/**
* Computes class distribution for an attribute. Not used anymore in 0.99. Based on the splitData
* function from "weka.classifiers.trees.RandomTree", with the following changes:
*
* <ul>
* <li>entropy pre-split is not computed at this point as the only thing relevant for the
* (comparative) goodness of a split is entropy after splitting
* <li>dist[][] is now computed only after the split point has been found, and not updated
* continually by copying from currDist
* <li>also, in Weka's RandomTree it was possible to create a split 'in the middle' of instance
* 0, which would result in empty nodes after the split; this is now fixed
* <li>instance 0 is now generally skipped when looking for split points, as the split point
* 'before instance 0' is not sensible; in versions prior to 0.96 this change introduced a
* bug where attributes with all missing values had their dists computed wrongly, which
* might result in useless (but harmless) branches being added to the tree
* </ul>
*
* @param props gets filled with relative sizes of branches (total = 1), indexed first per
* attribute
* @param dists these are the contingency matrices, indexed first per attribute
* @param att the attribute index (which one to change)
* @param sortedIndices the sorted indices of the vals
*/
protected double distribution(
double[][] props, double[][][] dists, int att, int[] sortedIndices) {
double splitPoint = -Double.MAX_VALUE;
double[][] dist = null; // a contingency table of the split point vs class
int i;
if (data.isAttrNominal(att)) { // ====================== nominal attributes
dist = new double[data.attNumVals[att]][data.numClasses];
for (i = 0; i < sortedIndices.length; i++) {
int inst = sortedIndices[i];
if (data.isValueMissing(att, inst)) break;
dist[(int) data.vals[att][inst]][data.instClassValues[inst]] += data.instWeights[inst];
}
splitPoint = 0; // signals we've found a sensible split point; by
// definition, a split on a nominal attribute is sensible
} else { // ============================================ numeric attributes
double[][] currDist = new double[2][data.numClasses];
dist = new double[2][data.numClasses];
// begin with moving all instances into second subset
for (int j = 0; j < sortedIndices.length; j++) {
int inst = sortedIndices[j];
if (data.isValueMissing(att, inst)) break;
currDist[1][data.instClassValues[inst]] += data.instWeights[inst];
}
copyDists(currDist, dist);
// for (int j = 0; j < currDist.length; j++)
// System.arraycopy(currDist[j], 0, dist[j], 0, dist[j].length);
double currVal = -Double.MAX_VALUE; // current value of splitting criterion
double bestVal = -Double.MAX_VALUE; // best value of splitting criterion
int bestI = 0; // the value of "i" BEFORE which the splitpoint is placed
for (i = 1; i < sortedIndices.length; i++) { // --- try all split points
int inst = sortedIndices[i];
if (data.isValueMissing(att, inst)) break;
int prevInst = sortedIndices[i - 1];
currDist[0][data.instClassValues[prevInst]] += data.instWeights[prevInst];
currDist[1][data.instClassValues[prevInst]] -= data.instWeights[prevInst];
// do not allow splitting between two instances with the same value
if (data.vals[att][inst] > data.vals[att][prevInst]) {
// we want the lowest impurity after split; at this point, we don't
// really care what we've had before spliting
currVal = -SplitCriteria.entropyConditionedOnRows(currDist);
if (currVal > bestVal) {
bestVal = currVal;
bestI = i;
}
}
} // ------- end split points
/*
* Determine the best split point:
* bestI == 0 only if all instances had missing values, or there were
* less than 2 instances; splitPoint will remain set as -Double.MAX_VALUE.
* This is not really a useful split, as all of the instances are 'below'
* the split line, but at least it's formally correct. And the dists[]
* also has a default value set previously.
*/
if (bestI > 0) { // ...at least one valid splitpoint was found
int instJustBeforeSplit = sortedIndices[bestI - 1];
int instJustAfterSplit = sortedIndices[bestI];
splitPoint =
(data.vals[att][instJustAfterSplit] + data.vals[att][instJustBeforeSplit]) / 2.0;
// Now make the correct dist[] from the default dist[] (all instances
// in the second branch, by iterating through instances until we reach
// bestI, and then stop.
for (int ii = 0; ii < bestI; ii++) {
int inst = sortedIndices[ii];
dist[0][data.instClassValues[inst]] += data.instWeights[inst];
dist[1][data.instClassValues[inst]] -= data.instWeights[inst];
}
}
} // ================================================== nominal or numeric?
