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#-------------------------------------------------------------
#
# Licensed to the Apache Software Foundation (ASF) under one
# or more contributor license agreements. See the NOTICE file
# distributed with this work for additional information
# regarding copyright ownership. The ASF licenses this file
# to you under the Apache License, Version 2.0 (the
# "License"); you may not use this file except in compliance
# with the License. You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing,
# software distributed under the License is distributed on an
# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
# KIND, either express or implied. See the License for the
# specific language governing permissions and limitations
# under the License.
#
#-------------------------------------------------------------
#
# THIS SCRIPT IMPLEMENTS CLASSIFICATION TREES WITH BOTH SCALE AND CATEGORICAL FEATURES
#
# INPUT PARAMETERS:
# ---------------------------------------------------------------------------------------------
# NAME TYPE DEFAULT MEANING
# ---------------------------------------------------------------------------------------------
# X String --- Location to read feature matrix X; note that X needs to be both recoded and dummy coded
# Y String --- Location to read label matrix Y; note that Y needs to be both recoded and dummy coded
# R String " " Location to read the matrix R which for each feature in X contains the following information
# - R[,1]: column ids
# - R[,2]: start indices
# - R[,3]: end indices
# If R is not provided by default all variables are assumed to be scale
# bins Int 20 Number of equiheight bins per scale feature to choose thresholds
# depth Int 25 Maximum depth of the learned tree
# num_leaf Int 10 Number of samples when splitting stops and a leaf node is added
# num_samples Int 3000 Number of samples at which point we switch to in-memory subtree building
# impurity String "Gini" Impurity measure: entropy or Gini (the default)
# M String --- Location to write matrix M containing the learned tree
# O String " " Location to write the training accuracy; by default is standard output
# S_map String " " Location to write the mappings from scale feature ids to global feature ids
# C_map String " " Location to write the mappings from categorical feature ids to global feature ids
# fmt String "text" The output format of the model (matrix M), such as "text" or "csv"
# ---------------------------------------------------------------------------------------------
# OUTPUT:
# Matrix M where each column corresponds to a node in the learned tree and each row contains the following information:
# M[1,j]: id of node j (in a complete binary tree)
# M[2,j]: Offset (no. of columns) to left child of j if j is an internal node, otherwise 0
# M[3,j]: Feature index of the feature (scale feature id if the feature is scale or categorical feature id if the feature is categorical)
# that node j looks at if j is an internal node, otherwise 0
# M[4,j]: Type of the feature that node j looks at if j is an internal node: 1 for scale and 2 for categorical features,
# otherwise the label that leaf node j is supposed to predict
# M[5,j]: If j is an internal node: 1 if the feature chosen for j is scale, otherwise the size of the subset of values
# stored in rows 6,7,... if j is categorical
# If j is a leaf node: number of misclassified samples reaching at node j
# M[6:,j]: If j is an internal node: Threshold the example's feature value is compared to is stored at M[6,j] if the feature chosen for j is scale,
# otherwise if the feature chosen for j is categorical rows 6,7,... depict the value subset chosen for j
# If j is a leaf node 1 if j is impure and the number of samples at j > threshold, otherwise 0
# -------------------------------------------------------------------------------------------
# HOW TO INVOKE THIS SCRIPT - EXAMPLE:
# hadoop jar SystemML.jar -f decision-tree.dml -nvargs X=INPUT_DIR/X Y=INPUT_DIR/Y R=INPUT_DIR/R M=OUTPUT_DIR/model
# bins=20 depth=25 num_leaf=10 num_samples=3000 impurity=Gini fmt=csv
# External function for binning
binning = externalFunction(Matrix[Double] A, Integer binsize, Integer numbins) return (Matrix[Double] B, Integer numbinsdef)
implemented in (classname="org.apache.sysml.udf.lib.BinningWrapper",exectype="mem")
# Default values of some parameters
fileR = ifdef ($R, " ");
fileO = ifdef ($O, " ");
fileS_map = ifdef ($S_map, " ");
fileC_map = ifdef ($C_map, " ");
fileM = $M;
num_bins = ifdef($bins, 20);
depth = ifdef($depth, 25);
num_leaf = ifdef($num_leaf, 10);
threshold = ifdef ($num_samples, 3000);
imp = ifdef($impurity, "Gini");
fmtO = ifdef($fmt, "text");
X = read($X);
Y_bin = read($Y);
num_records = nrow (X);
num_classes = ncol (Y_bin);
# check if there is only one class label
Y_bin_sum = sum (colSums (Y_bin) == num_records);
if (Y_bin_sum == 1) {
stop ("Y contains only one class label. No model will be learned!");
} else if (Y_bin_sum > 1) {
stop ("Y is not properly dummy coded. Multiple columns of Y contain only ones!")
}
# split data into X_scale and X_cat
if (fileR != " ") {
R = read (fileR);
R = order (target = R, by = 2); # sort by start indices
dummy_coded = (R[,2] != R[,3]);
R_scale = removeEmpty (target = R[,2:3] * (1 - dummy_coded), margin = "rows");
R_cat = removeEmpty (target = R[,2:3] * dummy_coded, margin = "rows");
if (fileS_map != " ") {
scale_feature_mapping = removeEmpty (target = (1 - dummy_coded) * seq (1, nrow (R)), margin = "rows");
write (scale_feature_mapping, fileS_map, format = fmtO);
}
if (fileC_map != " ") {
cat_feature_mapping = removeEmpty (target = dummy_coded * seq (1, nrow (R)), margin = "rows");
write (cat_feature_mapping, fileC_map, format = fmtO);
}
sum_dummy = sum (dummy_coded);
if (sum_dummy == nrow (R)) { # all features categorical
print ("All features categorical");
num_cat_features = nrow (R_cat);
num_scale_features = 0;
X_cat = X;
distinct_values = t (R_cat[,2] - R_cat[,1] + 1);
distinct_values_max = max (distinct_values);
distinct_values_offset = cumsum (t (distinct_values));
distinct_values_overall = sum (distinct_values);
} else if (sum_dummy == 0) { # all features scale
print ("All features scale");
num_scale_features = ncol (X);
num_cat_features = 0;
X_scale = X;
distinct_values_max = 1;
} else { # some features scale some features categorical
num_cat_features = nrow (R_cat);
num_scale_features = nrow (R_scale);
distinct_values = t (R_cat[,2] - R_cat[,1] + 1);
distinct_values_max = max (distinct_values);
