameters:", "kernel =", model_3$best.parameters$kernel, ", k =", model_3$best.parameters$k))
+#print(model_3$MISCLASS)
\ No newline at end of file
diff --git a/optimizeKNN.R b/optimizeKNN.R
index 645ebaf..a847863 100644
--- a/optimizeKNN.R
+++ b/optimizeKNN.R
@@ -1,18 +1,18 @@
 # Kaggle: Digit Recognizer
 # https://www.kaggle.com/c/digit-recognizer/data
+# optimize a knn model using the FNN implementation
 
-#library(class)   # "recommended" k-Nearest Neighbour Classification: TOO SLOW
-library(FNN)    # Fast Nearest Neighbor Search Algorithms and Applications
+# Fast Nearest Neighbor Search Algorithms and Applications
+library(FNN)
 
 # load the data
-rawTrainData <- read.csv("train.csv", header=TRUE)#[1:25000,]
-#test <- read.csv("test.csv", header=TRUE)[1:1000,]
+rawTrainData <- read.csv("train.csv", header=TRUE)[1:1000,]
 
-# randomly permute row order of training dataset
-train <- rawTrainData[sample(nrow(rawTrainData)), ]
-# then split up into training and cross-validation sets
-cv <- train[(1+(0.6*nrow(train))):nrow(train), ]   # 2 needed instead of 1 to avoid overlap row?
-train <- train[1:(0.6*nrow(train)), ]
+# randomly sample rows of training data
+indices <- sample(1:nrow(rawTrainData), trunc(0.6*nrow(rawTrainData)))
+# assign training and cross-validation sets to orthogonal sub-sets
+train <- rawTrainData[indices, ]
+cv <- rawTrainData[-indices, ]
 
 # drop label columns for use in KNN
 trainCl <- train[, 1]
@@ -26,12 +26,22 @@ badCols <- nearZeroVar(train)
 print(paste("Fraction of nearZeroVar columns:", length(badCols)/length(train)))
 train <- train[, -badCols]
 cv <- cv[, -badCols]
-            
+
+# what about centering and scaling? i.e. standardizing
+trainColMeans <- apply(train, 2, mean)
+trainColSD <- apply(train, 2, sd)
+train <- apply(train, 2, scale, center=TRUE, scale=TRUE)
+#cv <- apply(cv, 2, scale, center=trainColMeans, scale=trainColSD)
+#train <- apply(train, 2, scale, center=TRUE, scale=TRUE)
+#cv <- apply(cv, 2, scale, center=TRUE, scale=TRUE)
+cv <- sweep(cv, 2, trainColMeans, FUN="-")
+cv <- sweep(cv, 2, trainColSD, FUN="/")
+
 # fit knn model to training set
 # get knn predictions for training set
 # compute fractional training error
 # for numK values of k
-numK <- 6
+numK <- 10
 trainErrs <- numeric(numK)
 for(i in 1:numK) {
     print(paste("Train:", i))