// compute total weights for each branch (= props)
props[att] = countsToFreqs(dist);
// distribute counts of instances with missing values
// ver 0.96 - check for special case when *all* instances have missing vals
if (data.isValueMissing(att, sortedIndices[0])) i = 0;
while (i < sortedIndices.length) {
int inst = sortedIndices[i];
for (int branch = 0; branch < dist.length; branch++) {
dist[branch][data.instClassValues[inst]] += props[att][branch] * data.instWeights[inst];
}
i++;
}
// return distribution after split and best split point
dists[att] = dist;
return splitPoint;
}
/**
* Computes class distribution for an attribute. New in FastRF 0.99, main changes:
*
* <ul>
* <li>now reuses the temporary counting arrays (this.tempDists, this.tempDistsOthers) instead
* of creating/destroying arrays
* <li>does not create a new "dists" for each attribute it examines; instead it replaces the
* existing "dists" (supplied as a parameter) but only if the split is better than the
* previous best split
* <li>always creates binary splits, even for categorical variables; thus might give slightly
* different classification results than the old RandomForest
* </ul>
*
* @param propsBestAtt gets filled with relative sizes of branches (total = 1) for the best
* examined attribute so far; updated ONLY if current attribute is better that the previous
* best
* @param distsBestAtt these are the contingency matrices for the best examined attribute so far;
* updated ONLY if current attribute is better that the previous best
* @param scoreBestAtt Checked against the score of the attToExamine to determine if the
* propsBestAtt and distsBestAtt need to be updated.
* @param attToExamine the attribute index (which one to examine, and change the above matrices if
* the attribute is better than the previous one)
* @param sortedIndices the sorted indices of the vals for the attToExamine.
* @param startAt Index in sortedIndicesOfAtt; do not touch anything below this index.
* @param endAt Index in sortedIndicesOfAtt; do not touch anything after this index.
*/
protected double distributionSequentialAtt(
double[] propsBestAtt,
double[][] distsBestAtt,
double scoreBestAtt,
int attToExamine,
int[] sortedIndicesOfAtt,
int startAt,
int endAt) {
double splitPoint = -Double.MAX_VALUE;
// a contingency table of the split point vs class.
double[][] dist = this.tempDists;
Arrays.fill(dist[0], 0.0);
Arrays.fill(dist[1], 0.0);
double[][] currDist = this.tempDistsOther;
Arrays.fill(currDist[0], 0.0);
Arrays.fill(currDist[1], 0.0);
// double[][] dist = new double[2][data.numClasses];
// double[][] currDist = new double[2][data.numClasses];
int i;
int sortedIndicesOfAttLength = endAt - startAt + 1;
// find how many missing values we have for this attribute (they're always at the end)
int lastNonmissingValIdx = endAt;
for (int j = endAt; j >= startAt; j--) {
if (data.isValueMissing(attToExamine, sortedIndicesOfAtt[j])) {
lastNonmissingValIdx = j - 1;
} else {
break;
}
}
if (lastNonmissingValIdx < startAt) { // only missing values in this feature??
return Double.NaN; // we cannot split on it
}
if (data.isAttrNominal(attToExamine)) { // ====================== nominal attributes
// 0.99: new routine - makes a one-vs-all split on categorical attributes
int numLvls = data.attNumVals[attToExamine];
int bestLvl = 0; // the index of the category which is best to "split out"
// note: if we have only two levels, it doesn't matter which one we "split out"
// we can thus safely check only the first one
if (numLvls <= 2) {
bestLvl = 0; // this means that the category with index 0 always
// goes 'above' the split and category with index 1 goes 'below' the split
for (i = startAt; i <= lastNonmissingValIdx; i++) {
int inst = sortedIndicesOfAtt[i];
dist[(int) data.vals[attToExamine][inst]][data.instClassValues[inst]] +=
data.instWeights[inst];
}
} else { // for >2 levels, we have to search different splits
// begin with moving all instances into second subset ("below split")
for (int j = startAt; j <= lastNonmissingValIdx; j++) {
int inst = sortedIndicesOfAtt[j];
currDist[1][data.instClassValues[inst]] += data.instWeights[inst];
}
// create a default dist[] which we'll modify after we find the best class to split out
copyDists(currDist, dist);