distinct_values_offset = cumsum (t (distinct_values));
distinct_values_overall = sum (distinct_values);
W = matrix (1, rows = num_cat_features, cols = 1) %*% matrix ("1 -1", rows = 1, cols = 2);
W = matrix (W, rows = 2 * num_cat_features, cols = 1);
if (as.scalar (R_cat[num_cat_features, 2]) == ncol (X)) {
W[2 * num_cat_features,] = 0;
}
last = (R_cat[,2] != ncol (X));
R_cat1 = (R_cat[,2] + 1) * last;
R_cat[,2] = (R_cat[,2] * (1 - last)) + R_cat1;
R_cat_vec = matrix (R_cat, rows = 2 * num_cat_features, cols = 1);
col_tab = table (R_cat_vec, 1, W, ncol (X), 1);
col_ind = cumsum (col_tab);
col_ind_cat = removeEmpty (target = col_ind * seq (1, ncol (X)), margin = "rows");
col_ind_scale = removeEmpty (target = (1 - col_ind) * seq (1, ncol (X)), margin = "rows");
X_cat = X %*% table (col_ind_cat, seq (1, nrow (col_ind_cat)), ncol (X), nrow (col_ind_cat));
X_scale = X %*% table (col_ind_scale, seq (1, nrow (col_ind_scale)), ncol (X), nrow (col_ind_scale));
}
} else { # only scale features exist
print ("All features scale");
num_scale_features = ncol (X);
num_cat_features = 0;
X_scale = X;
distinct_values_max = 1;
}
if (num_scale_features > 0) {
print ("COMPUTING BINNING...");
bin_size = max (as.integer (num_records / num_bins), 1);
count_thresholds = matrix (0, rows = 1, cols = num_scale_features)
thresholds = matrix (0, rows = num_bins + 1, cols = num_scale_features)
parfor(i1 in 1:num_scale_features) {
col = order (target = X_scale[,i1], by = 1, decreasing = FALSE);
[col_bins, num_bins_defined] = binning (col, bin_size, num_bins);
count_thresholds[,i1] = num_bins_defined;
thresholds[,i1] = col_bins;
}
print ("PREPROCESSING SCALE FEATURE MATRIX...");
min_num_bins = min (count_thresholds);
max_num_bins = max (count_thresholds);
total_num_bins = sum (count_thresholds);
cum_count_thresholds = t (cumsum (t (count_thresholds)));
X_scale_ext = matrix (0, rows = num_records, cols = total_num_bins);
parfor (i2 in 1:num_scale_features, check = 0) {
Xi2 = X_scale[,i2];
count_threshold = as.scalar (count_thresholds[,i2]);
offset_feature = 1;
if (i2 > 1) {
offset_feature = offset_feature + as.integer (as.scalar (cum_count_thresholds[, (i2 - 1)]));
}
ti2 = t(thresholds[1:count_threshold, i2]);
X_scale_ext[,offset_feature:(offset_feature + count_threshold - 1)] = outer (Xi2, ti2, "<");
}
}
##### INITIALIZATION
L = matrix (1, rows = num_records, cols = 1); # last visited node id for each training sample
# ---- model ----
# leaf nodes
# NC_large[,1]: node id
# NC_large[,2]: class label
# NC_large[,3]: no. of misclassified samples
# NC_large[,4]: 1 if special leaf (impure and # samples at that leaf > threshold) or 0 otherwise
NC_large = matrix (0, rows = 4, cols = 1);
NC_small = matrix (0, rows = 4, cols = 1); # same schema as NC_large
# internal nodes
# Q_large[,1]: node id
Q_large = matrix (1, rows = 1, cols = 1);
Q_small = matrix (0, rows = 1, cols = 1); # same schema as Q_large
# F_large[,1]: feature
# F_large[,2]: type
# F_large[,3]: offset
F_large = matrix (0, rows = 3, cols = 1);
F_small = matrix (0, rows = 3, cols = 1); # same schema as F_large
S_large = matrix (0, rows = 1, cols = 1); # split points for LARGE internal nodes
S_small = matrix (0, rows = 1, cols = 1); # split points for SMALL internal nodes
# temp matrix for tree traversal
# first row: ids of SMALL internal nodes
# second row: no. of samples for these nodes
cur_nodes_large = matrix (1, rows = 1, cols = 1);
num_cur_nodes_large = 1;
num_cur_nodes_small = 0;
level = 0;
while ((num_cur_nodes_large + num_cur_nodes_small) > 0 & level < depth) {
level = level + 1;
print (" --- start level " + level + " --- ");
##### PREPARE MODEL
if (num_cur_nodes_large > 0) { # LARGE nodes to process
cur_Q_large = matrix (0, rows = 1, cols = 2 * num_cur_nodes_large);
cur_NC_large = matrix (0, rows = 4, cols = 2 * num_cur_nodes_large);
cur_F_large = matrix (0, rows = 3, cols = num_cur_nodes_large);
cur_S_large = matrix (0, rows = 1, cols = num_cur_nodes_large * distinct_values_max);
cur_nodes_small = matrix (0, rows = 2, cols = 2 * num_cur_nodes_large);
}
##### LOOP OVER LARGE NODES...
parfor (i6 in 1:num_cur_nodes_large, check = 0) {
cur_node = as.scalar (cur_nodes_large[,i6]);
# --- find best split ---
# samples that reach cur_node
Ix = (L[,1] == cur_node);
cur_Y_bin = Y_bin * Ix;
label_counts_overall = colSums (cur_Y_bin);
label_sum_overall = sum (label_counts_overall);
label_dist_overall = label_counts_overall / label_sum_overall;
if (imp == "entropy") {
label_dist_zero = (label_dist_overall == 0);
cur_impurity = - sum (label_dist_overall * log (label_dist_overall + label_dist_zero)); # / log (2); # impurity before
} else { # imp == "Gini"
cur_impurity = sum (label_dist_overall * (1 - label_dist_overall)); # impurity before
}
best_scale_gain = 0;
best_cat_gain = 0;
if (num_scale_features > 0) {
# main operation
label_counts_left_scale = t (t (cur_Y_bin) %*% X_scale_ext);
# compute left and right label distribution
label_sum_left = rowSums (label_counts_left_scale);
label_dist_left = label_counts_left_scale / label_sum_left;
if (imp == "entropy") {
label_dist_left = replace (target = label_dist_left, pattern = 0, replacement = 1);
log_label_dist_left = log (label_dist_left); # / log (2)
impurity_left_scale = - rowSums (label_dist_left * log_label_dist_left);
} else { # imp == "Gini"
impurity_left_scale = rowSums (label_dist_left * (1 - label_dist_left));
}
#
label_counts_right_scale = - label_counts_left_scale + label_counts_overall;
label_sum_right = rowSums (label_counts_right_scale);
label_dist_right = label_counts_right_scale / label_sum_right;
if (imp == "entropy") {
label_dist_right = replace (target = label_dist_right, pattern = 0, replacement = 1);
log_label_dist_right = log (label_dist_right); # / log (2)
impurity_right_scale = - rowSums (label_dist_right * log_label_dist_right);
} else { # imp == "Gini"
impurity_right_scale = rowSums (label_dist_right * (1 - label_dist_right));
}
I_gain_scale = cur_impurity - ( ( label_sum_left / label_sum_overall ) * impurity_left_scale + ( label_sum_right / label_sum_overall ) * impurity_right_scale);
I_gain_scale = replace (target = I_gain_scale, pattern = "NaN", replacement = 0);
# determine best feature to split on and the split value
best_scale_gain = max (I_gain_scale);
max_I_gain_ind_scale = as.scalar (rowIndexMax (t (I_gain_scale)));
p = (cum_count_thresholds < max_I_gain_ind_scale);
sum_cum_count_thresholds = sum (p);
best_scale_feature = sum_cum_count_thresholds + 1;
best_scale_split = max_I_gain_ind_scale;
if (best_scale_feature != 1) {
