src/supervised/trees/decision-tree.js
// Internal dependencies
import { Classifier } from '../base';
import * as Arrays from '../../arrays';
import * as Random from '../../random';
/**
* @typedef {Object} DataSplitGroups
* @property {Array.<Array.<number>>} indices - Two-dimensional array containing, for both groups,
* the indices of the samples belonging to the group
* @property {Array.<Array.<number>>} features - Two-dimensional array containing, for both groups,
* the features of the samples belonging to the group
* @property {Array.<Array.<number>>} labels - Two-dimensional array containing, for both groups,
* the labels of the samples belonging to the group
*/
/**
* @typedef {Object} DataSplit
* @property {number} feature - Index of the feature by which to split
* @property {number} featureValue - Split value of the feature by which to split
* @property {DataSplitGroups} groups - Data groups resulting from the split
*/
/**
* Decision tree node. Holds properties of a single tree node.
*/
export class DecisionTreeNode {}
/**
* Decision tree learner. Builds a decision tree by greedily splitting samples on one feature
* hierarchically.
*/
export default class DecisionTree extends Classifier {
/**
* Constructor. Initialize class members and store user-defined options.
*
* @param {Object} [optionsUser] - User-defined options for decision tree
* @param {string} [optionsUser.criterion = 'gini'] - Splitting criterion. Either 'gini', for the
* Gini coefficient, or 'entropy' for the Shannon entropy
* @param {number|string} [optionsUser.numFeatures = 1.0] - Number of features to subsample at
* each node. Either a number (float), in which case the input fraction of features is used
* (e.g., 1.0 for all features), or a string. If string, 'sqrt' and 'log2' are supported,
* causing the algorithm to use sqrt(n) and log2(n) features, respectively (where n is the
* total number of features)
* @param {number} [optionsUser.maxDepth = -1] - Maximum depth of the tree. The depth of the
* tree is the number of nodes in the longest path from the decision tree root to a leaf. It
* is an indicator of the complexity of the tree. Use -1 for no maximum depth
*/
constructor(optionsUser = {}) {
super();
// Parse options
const optionsDefault = {
criterion: 'gini',
numFeatures: 1.0,
maxDepth: -1,
};
const options = {
...optionsDefault,
...optionsUser,
};
// Set options
this.criterion = options.criterion;
this.numFeatures = options.numFeatures;
this.maxDepth = options.maxDepth;
}
/**
* Calculate the impurity for multiple groups of labels. The impurity criterion used can be
* specified by the user through the user-defined options.
*
* @param {Array.<Array.<mixed>>} groups - Groups of labels. Each group is an array of labels
* @return {number} Impurity for the provided groups
*/
calculateImpurity(groups) {
if (this.criterion === 'gini') {
return this.calculateWeightedImpurity(groups, this.gini);
} else if (this.criterion === 'entropy') {
return this.calculateWeightedImpurity(groups, this.entropy);
}
return null;
}
/**
* Calculate the weighted impurity for multiple groups of labels. The returned impurity is
* calculated as the weighted sum of the impurities of the individual groups, where the
* weights are determined by the number of samples in the group.
*
* @param {Array.<Array.<mixed>>} groups - Groups of labels. Each group is an array of labels
* @param {function(labels: Array.<number>): number} impurityCallback - Callback function taking
* an array of labels as its first and only argument
* @return {number} Weighted impurity for the provided groups
*/
calculateWeightedImpurity(groups, impurityCallback) {
// Impurity per group
const impurities = [];
// Total number of elements
let numElements = 0;
// Loop over the groups and calculate the group's impurity
for (const group of groups) {
impurities.push(impurityCallback(group));
numElements += group.length;
}
// Return the weighted sum of impurities
return impurities.reduce((r, a, i) =>
r + a * groups[i].length / numElements
, 0);
}
/**
* Calculate the Gini coefficient a set of labels.
*
* @param {Array.<mixed>} labels - Array of predicted labels
* @return {number} Gini impurity
*/
gini(labels) {
const uniqueLabels = Arrays.unique(labels);
return uniqueLabels.reduce((r, label) => {
const frac = labels.filter(x => x === label).length / labels.length;
return r + frac * (1 - frac);
}, 0);
}
/**
* Calculate the Shannon entropy a set of labels.
*
* @param {Array.<mixed>} labels - Array of predicted labels
* @return {number} Shannon entropy
*/
entropy(labels) {
const uniqueLabels = Arrays.unique(labels);
return uniqueLabels.reduce((r, label) => {
const frac = labels.filter(x => x === label).length / labels.length;
return r - frac * Math.log(frac);
}, 0);
}
/**
* Split a set of samples into two groups by some splitting value for a feature. The samples with
* a feature value lower than the split value go the left (first) group, and the other samples go
* to the right (second) group.
*
* @param {Array.<number>} XSub - Features of samples to split by some feature
* @param {Array.<mixed>} ySub - Labels of samples
* @param {number} fInd - Index of feature to split by
* @param {number} splitValue - Value to be used as the splitting point for the feature
* @return {DataSplitGroups} Assigned sample indices, features, and labels for both of the groups
*/
splitSamples(XSub, ySub, fInd, splitValue) {
const groupsIndices = [[], []];
const groupsX = [[], []];
const groupsY = [[], []];
XSub.forEach((x, i) => {
if (x[fInd] < splitValue) {
groupsIndices[0].push(i);
groupsX[0].push(x);
groupsY[0].push(ySub[i]);
} else {
groupsIndices[1].push(i);
groupsX[1].push(x);
groupsY[1].push(ySub[i]);
}
});
return {
indices: groupsIndices,
features: groupsX,
labels: groupsY
};
}
/**
* Find the best splitting feature and feature value for a set of data points.