double currVal = -Double.MAX_VALUE; // current value of splitting criterion
double bestVal = -Double.MAX_VALUE; // best value of splitting criterion
int lastSeen = startAt; // used to avoid looping through all instances for every lvl
for (int lvl = 0; lvl < numLvls; lvl++) {
// reset the currDist to the default (everything "below split") - conveniently stored in
// dist[][]
copyDists(dist, currDist);
for (i = lastSeen; i <= lastNonmissingValIdx; i++) {
lastSeen = i;
int inst = sortedIndicesOfAtt[i];
if ((int) data.vals[attToExamine][inst] < lvl) {
continue;
} else if ((int) data.vals[attToExamine][inst] == lvl) {
// move to "above split" from "below split"
currDist[0][data.instClassValues[inst]] += data.instWeights[inst];
currDist[1][data.instClassValues[inst]] -= data.instWeights[inst];
} else {
break; // no need to loop forward, no more instances of this category
}
}
// we filled the "dist" for the current level, find score and see if we like it
currVal = -SplitCriteria.entropyConditionedOnRows(currDist);
if (currVal > bestVal) {
bestVal = currVal;
bestLvl = lvl;
}
} // examine how well "splitting out" of individual levels works for us
// remember the contingency table from the best "lvl" and store it in "dist"
for (i = startAt; i <= lastNonmissingValIdx; i++) {
int inst = sortedIndicesOfAtt[i];
if ((int) data.vals[attToExamine][inst] == bestLvl) {
// move to "above split" from "below split"
dist[0][data.instClassValues[inst]] += data.instWeights[inst];
dist[1][data.instClassValues[inst]] -= data.instWeights[inst];
} else {
break; // no need to loop forward, no more instances of this category
}
}
}
splitPoint = bestLvl; // signals we've found a sensible split point; by
// definition, a split on a nominal attribute
// will always be sensible
} else { // ============================================ numeric attributes
// re-use the 2 x nClass temporary arrays created when tree was initialized
// Arrays.fill( dist[0], 0.0 );
// Arrays.fill( dist[1], 0.0 );
// begin with moving all instances into second subset ("below split")
for (int j = startAt; j <= lastNonmissingValIdx; j++) {
int inst = sortedIndicesOfAtt[j];
currDist[1][data.instClassValues[inst]] += data.instWeights[inst];
}
copyDists(currDist, dist);
double currVal = -Double.MAX_VALUE; // current value of splitting criterion
double bestVal = -Double.MAX_VALUE; // best value of splitting criterion
int bestI = 0; // the value of "i" BEFORE which the splitpoint is placed
for (i = startAt + 1; i <= lastNonmissingValIdx; i++) { // --- try all split points
int inst = sortedIndicesOfAtt[i];
int prevInst = sortedIndicesOfAtt[i - 1];
currDist[0][data.instClassValues[prevInst]] += data.instWeights[prevInst];
currDist[1][data.instClassValues[prevInst]] -= data.instWeights[prevInst];
// do not allow splitting between two instances with the same value
if (data.vals[attToExamine][inst] > data.vals[attToExamine][prevInst]) {
// we want the lowest impurity after split; at this point, we don't
// really care what we've had before spliting
currVal = -SplitCriteria.entropyConditionedOnRows(currDist);
if (currVal > bestVal) {
bestVal = currVal;
bestI = i;
}
}
} // ------- end trying split points
/*
* Determine the best split point:
* bestI == 0 only if all instances had missing values, or there were
* less than 2 instances; splitPoint will remain set as -Double.MAX_VALUE.
* This is not really a useful split, as all of the instances are 'below'
* the split line, but at least it's formally correct. And the dists[]
* also has a default value set previously.
*/
if (bestI > startAt) { // ...at least one valid splitpoint was found
int instJustBeforeSplit = sortedIndicesOfAtt[bestI - 1];
int instJustAfterSplit = sortedIndicesOfAtt[bestI];
splitPoint =
(data.vals[attToExamine][instJustAfterSplit]
+ data.vals[attToExamine][instJustBeforeSplit])
/ 2.0;
// now make the correct dist[] (for the best split point) from the
// default dist[] (all instances in the second branch, by iterating
// through instances until we reach bestI, and then stop.
for (int ii = startAt; ii < bestI; ii++) {
int inst = sortedIndicesOfAtt[ii];
dist[0][data.instClassValues[inst]] += data.instWeights[inst];
dist[1][data.instClassValues[inst]] -= data.instWeights[inst];
}
}
} // ================================================== nominal or numeric?