best_scale_split = best_scale_split - as.scalar(cum_count_thresholds[,(best_scale_feature - 1)]);
}
}
if (num_cat_features > 0){
# initialization
split_values_bin = matrix (0, rows = 1, cols = distinct_values_overall);
split_values = split_values_bin;
split_values_offset = matrix (0, rows = 1, cols = num_cat_features);
I_gains = split_values_offset;
impurities_left = split_values_offset;
impurities_right = split_values_offset;
best_label_counts_left = matrix (0, rows = num_cat_features, cols = num_classes);
best_label_counts_right = matrix (0, rows = num_cat_features, cols = num_classes);
# main operation
label_counts = t (t (cur_Y_bin) %*% X_cat);
parfor (i9 in 1:num_cat_features, check = 0){
start_ind = 1;
if (i9 > 1) {
start_ind = start_ind + as.scalar (distinct_values_offset[(i9 - 1),]);
}
offset = as.scalar (distinct_values[1,i9]);
cur_label_counts = label_counts[start_ind:(start_ind + offset - 1),];
label_sum = rowSums (cur_label_counts);
label_dist = cur_label_counts / label_sum;
if (imp == "entropy") {
label_dist = replace (target = label_dist, pattern = 0, replacement = 1);
log_label_dist = log (label_dist); # / log(2)
impurity = - rowSums (label_dist * log_label_dist);
impurity = replace (target = impurity, pattern = "NaN", replacement = 1/0);
} else { # imp == "Gini"
impurity = rowSums (label_dist * (1 - label_dist));
}
# sort cur feature by impurity
cur_distinct_values = seq (1, nrow (cur_label_counts));
cur_distinct_values_impurity = cbind (cur_distinct_values, impurity);
cur_feature_sorted = order (target = cur_distinct_values_impurity, by = 2, decreasing = FALSE);
P = table (cur_distinct_values, cur_feature_sorted); # permutation matrix
label_counts_sorted = P %*% cur_label_counts;
# compute left and right label distribution
label_counts_left = cumsum (label_counts_sorted);
label_sum_left = rowSums (label_counts_left);
label_dist_left = label_counts_left / label_sum_left;
label_dist_left = replace (target = label_dist_left, pattern = "NaN", replacement = 1);
if (imp == "entropy") {
label_dist_left = replace (target = label_dist_left, pattern = 0, replacement = 1);
log_label_dist_left = log (label_dist_left); # / log(2)
impurity_left = - rowSums (label_dist_left * log_label_dist_left);
} else { # imp == "Gini"
impurity_left = rowSums (label_dist_left * (1 - label_dist_left));
}
#
label_counts_right = - label_counts_left + label_counts_overall;
label_sum_right = rowSums (label_counts_right);
label_dist_right = label_counts_right / label_sum_right;
label_dist_right = replace (target = label_dist_right, pattern = "NaN", replacement = 1);
if (imp == "entropy") {
label_dist_right = replace (target = label_dist_right, pattern = 0, replacement = 1);
log_label_dist_right = log (label_dist_right); # / log (2)
impurity_right = - rowSums (label_dist_right * log_label_dist_right);
} else { # imp == "Gini"
impurity_right = rowSums (label_dist_right * (1 - label_dist_right));
}
I_gain = cur_impurity - ( ( label_sum_left / label_sum_overall ) * impurity_left + ( label_sum_right / label_sum_overall ) * impurity_right);
Ix_label_sum_left_zero = (label_sum_left == 0);
Ix_label_sum_right_zero = (label_sum_right == 0);
Ix_label_sum_zero = Ix_label_sum_left_zero * Ix_label_sum_right_zero;
I_gain = I_gain * (1 - Ix_label_sum_zero);
I_gain[nrow (I_gain),] = 0; # last entry invalid
max_I_gain_ind = as.scalar (rowIndexMax (t (I_gain)));
split_values[1, start_ind:(start_ind + max_I_gain_ind - 1)] = t (cur_feature_sorted[1:max_I_gain_ind,1]);
for (i10 in 1:max_I_gain_ind) {
ind = as.scalar (cur_feature_sorted[i10,1]);
if (ind == 1) {
split_values_bin[1,start_ind] = 1.0;
} else {
split_values_bin[1,(start_ind + ind - 1)] = 1.0;
}
}
split_values_offset[1,i9] = max_I_gain_ind;
I_gains[1,i9] = max (I_gain);
impurities_left[1,i9] = as.scalar (impurity_left[max_I_gain_ind,]);
impurities_right[1,i9] = as.scalar (impurity_right[max_I_gain_ind,]);
best_label_counts_left[i9,] = label_counts_left[max_I_gain_ind,];
best_label_counts_right[i9,] = label_counts_right[max_I_gain_ind,];
}
# determine best feature to split on and the split values
best_cat_feature = as.scalar (rowIndexMax (I_gains));
best_cat_gain = max (I_gains);
start_ind = 1;
if (best_cat_feature > 1) {
start_ind = start_ind + as.scalar (distinct_values_offset[(best_cat_feature - 1),]);
}
offset = as.scalar (distinct_values[1,best_cat_feature]);
best_split_values_bin = split_values_bin[1, start_ind:(start_ind + offset - 1)];
}
# compare best scale feature to best cat. feature and pick the best one
if (num_scale_features > 0 & best_scale_gain >= best_cat_gain & best_scale_gain > 0) {
# --- update model ---
cur_F_large[1,i6] = best_scale_feature;
cur_F_large[2,i6] = 1;
cur_F_large[3,i6] = 1;
cur_S_large[1,(i6 - 1) * distinct_values_max + 1] = thresholds[best_scale_split, best_scale_feature];
left_child = 2 * (cur_node - 1) + 1 + 1;
right_child = 2 * (cur_node - 1) + 2 + 1;
# samples going to the left subtree
Ix_left = X_scale_ext[, max_I_gain_ind_scale];
Ix_left = Ix * Ix_left;
Ix_right = Ix * (1 - Ix_left);
L[,1] = L[,1] * (1 - Ix_left) + (Ix_left * left_child);
L[,1] = L[,1] * (1 - Ix_right) + (Ix_right * right_child);
left_child_size = sum (Ix_left);
right_child_size = sum (Ix_right);
# check if left or right child is a leaf
left_pure = FALSE;
right_pure = FALSE;
cur_impurity_left = as.scalar(impurity_left_scale[max_I_gain_ind_scale,]);
cur_impurity_right = as.scalar(impurity_right_scale[max_I_gain_ind_scale,]);
if ( (left_child_size <= num_leaf | cur_impurity_left == 0 | (level == depth)) &
(right_child_size <= num_leaf | cur_impurity_right == 0 | (level == depth)) |
(left_child_size <= threshold & right_child_size <= threshold & (level == depth)) ) { # both left and right nodes are leaf
cur_label_counts_left = label_counts_left_scale[max_I_gain_ind_scale,];
cur_NC_large[1,(2 * (i6 - 1) + 1)] = left_child;
cur_NC_large[2,(2 * (i6 - 1) + 1)] = as.scalar( rowIndexMax (cur_label_counts_left)); # leaf class label
left_pure = TRUE;
cur_NC_large[3,(2 * (i6 - 1) + 1)] = left_child_size - max (cur_label_counts_left); # no. of misclassified samples
cur_label_counts_right = label_counts_overall - cur_label_counts_left;
cur_NC_large[1,(2 * i6)] = right_child;
cur_NC_large[2,(2 * i6)] = as.scalar( rowIndexMax (cur_label_counts_right)); # leaf class label
right_pure = TRUE;
cur_NC_large[3,(2 * i6)] = right_child_size - max (cur_label_counts_right); # no. of misclassified samples
} else if (left_child_size <= num_leaf | cur_impurity_left == 0 | (level == depth) |