*
* @param {Array.<Array.<number>>} XSub - Features of samples to find the split for
* @param {Array.<mixed>} ySub - Labels of samples
* @param {number} baseImpurity - Impurity of parent node
* @return {DataSplit}
*/
findSplit(XSub, ySub, baseImpurity) {
// Extract information from training data
const shape = Arrays.getShape(XSub);
// Best split found
let bestSplitGain = -Infinity;
let bestSplitFeature;
let bestSplitFeatureValue;
let bestSplitGroups;
// Transpose features array to easily access all sample values for a given feature
const XSubT = Arrays.transpose(XSub);
// Randomly sample features to consider
const possibleIndices = [...Array(shape[1])].map((x, i) => i);
const fIndices = Random.sample(possibleIndices, this.numFeaturesInt, false);
// Calculate best split by looping over all features and considering the split quality for
// all of each feature's values. The best split is the feature value at which to split such
// that the impurity is minimized
fIndices.forEach((fInd) => {
// Extract unique, sorted sample values for this feature
const sampleValues = Arrays.unique(XSubT[fInd]);
sampleValues.sort((a, b) => (a > b) * 2 - 1);
// Find split values as the average value between all sorted unique values
const splitValues = Arrays.scale(
Arrays.sum(
sampleValues.slice(1),
sampleValues.slice(0, -1)
),
0.5
);
// Loop over all split values
splitValues.forEach((splitValue) => {
// Groups samples. The first and second group correspond with the samples in the left
// and right parts of the split, respectively
const groups = this.splitSamples(XSub, ySub, fInd, splitValue);
// Calculate impurity and impurity gain
const impurity = this.calculateImpurity(groups.labels);
const gain = baseImpurity - impurity;
// Check whether this split is better than the current best split
if (gain > bestSplitGain && groups.features[0].length > 0
&& groups.features[1].length > 0) {
bestSplitGain = gain;
bestSplitFeature = fInd;
bestSplitFeatureValue = splitValue;
bestSplitGroups = groups;
}
});
});
return {
feature: bestSplitFeature,
featureValue: bestSplitFeatureValue,
groups: bestSplitGroups,
};
}
/**
* Build a (sub-)tree from a set of samples.
*
* @param {Array.<Array.<number>>} XSub - Features of samples to build a tree for
* @param {Array.<mixed>} ySub - Labels of samples
* @param {number} [depth = 0] - Current tree depth. 0 indicates the root node
* @return {DecisionTreeNode} Decision tree node
*/
buildTree(XSub, ySub, depth = 0) {
// Create tree node
const node = new DecisionTreeNode();
// Calculate node impurity
const impurity = this.calculateImpurity([ySub]);
node.impurity = impurity;
// If the node has only samples from a single class, no further splitting is possible
if (impurity === 0) {
node.type = 'leaf';
node.prediction = ySub[0];
return node;
}
// Check whether the maximum depth has been reached, and make the node a leaf if that's the case
if (this.maxDepth >= 0 && depth >= this.maxDepth) {
node.type = 'leaf';
node.prediction = Arrays.valueCounts(ySub).reduce((r, x) => (x[1] > r[1] ? x : r))[0];
return node;
}
const { feature, featureValue, groups } = this.findSplit(XSub, ySub, impurity);
// Fill node details
node.type = 'node';
node.feature = feature;
node.featureValue = featureValue;
node.left = this.buildTree(groups.features[0], groups.labels[0], depth + 1);
node.right = this.buildTree(groups.features[1], groups.labels[1], depth + 1);
return node;
}
/**
* @see {@link Classifier#train}
*/
train(X, y) {
if (X.length !== y.length) {
throw new Error('Number of data points should match number of labels.');
}
// Process training options
const shape = Arrays.getShape(X);
if (this.numFeatures === 'sqrt') {
this.numFeaturesInt = Math.floor(Math.sqrt(shape[1]));
} else if (this.numFeatures === 'log2') {
this.numFeaturesInt = Math.floor(Math.log2(shape[1]));
} else {
this.numFeaturesInt = Math.max(1, Math.min(
shape[1],
Math.floor(this.numFeatures * shape[1])
));
}
// Construct decision tree
this.tree = this.buildTree(X, y);
}
/**
* @see {@link Classifier#predict}
*/
predict(X) {
if (typeof this.tree === 'undefined') {
throw new Error('Model has to be trained in order to make predictions.');
}
// Make prediction for each data point
const predictions = X.map(x => this.predictSample(x));
return predictions;
}
/**
* Make a prediction for a single sample.
*
* @param {Array.<number>} sampleFeatures - Data point features
* @return {mixed} Prediction. Label of class with highest prevalence among k nearest neighbours
*/
predictSample(sampleFeatures) {
let node = this.tree;
while (node.type === 'node') {
node = (sampleFeatures[node.feature] < node.featureValue) ? node.left : node.right;
}
return node.prediction;
}
}