// compute total weights for each branch (= props)
// again, we reuse the tempProps of the tree not to create/destroy new arrays
double[] props = this.tempProps;
countsToFreqs(dist, props); // props gets overwritten, previous contents don't matters
// distribute *counts* of instances with missing values using the "props"
i = lastNonmissingValIdx + 1; // / start 1 after the non-missing val (if there is anything)
while (i <= endAt) {
int inst = sortedIndicesOfAtt[i];
dist[0][data.instClassValues[inst]] += props[0] * data.instWeights[inst];
dist[1][data.instClassValues[inst]] += props[1] * data.instWeights[inst];
i++;
}
// update the distribution after split and best split point
// but ONLY if better than the previous one -- we need to recalculate the
// entropy (because this changes after redistributing the instances with
// missing values in the current attribute). Also, for categorical variables
// it was not calculated before.
double curScore = -SplitCriteria.entropyConditionedOnRows(dist);
if (curScore > scoreBestAtt
&& splitPoint
> -Double
.MAX_VALUE) { // overwrite the "distsBestAtt" and "propsBestAtt" with current values
copyDists(dist, distsBestAtt);
System.arraycopy(props, 0, propsBestAtt, 0, props.length);
return splitPoint;
} else {
// returns a NaN instead of the splitpoint if the attribute was not better than a previous
// one.
return Double.NaN;
}
}
/**
* Recursively generates a tree. A derivative of the buildTree function from the
* "weka.classifiers.trees.RandomTree" class, with the following changes made:
*
* <ul>
* <li>m_ClassProbs are now remembered only in leaves, not in every node of the tree
* <li>m_Distribution has been removed
* <li>members of dists, splits, props and vals arrays which are not used are dereferenced prior
* to recursion to reduce memory requirements
* <li>a check for "branch with no training instances" is now (FastRF 0.98) made before
* recursion; with the current implementation of splitData(), empty branches can appear only
* with nominal attributes with more than two categories
* <li>each new 'tree' (i.e. node or leaf) is passed a reference to its 'mother forest',
* necessary to look up parameters such as maxDepth and K
* <li>pre-split entropy is not recalculated unnecessarily
* <li>uses DataCache instead of weka.core.Instances, the reference to the DataCache is stored
* as a field in FastRandomTree class and not passed recursively down new buildTree() calls
* <li>similarly, a reference to the random number generator is stored in a field of the
* DataCache
* <li>m_ClassProbs are now normalized by dividing with number of instances in leaf, instead of
* forcing the sum of class probabilities to 1.0; this has a large effect when
* class/instance weights are set by user
* <li>a little imprecision is allowed in checking whether there was a decrease in entropy after
* splitting
* <li>0.99: the temporary arrays splits, props, vals now are not wide as the full number of
* attributes in the dataset (of which only "k" columns of randomly chosen attributes get
* filled). Now, it's just a single array which gets replaced as the k features are
* evaluated sequentially, but it gets replaced only if a next feature is better than a
* previous one.
* <li>0.99: the SortedIndices are now not cut up into smaller arrays on every split, but rather
* re-sorted within the same array in the splitDataNew(), and passed down to buildTree() as
* the original large matrix, but with start and end points explicitly specified
* </ul>
*
* @param sortedIndices the indices of the instances of the whole bootstrap replicate
* @param startAt First index of the instance to consider in this split; inclusive.
* @param endAt Last index of the instance to consider; inclusive.
* @param classProbs the class distribution
* @param debug whether debugging is on
* @param attIndicesWindow the attribute window to choose attributes from
* @param depth the current depth
*/
protected void buildTree(
int[][] sortedIndices,
int startAt,
int endAt,
double[] classProbs,
boolean debug,
int[] attIndicesWindow,
int depth) {
m_Debug = debug;
int sortedIndicesLength = endAt - startAt + 1;
// Check if node doesn't contain enough instances or is pure
// or maximum depth reached, make leaf.