(left_child_size <= threshold & (level == depth))) {
cur_label_counts_left = label_counts_left_scale[max_I_gain_ind_scale,];
cur_NC_large[1,(2 * (i6 - 1) + 1)] = left_child;
cur_NC_large[2,(2 * (i6 - 1) + 1)] = as.scalar( rowIndexMax (cur_label_counts_left)); # leaf class label
left_pure = TRUE;
cur_NC_large[3,(2 * (i6 - 1) + 1)] = left_child_size - max (cur_label_counts_left); # no. of misclassified samples
} else if (right_child_size <= num_leaf | cur_impurity_right == 0 | (level == depth) |
(right_child_size <= threshold & (level == depth))) {
cur_label_counts_right = label_counts_right_scale[max_I_gain_ind_scale,];
cur_NC_large[1,(2 * i6)] = right_child;
cur_NC_large[2,(2 * i6)] = as.scalar( rowIndexMax (cur_label_counts_right)); # leaf class label
right_pure = TRUE;
cur_NC_large[3,(2 * i6)] = right_child_size - max (cur_label_counts_right); # no. of misclassified samples
}
} else if (num_cat_features > 0 & best_cat_gain > 0) {
# --- update model ---
cur_F_large[1,i6] = best_cat_feature;
offset_nonzero = as.scalar (split_values_offset[1,best_cat_feature]);
S_start_ind = (i6 - 1) * distinct_values_max + 1;
cur_S_large[1,S_start_ind:(S_start_ind + offset_nonzero - 1)] = split_values[1,start_ind:(start_ind + offset_nonzero - 1)];
cur_F_large[3,i6] = offset_nonzero;
cur_F_large[2,i6] = 2;
left_child = 2 * (cur_node - 1) + 1 + 1;
right_child = 2 * (cur_node - 1) + 2 + 1;
# samples going to the left subtree
Ix_left = rowSums (X_cat[,start_ind:(start_ind + offset - 1)] * best_split_values_bin);
Ix_left = (Ix_left >= 1);
Ix_left = Ix * Ix_left;
Ix_right = Ix * (1 - Ix_left);
L[,1] = L[,1] * (1 - Ix_left) + (Ix_left * left_child);
L[,1] = L[,1] * (1 - Ix_right) + (Ix_right * right_child);
left_child_size = sum (Ix_left);
right_child_size = sum (Ix_right);
# check if left or right child is a leaf
left_pure = FALSE;
right_pure = FALSE;
cur_impurity_left = as.scalar(impurities_left[,best_cat_feature]);
cur_impurity_right = as.scalar(impurities_right[,best_cat_feature]);
if ( (left_child_size <= num_leaf | cur_impurity_left == 0 | (level == depth)) &
(right_child_size <= num_leaf | cur_impurity_right == 0 | (level == depth)) |
(left_child_size <= threshold & right_child_size <= threshold & (level == depth)) ) { # both left and right nodes are leaf
cur_label_counts_left = best_label_counts_left[best_cat_feature,];
cur_NC_large[1,(2 * (i6 - 1) + 1)] = left_child;
cur_NC_large[2,(2 * (i6 - 1) + 1)] = as.scalar( rowIndexMax (cur_label_counts_left)); # leaf class label
left_pure = TRUE;
cur_NC_large[3,(2 * (i6 - 1) + 1)] = left_child_size - max (cur_label_counts_left); # no. of misclassified samples
cur_label_counts_right = label_counts_overall - cur_label_counts_left;
cur_NC_large[1,(2 * i6)] = right_child;
cur_NC_large[2,(2 * i6)] = as.scalar( rowIndexMax (cur_label_counts_right)); # leaf class label
right_pure = TRUE;
cur_NC_large[3,(2 * i6)] = right_child_size - max (cur_label_counts_right); # no. of misclassified samples
} else if (left_child_size <= num_leaf | cur_impurity_left == 0 | (level == depth) |
(left_child_size <= threshold & (level == depth))) {
cur_label_counts_left = best_label_counts_left[best_cat_feature,];
cur_NC_large[1,(2 * (i6 - 1) + 1)] = left_child;
cur_NC_large[2,(2 * (i6 - 1) + 1)] = as.scalar( rowIndexMax (cur_label_counts_left)); # leaf class label
left_pure = TRUE;
cur_NC_large[3,(2 * (i6 - 1) + 1)] = left_child_size - max (cur_label_counts_left); # no. of misclassified samples
} else if (right_child_size <= num_leaf | cur_impurity_right == 0 | (level == depth) |
(right_child_size <= threshold & (level == depth))) {
cur_label_counts_right = best_label_counts_right[best_cat_feature,];
cur_NC_large[1,(2 * i6)] = right_child;
cur_NC_large[2,(2 * i6)] = as.scalar( rowIndexMax (cur_label_counts_right)); # leaf class label
right_pure = TRUE;
cur_NC_large[3,(2 * i6)] = right_child_size - max (cur_label_counts_right); # no. of misclassified samples
}
} else {
print ("NUMBER OF SAMPLES AT NODE " + cur_node + " CANNOT BE REDUCED TO MATCH " + num_leaf + ". THIS NODE IS DECLARED AS LEAF!");
right_pure = TRUE;
left_pure = TRUE;
cur_NC_large[1,(2 * (i6 - 1) + 1)] = cur_node;
class_label = as.scalar (rowIndexMax (label_counts_overall));
cur_NC_large[2,(2 * (i6 - 1) + 1)] = class_label;
cur_NC_large[3,(2 * (i6 - 1) + 1)] = label_sum_overall - max (label_counts_overall);
cur_NC_large[4,(2 * (i6 - 1) + 1)] = 1; # special leaf
}
# add nodes to Q
if (!left_pure) {
if (left_child_size > threshold) {
cur_Q_large[1,(2 * (i6 - 1)+ 1)] = left_child;
} else {
# first row: ids of SMALL internal nodes, second row: no. of samples for these nodes
cur_nodes_small[1,(2 * (i6 - 1)+ 1)] = left_child;
cur_nodes_small[2,(2 * (i6 - 1)+ 1)] = left_child_size;
}
}
if (!right_pure) {
if (right_child_size > threshold) {
cur_Q_large[1,(2 * i6)] = right_child;
} else{
# first row: ids of SMALL internal nodes, second row: no. of samples for these nodes
cur_nodes_small[1,(2 * i6)] = right_child;
cur_nodes_small[2,(2 * i6)] = right_child_size;
}
}
}
##### PREPARE MODEL FOR LARGE NODES
if (num_cur_nodes_large > 0) {
cur_Q_large = removeEmpty (target = cur_Q_large, margin = "cols");
if (as.scalar (cur_Q_large[1,1]) != 0) Q_large = cbind (Q_large, cur_Q_large);
cur_NC_large = removeEmpty (target = cur_NC_large, margin = "cols");
if (as.scalar (cur_NC_large[1,1]) != 0) NC_large = cbind (NC_large, cur_NC_large);
cur_F_large = removeEmpty (target = cur_F_large, margin = "cols");
if (as.scalar (cur_F_large[1,1]) != 0) F_large = cbind (F_large, cur_F_large);
cur_S_large = removeEmpty (target = cur_S_large, margin = "cols");
if (as.scalar (cur_S_large[1,1]) != 0) S_large = cbind (S_large, cur_S_large);
num_cur_nodes_large_pre = 2 * num_cur_nodes_large;
if (as.scalar (cur_Q_large[1,1]) == 0) {
num_cur_nodes_large = 0;
} else {
cur_nodes_large = cur_Q_large;
num_cur_nodes_large = ncol (cur_Q_large);
}
}
##### PREPARE MODEL FOR SMALL NODES
cur_nodes_small_nonzero = removeEmpty (target = cur_nodes_small, margin = "cols");
if (as.scalar (cur_nodes_small_nonzero[1,1]) != 0) { # if SMALL nodes exist
num_cur_nodes_small = ncol (cur_nodes_small_nonzero);
}
if (num_cur_nodes_small > 0) { # SMALL nodes to process
reserve_len = sum (2 ^ (ceil (log (cur_nodes_small_nonzero[2,]) / log (2)))) + num_cur_nodes_small;
cur_Q_small = matrix (0, rows = 1, cols = reserve_len);
cur_NC_small = matrix (0, rows = 4, cols = reserve_len);
cur_F_small = matrix (0, rows = 3, cols = reserve_len);
cur_S_small = matrix (0, rows = 1, cols = reserve_len * distinct_values_max); # split values of the best feature
}
##### LOOP OVER SMALL NODES...
parfor (i7 in 1:num_cur_nodes_small, check = 0) {
cur_node_small = as.scalar (cur_nodes_small_nonzero[1,i7]);
# build dataset for SMALL node
Ix = (L[,1] == cur_node_small);
if (num_scale_features > 0) {
X_scale_ext_small = removeEmpty (target = X_scale_ext, margin = "rows", select = Ix);
}
if (num_cat_features > 0) {
X_cat_small = removeEmpty (target = X_cat, margin = "rows", select = Ix);
}
L_small = removeEmpty (target = L * Ix, margin = "rows");
Y_bin_small = removeEmpty (target = Y_bin * Ix, margin = "rows");
# compute offset
start_ind_global = 1;
start_ind_S_global = 1;
if (i7 > 1) {
offsets = cumsum (t (2 ^ ceil (log (cur_nodes_small_nonzero[2,]) / log (2))));
start_ind_global = start_ind_global + as.scalar (offsets[(i7 - 1),]);
start_ind_S_global = start_ind_S_global + (as.scalar (offsets[(i7 - 1),]) * distinct_values_max);
}
Q = matrix (cur_node_small, rows = 1, cols = 1);
NC = matrix (0, rows = 4, cols = 1);
F = matrix (0, rows = 3, cols = 1);
S = matrix (0, rows = 1, cols = 1);
cur_nodes_ = matrix (cur_node_small, rows = 1, cols = ncol(cur_Q_small));
num_cur_nodes = 1;
level_ = level;
while (num_cur_nodes > 0 & level_ < depth) {
level_ = level_ + 1;
cur_Q = matrix (0, rows = 1, cols = 2 * num_cur_nodes);
cur_NC = matrix (0, rows = 4, cols = 2 * num_cur_nodes);
cur_F = matrix (0, rows = 3, cols = num_cur_nodes);
cur_S = matrix (0, rows = 1, cols = num_cur_nodes * distinct_values_max);
parfor (i8 in 1:num_cur_nodes, check = 0) {
cur_node = as.scalar (cur_nodes_[,i8]);
# --- find best split ---
# samples that reach cur_node
Ix = (L_small[,1] == cur_node);
cur_Y_bin = Y_bin_small * Ix;
label_counts_overall = colSums (cur_Y_bin);
label_sum_overall = sum (label_counts_overall);
label_dist_overall = label_counts_overall / label_sum_overall;
if (imp == "entropy") {
label_dist_zero = (label_dist_overall == 0);
cur_impurity = - sum (label_dist_overall * log (label_dist_overall + label_dist_zero));
} else { # imp == "Gini"
cur_impurity = sum (label_dist_overall * (1 - label_dist_overall));
}
best_scale_gain = 0;
best_cat_gain = 0;
if (num_scale_features > 0) {
# main operation
label_counts_left_scale = t (t (cur_Y_bin) %*% X_scale_ext_small);
# compute left and right label distribution
label_sum_left = rowSums (label_counts_left_scale);
label_dist_left = label_counts_left_scale / label_sum_left;
if (imp == "entropy") {
label_dist_left = replace (target = label_dist_left, pattern = 0, replacement = 1);
log_label_dist_left = log (label_dist_left); # / log (2)
impurity_left_scale = - rowSums (label_dist_left * log_label_dist_left);
} else { # imp == "Gini"
impurity_left_scale = rowSums (label_dist_left * (1 - label_dist_left));
}
#
label_counts_right_scale = - label_counts_left_scale + label_counts_overall;
label_sum_right = rowSums (label_counts_right_scale);
label_dist_right = label_counts_right_scale / label_sum_right;
if (imp == "entropy") {
label_dist_right = replace (target = label_dist_right, pattern = 0, replacement = 1);
log_label_dist_right = log (label_dist_right); # log (2)
impurity_right_scale = - rowSums (label_dist_right * log_label_dist_right);
} else { # imp == "Gini"
impurity_right_scale = rowSums (label_dist_right * (1 - label_dist_right));
}
I_gain_scale = cur_impurity - ( ( label_sum_left / label_sum_overall ) * impurity_left_scale + ( label_sum_right / label_sum_overall ) * impurity_right_scale); # I_gain -> I_gain_scale
I_gain_scale = replace (target = I_gain_scale, pattern = "NaN", replacement = 0);
# determine best feature to split on and the split value
best_scale_gain = max (I_gain_scale);
max_I_gain_ind_scale = as.scalar (rowIndexMax (t (I_gain_scale)));
p = (cum_count_thresholds < max_I_gain_ind_scale);
sum_cum_count_thresholds = sum (p);
best_scale_feature = sum_cum_count_thresholds + 1;
best_scale_split = max_I_gain_ind_scale;
if (best_scale_feature != 1) {
best_scale_split = best_scale_split - as.scalar(cum_count_thresholds[,(best_scale_feature - 1)]);
}
}
if (num_cat_features > 0){
# initialization
split_values_bin = matrix (0, rows = 1, cols = distinct_values_overall);
split_values = split_values_bin;
split_values_offset = matrix (0, rows = 1, cols = num_cat_features);
I_gains = split_values_offset;
impurities_left = split_values_offset;
impurities_right = split_values_offset;
best_label_counts_left = matrix (0, rows = num_cat_features, cols = num_classes);
best_label_counts_right = matrix (0, rows = num_cat_features, cols = num_classes);
# main operation
label_counts = t (t (cur_Y_bin) %*% X_cat_small);
parfor (i9 in 1:num_cat_features, check = 0){
start_ind = 1;
if (i9 > 1) {
start_ind = start_ind + as.scalar (distinct_values_offset[(i9 - 1),]);
}
offset = as.scalar (distinct_values[1,i9]);
cur_label_counts = label_counts[start_ind:(start_ind + offset - 1),];
label_sum = rowSums (cur_label_counts);
label_dist = cur_label_counts / label_sum;
if (imp == "entropy") {
label_dist = replace (target = label_dist, pattern = 0, replacement = 1);
log_label_dist = log (label_dist); # / log(2)
impurity = - rowSums (label_dist * log_label_dist);
impurity = replace (target = impurity, pattern = "NaN", replacement = 1/0);
} else { # imp == "Gini"
impurity = rowSums (label_dist * (1 - label_dist));
}
# sort cur feature by impurity
cur_distinct_values = seq (1, nrow (cur_label_counts));
cur_distinct_values_impurity = cbind (cur_distinct_values, impurity);