if ((sortedIndicesLength < Math.max(2, getMinNum())) // small
|| Utils.eq(classProbs[Utils.maxIndex(classProbs)], Utils.sum(classProbs)) // pure
|| ((getMaxDepth() > 0) && (depth >= getMaxDepth())) // deep
) {
m_Attribute = -1; // indicates leaf (no useful attribute to split on)
// normalize by dividing with the number of instances (as of ver. 0.97)
// unless leaf is empty - this can happen with splits on nominal
// attributes with more than two categories
if (sortedIndicesLength != 0)
for (int c = 0; c < classProbs.length; c++) {
classProbs[c] /= sortedIndicesLength;
}
m_ClassProbs = classProbs;
this.data = null;
return;
} // (leaf making)
// new 0.99: all the following are for the best attribute only! they're updated while
// sequentially through the attributes
double val = Double.NaN; // value of splitting criterion
double[][] dist =
new double[2]
[data.numClasses]; // class distributions (contingency table), indexed first by branch,
// then by class
double[] prop = new double[2]; // the branch sizes (as fraction)
double split = Double.NaN; // split point
// Investigate K random attributes
int attIndex = 0;
int windowSize = attIndicesWindow.length;
int k = getKValue();
boolean sensibleSplitFound = false;
double prior = Double.NaN;
double bestNegPosterior = -Double.MAX_VALUE;
int bestAttIdx = -1;
while ((windowSize > 0) && (k-- > 0 || !sensibleSplitFound)) {
int chosenIndex = data.reusableRandomGenerator.nextInt(windowSize);
attIndex = attIndicesWindow[chosenIndex];
// shift chosen attIndex out of window
attIndicesWindow[chosenIndex] = attIndicesWindow[windowSize - 1];
attIndicesWindow[windowSize - 1] = attIndex;
windowSize--;
// new: 0.99
double candidateSplit =
distributionSequentialAtt(
prop, dist, bestNegPosterior, attIndex, sortedIndices[attIndex], startAt, endAt);
if (Double.isNaN(candidateSplit)) {
continue; // we did not improve over a previous attribute! "dist" is unchanged from before
}
// by this point we know we have an improvement, so we keep the new split point
split = candidateSplit;
bestAttIdx = attIndex;
if (Double.isNaN(
prior)) { // needs to be computed only once per branch - is same for all attributes (even
// regardless of missing values)
prior = SplitCriteria.entropyOverColumns(dist);
}
double negPosterior =
-SplitCriteria.entropyConditionedOnRows(dist); // this is an updated dist
if (negPosterior > bestNegPosterior) {
bestNegPosterior = negPosterior;
} else {
throw new IllegalArgumentException("Very strange!");
}
val = prior - (-negPosterior); // we want the greatest reduction in entropy
if (val > 1e-2) { // we allow some leeway here to compensate
sensibleSplitFound = true; // for imprecision in entropy computation
}
} // feature by feature in window
if (sensibleSplitFound) {
m_Attribute = bestAttIdx; // find best attribute
m_SplitPoint = split;
m_Prop = prop;
prop = null; // can be GC'ed
// int[][][] subsetIndices =
// new int[dist.length][data.numAttributes][];
// splitData( subsetIndices, m_Attribute,
// m_SplitPoint, sortedIndices );
// int numInstancesBeforeSplit = sortedIndices[0].length;
int belowTheSplitStartsAt =
splitDataNew(m_Attribute, m_SplitPoint, sortedIndices, startAt, endAt);
m_Successors = new FastRandomTree[dist.length]; // dist.length now always == 2
for (int i = 0; i < dist.length; i++) {
m_Successors[i] = new FastRandomTree();
m_Successors[i].m_MotherForest = this.m_MotherForest;
m_Successors[i].data = this.data;
// new in 0.99 - used in distributionSequentialAtt()
m_Successors[i].tempDists = this.tempDists;
m_Successors[i].tempDistsOther = this.tempDistsOther;
m_Successors[i].tempProps = this.tempProps;
// check if we're about to make an empty branch - this can happen with
// nominal attributes with more than two categories (as of ver. 0.98)
if (belowTheSplitStartsAt - startAt == 0) {
// in this case, modify the chosenAttDists[i] so that it contains
// the current, before-split class probabilities, properly normalized
// by the number of instances (as we won't be able to normalize
// after the split)
for (int j = 0; j < dist[i].length; j++) dist[i][j] = classProbs[j] / sortedIndicesLength;
}
if (i == 0) { // before split
m_Successors[i].buildTree(
sortedIndices,
startAt,
belowTheSplitStartsAt - 1,
dist[i],
m_Debug,
attIndicesWindow,
depth + 1);
} else { // after split
m_Successors[i].buildTree(
sortedIndices,
belowTheSplitStartsAt,
endAt,
dist[i],
m_Debug,
attIndicesWindow,
depth + 1);
}
dist[i] = null;
}
sortedIndices = null;
} else { // ------ make leaf --------
m_Attribute = -1;
// normalize by dividing with the number of instances (as of ver. 0.97)
// unless leaf is empty - this can happen with splits on nominal attributes
if (sortedIndicesLength != 0)
for (int c = 0; c < classProbs.length; c++) {
classProbs[c] /= sortedIndicesLength;
}
m_ClassProbs = classProbs;
}
this.data = null; // dereference all pointers so data can be GC'd after tree is built
}