cur_feature_sorted = order (target = cur_distinct_values_impurity, by = 2, decreasing = FALSE);
P = table (cur_distinct_values, cur_feature_sorted); # permutation matrix
label_counts_sorted = P %*% cur_label_counts;
# compute left and right label distribution
label_counts_left = cumsum (label_counts_sorted);
label_sum_left = rowSums (label_counts_left);
label_dist_left = label_counts_left / label_sum_left;
label_dist_left = replace (target = label_dist_left, pattern = "NaN", replacement = 1);
if (imp == "entropy") {
label_dist_left = replace (target = label_dist_left, pattern = 0, replacement = 1);
log_label_dist_left = log (label_dist_left); # / log(2)
impurity_left = - rowSums (label_dist_left * log_label_dist_left);
} else { # imp == "Gini"
impurity_left = rowSums (label_dist_left * (1 - label_dist_left));
}
#
label_counts_right = - label_counts_left + label_counts_overall;
label_sum_right = rowSums (label_counts_right);
label_dist_right = label_counts_right / label_sum_right;
label_dist_right = replace (target = label_dist_right, pattern = "NaN", replacement = 1);
if (imp == "entropy") {
label_dist_right = replace (target = label_dist_right, pattern = 0, replacement = 1);
log_label_dist_right = log (label_dist_right); # / log (2)
impurity_right = - rowSums (label_dist_right * log_label_dist_right);
} else { # imp == "Gini"
impurity_right = rowSums (label_dist_right * (1 - label_dist_right));
}
I_gain = cur_impurity - ( ( label_sum_left / label_sum_overall ) * impurity_left + ( label_sum_right / label_sum_overall ) * impurity_right);
Ix_label_sum_left_zero = (label_sum_left == 0);
Ix_label_sum_right_zero = (label_sum_right == 0);
Ix_label_sum_zero = Ix_label_sum_left_zero * Ix_label_sum_right_zero;
I_gain = I_gain * (1 - Ix_label_sum_zero);
I_gain[nrow (I_gain),] = 0; # last entry invalid
max_I_gain_ind = as.scalar (rowIndexMax (t (I_gain)));
split_values[1, start_ind:(start_ind + max_I_gain_ind - 1)] = t (cur_feature_sorted[1:max_I_gain_ind,1]);
for (i10 in 1:max_I_gain_ind) {
ind = as.scalar (cur_feature_sorted[i10,1]);
if (ind == 1) {
split_values_bin[1,start_ind] = 1.0;
} else {
split_values_bin[1,(start_ind + ind - 1)] = 1.0;
}
}
split_values_offset[1,i9] = max_I_gain_ind;
I_gains[1,i9] = max (I_gain);
impurities_left[1,i9] = as.scalar (impurity_left[max_I_gain_ind,]);
impurities_right[1,i9] = as.scalar (impurity_right[max_I_gain_ind,]);
best_label_counts_left[i9,] = label_counts_left[max_I_gain_ind,];
best_label_counts_right[i9,] = label_counts_right[max_I_gain_ind,];
}
# determine best feature to split on and the split values
best_cat_feature = as.scalar (rowIndexMax (I_gains));
best_cat_gain = max (I_gains);
start_ind = 1;
if (best_cat_feature > 1) {
start_ind = start_ind + as.scalar (distinct_values_offset[(best_cat_feature - 1),]);
}
offset = as.scalar (distinct_values[1,best_cat_feature]);
best_split_values_bin = split_values_bin[1, start_ind:(start_ind + offset - 1)];
}
# compare best scale feature to best cat. feature and pick the best one
if (num_scale_features > 0 & best_scale_gain >= best_cat_gain & best_scale_gain > 0) {
# --- update model ---
cur_F[1,i8] = best_scale_feature;
cur_F[2,i8] = 1;
cur_F[3,i8] = 1;
cur_S[1,(i8 - 1) * distinct_values_max + 1] = thresholds[best_scale_split, best_scale_feature];
left_child = 2 * (cur_node - 1) + 1 + 1;
right_child = 2 * (cur_node - 1) + 2 + 1;
# samples going to the left subtree
Ix_left = X_scale_ext_small[, max_I_gain_ind_scale];
Ix_left = Ix * Ix_left;
Ix_right = Ix * (1 - Ix_left);
L_small[,1] = L_small[,1] * (1 - Ix_left) + (Ix_left * left_child);
L_small[,1] = L_small[,1] * (1 - Ix_right) + (Ix_right * right_child);
left_child_size = sum (Ix_left);
right_child_size = sum (Ix_right);
# check if left or right child is a leaf
left_pure = FALSE;
right_pure = FALSE;
cur_impurity_left = as.scalar(impurity_left_scale[max_I_gain_ind_scale,]);
cur_impurity_right = as.scalar(impurity_right_scale[max_I_gain_ind_scale,]);
if ( (left_child_size <= num_leaf | cur_impurity_left == 0 | (level_ == depth)) &
(right_child_size <= num_leaf | cur_impurity_right == 0 | (level_ == depth)) ) { # both left and right nodes are leaf
cur_label_counts_left = label_counts_left_scale[max_I_gain_ind_scale,];
cur_NC[1,(2 * (i8 - 1) + 1)] = left_child;
cur_NC[2,(2 * (i8 - 1) + 1)] = as.scalar( rowIndexMax (cur_label_counts_left)); # leaf class label
left_pure = TRUE;
cur_NC[3,(2 * (i8 - 1) + 1)] = left_child_size - max (cur_label_counts_left); # no. of misclassified samples
cur_label_counts_right = label_counts_overall - cur_label_counts_left;
cur_NC[1,(2 * i8)] = right_child;
cur_NC[2,(2 * i8)] = as.scalar( rowIndexMax (cur_label_counts_right)); # leaf class label
right_pure = TRUE;
cur_NC[3,(2 * i8)] = right_child_size - max (cur_label_counts_right); # no. of misclassified samples
} else if (left_child_size <= num_leaf | cur_impurity_left == 0 | (level == depth)) {
cur_label_counts_left = label_counts_left_scale[max_I_gain_ind_scale,];
cur_NC[1,(2 * (i8 - 1) + 1)] = left_child;
cur_NC[2,(2 * (i8 - 1) + 1)] = as.scalar( rowIndexMax (cur_label_counts_left)); # leaf class label
left_pure = TRUE;
cur_NC[3,(2 * (i8 - 1) + 1)] = left_child_size - max (cur_label_counts_left); # no. of misclassified samples
} else if (right_child_size <= num_leaf | cur_impurity_right == 0 | (level == depth)) {
cur_label_counts_right = label_counts_right_scale[max_I_gain_ind_scale,];
cur_NC[1,(2 * i8)] = right_child;
cur_NC[2,(2 * i8)] = as.scalar( rowIndexMax (cur_label_counts_right)); # leaf class label
right_pure = TRUE;
cur_NC[3,(2 * i8)] = right_child_size - max (cur_label_counts_right); # no. of misclassified samples
}
} else if (num_cat_features > 0 & best_cat_gain > 0) {
# --- update model ---
cur_F[1,i8] = best_cat_feature;
offset_nonzero = as.scalar (split_values_offset[1,best_cat_feature]);
S_start_ind = (i8 - 1) * distinct_values_max + 1;
cur_S[1,S_start_ind:(S_start_ind + offset_nonzero - 1)] = split_values[1,start_ind:(start_ind + offset_nonzero - 1)];
cur_F[3,i8] = offset_nonzero;
cur_F[2,i8] = 2;
left_child = 2 * (cur_node - 1) + 1 + 1;
right_child = 2 * (cur_node - 1) + 2 + 1;
# samples going to the left subtree
Ix_left = rowSums (X_cat_small[,start_ind:(start_ind + offset - 1)] * best_split_values_bin);
Ix_left = (Ix_left >= 1);
Ix_left = Ix * Ix_left;
Ix_right = Ix * (1 - Ix_left);
L_small[,1] = L_small[,1] * (1 - Ix_left) + (Ix_left * left_child);
L_small[,1] = L_small[,1] * (1 - Ix_right) + (Ix_right * right_child);
left_child_size = sum (Ix_left);
right_child_size = sum (Ix_right);
# check if left or right child is a leaf
left_pure = FALSE;
right_pure = FALSE;
cur_impurity_left = as.scalar(impurities_left[,best_cat_feature]);
cur_impurity_right = as.scalar(impurities_right[,best_cat_feature]);
if ( (left_child_size <= num_leaf | cur_impurity_left == 0 | (level_ == depth)) &
(right_child_size <= num_leaf | cur_impurity_right == 0 | (level_ == depth)) ) { # both left and right nodes are leaf
cur_label_counts_left = best_label_counts_left[best_cat_feature,];
cur_NC[1,(2 * (i8 - 1) + 1)] = left_child;
cur_NC[2,(2 * (i8 - 1) + 1)] = as.scalar( rowIndexMax (cur_label_counts_left)); # leaf class label
left_pure = TRUE;
cur_NC[3,(2 * (i8 - 1) + 1)] = left_child_size - max (cur_label_counts_left); # no. of misclassified samples
cur_label_counts_right = label_counts_overall - cur_label_counts_left;
cur_NC[1,(2 * i8)] = right_child;
cur_NC[2,(2 * i8)] = as.scalar( rowIndexMax (cur_label_counts_right)); # leaf class label
right_pure = TRUE;
cur_NC[3,(2 * i8)] = right_child_size - max (cur_label_counts_right); # no. of misclassified samples
} else if (left_child_size <= num_leaf | cur_impurity_left == 0 | (level == depth)) {
cur_label_counts_left = best_label_counts_left[best_cat_feature,];
cur_NC[1,(2 * (i8 - 1) + 1)] = left_child;
cur_NC[2,(2 * (i8 - 1) + 1)] = as.scalar( rowIndexMax (cur_label_counts_left)); # leaf class label
left_pure = TRUE;
cur_NC[3,(2 * (i8 - 1) + 1)] = left_child_size - max (cur_label_counts_left); # no. of misclassified samples
} else if (right_child_size <= num_leaf | cur_impurity_right == 0 | (level == depth)) {
cur_label_counts_right = best_label_counts_right[best_cat_feature,];
cur_NC[1,(2 * i8)] = right_child;
cur_NC[2,(2 * i8)] = as.scalar( rowIndexMax (cur_label_counts_right)); # leaf class label
right_pure = TRUE;
cur_NC[3,(2 * i8)] = right_child_size - max (cur_label_counts_right); # no. of misclassified samples
}
} else {
print ("NUMBER OF SAMPLES AT NODE " + cur_node + " CANNOT BE REDUCED TO MATCH " + num_leaf + ". THIS NODE IS DECLARED AS LEAF!");
right_pure = TRUE;
left_pure = TRUE;
cur_NC[1,(2 * (i8 - 1) + 1)] = cur_node;
class_label = as.scalar (rowIndexMax (label_counts_overall));
cur_NC[2,(2 * (i8 - 1) + 1)] = class_label;
cur_NC[3,(2 * (i8 - 1) + 1)] = label_sum_overall - max (label_counts_overall);
cur_NC[4,(2 * (i8 - 1) + 1)] = 1; # special leaf
}
# add nodes to Q
if (!left_pure) {
cur_Q[1,(2 * (i8 - 1)+ 1)] = left_child;
}
if (!right_pure) {
cur_Q[1,(2 * i8)] = right_child;
}
}
cur_Q = removeEmpty (target = cur_Q, margin = "cols");
Q = cbind (Q, cur_Q);
NC = cbind (NC, cur_NC);
F = cbind (F, cur_F);
S = cbind (S, cur_S);
num_cur_nodes_pre = 2 * num_cur_nodes;
if (as.scalar (cur_Q[1,1]) == 0) {
num_cur_nodes = 0;
} else {
cur_nodes_[,1:ncol(cur_Q)] = cur_Q;
num_cur_nodes = ncol (cur_Q);
}
}
cur_Q_small[,start_ind_global:(start_ind_global + ncol (Q) - 1)] = Q;
cur_NC_small[,start_ind_global:(start_ind_global + ncol (NC) - 1)] = NC;
cur_F_small[,start_ind_global:(start_ind_global + ncol (F) - 1)] = F;
cur_S_small[,start_ind_S_global:(start_ind_S_global + ncol (S) - 1)] = S;
}
##### PREPARE MODEL FOR SMALL NODES
if (num_cur_nodes_small > 0) { # small nodes already processed
cur_Q_small = removeEmpty (target = cur_Q_small, margin = "cols");
if (as.scalar (cur_Q_small[1,1]) != 0) Q_small = cbind (Q_small, cur_Q_small);
cur_NC_small = removeEmpty (target = cur_NC_small, margin = "cols");
if (as.scalar (cur_NC_small[1,1]) != 0) NC_small = cbind (NC_small, cur_NC_small);
cur_F_small = removeEmpty (target = cur_F_small, margin = "cols");
if (as.scalar (cur_F_small[1,1]) != 0) F_small = cbind (F_small, cur_F_small);
cur_S_small = removeEmpty (target = cur_S_small, margin = "cols");
if (as.scalar (cur_S_small[1,1]) != 0) S_small = cbind (S_small, cur_S_small);
num_cur_nodes_small = 0; # reset
}
print (" --- end level " + level + ", remaining no. of LARGE nodes to expand " + num_cur_nodes_large + " --- ");
}
num_misclassified = sum (NC_large[3,]) + sum (NC_small[3,]);
accuracy = (1 - (num_misclassified / num_records)) * 100;
str_o = "no. of misclassified " + num_misclassified + " training accuracy " + accuracy + " %";
if (fileO != " ") {
ACCURACY = matrix (accuracy, rows = 1, cols = 1);
write (ACCURACY, fileO, format = fmtO)
} else {
print (str_o);
}
#### prepare model
print ("PREPARING MODEL...")
# large nodes
if (as.scalar (Q_large[1,1]) == 0 & ncol (Q_large) > 1) {
Q_large = Q_large[,2:ncol (Q_large)];
}
if (as.scalar (NC_large[1,1]) == 0 & ncol (NC_large) > 1) {
NC_large = NC_large[,2:ncol (NC_large)];
}
if (as.scalar (S_large[1,1]) == 0 & ncol (S_large) > 1) {
S_large = S_large[,2:ncol (S_large)];
}
if (as.scalar (F_large[1,1]) == 0 & ncol (F_large) > 1) {
F_large = F_large[,2:ncol (F_large)];
}
# small nodes
if (as.scalar (Q_small[1,1]) == 0 & ncol (Q_small) > 1) {
Q_small = Q_small[,2:ncol (Q_small)];
}
if (as.scalar (NC_small[1,1]) == 0 & ncol (NC_small) > 1) {
NC_small = NC_small[,2:ncol (NC_small)];
}
if (as.scalar (S_small[1,1]) == 0 & ncol (S_small) > 1) {
S_small = S_small[,2:ncol (S_small)];
}
if (as.scalar (F_small[1,1]) == 0 & ncol (F_small) > 1) {
F_small = F_small[,2:ncol (F_small)];
}
# check for special leaves and if there are any remove them from Q_large and Q_small
special_large_leaves_ind = NC_large[4,];
if (sum (special_large_leaves_ind) > 0) {
print ("PROCESSING SPECIAL LARGE LEAVES...");
special_large_leaves = removeEmpty (target = NC_large[1,] * special_large_leaves_ind, margin = "cols");
large_internal_ind = 1 - colSums (outer (t (special_large_leaves), Q_large[1,], "=="));
Q_large = removeEmpty (target = Q_large * large_internal_ind, margin = "cols");
F_large = removeEmpty (target = F_large, margin = "cols"); # remove special leaves from F
}
special_small_leaves_ind = NC_small[4,];
if (sum (special_small_leaves_ind) > 0) {
print ("PROCESSING SPECIAL SMALL LEAVES...");
special_small_leaves = removeEmpty (target = NC_small[1,] * special_small_leaves_ind, margin = "cols");
small_internal_ind = 1 - colSums (outer (t (special_small_leaves), Q_small[1,], "=="));
Q_small = removeEmpty (target = Q_small * small_internal_ind, margin = "cols");
F_small = removeEmpty (target = F_small, margin = "cols"); # remove special leaves from F
}
# model corresponding to large internal nodes
max_offset = 1;
no_large_internal_node = FALSE;
if (as.scalar (Q_large[1,1]) != 0) {
print ("PROCESSING LARGE INTERNAL NODES...");
num_large_internal = ncol (Q_large);
max_offset = max (max (F_large[3,]), max (F_small[3,]));
M1_large = matrix (0, rows = 5 + max_offset, cols = num_large_internal);
M1_large[1,] = Q_large;
M1_large[3:5,] = F_large;
# process S_large
cum_offsets_large = cumsum (t (F_large[3,]));
parfor (it in 1:num_large_internal, check = 0) {
start_ind = 1;
if (it > 1) {
start_ind = start_ind + as.scalar (cum_offsets_large[(it - 1),]);
}
offset = as.scalar (F_large[3,it]);
M1_large[6:(6 + offset - 1),it] = t (S_large[1,start_ind:(start_ind + offset - 1)]);
}
} else {
print ("No LARGE internal nodes available");
no_large_internal_node = TRUE;
}
# model corresponding to small internal nodes
no_small_internal_node = FALSE;
if (as.scalar (Q_small[1,1]) != 0) {
print ("PROCESSING SMALL INTERNAL NODES...");
num_small_internal = ncol (Q_small);
M1_small = matrix (0, rows = 5 + max_offset, cols = num_small_internal);
M1_small[1,] = Q_small;
M1_small[3:5,] = F_small;
# process S_small
cum_offsets_small = cumsum (t (F_small[3,]));
parfor (it in 1:num_small_internal, check = 0) {
start_ind = 1;
if (it > 1) {
start_ind = start_ind + as.scalar (cum_offsets_small[(it - 1),]);
}
offset = as.scalar (F_small[3,it]);
M1_small[6:(6 + offset - 1),it] = t (S_small[1,start_ind:(start_ind + offset - 1)]);
}
} else {
print ("No SMALL internal nodes available");
no_small_internal_node = TRUE;
}
# model corresponding to large leaf nodes
no_large_leaf_node = FALSE;
if (as.scalar (NC_large[1,1]) != 0) {
print ("PROCESSING LARGE LEAF NODES...");
num_large_leaf = ncol (NC_large);
M2_large = matrix (0, rows = 5 + max_offset, cols = num_large_leaf);
M2_large[1,] = NC_large[1,];
M2_large[4:6,] = NC_large[2:4,];
} else {
print ("No LARGE leaf nodes available");
no_large_leaf_node = TRUE;
}
# model corresponding to small leaf nodes
no_small_leaf_node = FALSE;
if (as.scalar (NC_small[1,1]) != 0) {
print ("PROCESSING SMALL LEAF NODES...");
num_small_leaf = ncol (NC_small);
M2_small = matrix (0, rows = 5 + max_offset, cols = num_small_leaf);
M2_small[1,] = NC_small[1,];
M2_small[4:6,] = NC_small[2:4,];
} else {
print ("No SMALL leaf nodes available");
no_small_leaf_node = TRUE;
}
if (no_large_internal_node) {
M1 = M1_small;
} else if (no_small_internal_node) {
M1 = M1_large;
} else {
M1 = cbind (M1_large, M1_small);
}
if (no_large_leaf_node) {
M2 = M2_small;
} else if (no_small_internal_node) {
M2 = M2_large;
} else {
M2 = cbind (M2_large, M2_small);
}
M = cbind (M1, M2);
M = t (order (target = t (M), by = 1));
# removing redundant subtrees
if (ncol (M) > 1) {
print ("CHECKING FOR REDUNDANT SUBTREES...");
red_leaf = TRUE;
process_red_subtree = FALSE;
invalid_node_ind = matrix (0, rows = 1, cols = ncol (M));
while (red_leaf & ncol (M) > 1) {
leaf_ind = (M[3,] == 0);
labels = M[4,] * leaf_ind;
parent_ids = floor (M[1,] /2);
cond1 = (labels[,1:(ncol (M) - 1)] == labels[,2:ncol (M)]); # siebling leaves with same label
cond2 = (parent_ids[,1:(ncol (M)- 1)] == parent_ids[,2:ncol (M)]); # same parents
red_leaf_ind = cond1 * cond2 * leaf_ind[,2:ncol (M)];
if (sum (red_leaf_ind) > 0) { # if redundant subtrees exist
red_leaf_ids = red_leaf_ind * M[1,2:ncol (M)];
red_leaf_ids_nonzero = removeEmpty (target = red_leaf_ids, margin = "cols");
parfor (it in 1:ncol (red_leaf_ids_nonzero), check = 0){
cur_right_leaf_id = as.scalar (red_leaf_ids_nonzero[1,it]);
cur_parent_id = floor (cur_right_leaf_id / 2);
cur_right_leaf_pos = as.scalar (rowIndexMax ((M[1,] == cur_right_leaf_id)));
cur_parent_pos = as.scalar(rowIndexMax (M[1,] == cur_parent_id));
M[2:nrow (M), cur_parent_pos] = M[2:nrow (M), cur_right_leaf_pos];
M[3,cur_right_leaf_pos] = -1;
M[3,cur_right_leaf_pos - 1] = -1;
M[5,cur_parent_pos] = M[5,cur_parent_pos] + M[5,cur_right_leaf_pos - 1];
invalid_node_ind[1,cur_right_leaf_pos] = 1;
invalid_node_ind[1,cur_right_leaf_pos - 1] = 1;
}
process_red_subtree = TRUE;
} else {
red_leaf = FALSE;
}
}
if (process_red_subtree) {
print ("REMOVING REDUNDANT SUBTREES...");
valid_node_ind = (invalid_node_ind == 0);
M = removeEmpty (target = M * valid_node_ind, margin = "cols");
}
}
if (ncol (M) > 1) { # if internal nodes exist
print ("COMPUTING OFFSETS TO THE LEFT CHILD FOR INTERNAL NODES...");
internal_ind = (M[3,] > 0);
internal_ids = internal_ind * M[1,];
internal_ids_nonzero = removeEmpty (target = internal_ids, margin = "cols");
a1 = internal_ids_nonzero;
a2 = internal_ids_nonzero * 2;
pos_a1 = rowIndexMax( outer(t(a1), M[1,], "==") );
pos_a2 = rowIndexMax( outer(t(a2), M[1,], "==") );
M[2,] = t(table(pos_a1, 1, pos_a2 - pos_a1, ncol(M), 1));
}
else {
print ("The tree model contains only one leaf with label " + as.scalar (M[4,]));
}
write (M, fileM, format = fmtO);