jam/js/ml/dti.js

806 lines
23 KiB
JavaScript

/**
** ==============================
** O O O OOOO
** O O O O O O
** O O O O O O
** OOOO OOOO O OOO OOOO
** O O O O O O O
** O O O O O O O
** OOOO OOOO O O OOOO
** ==============================
** Dr. Stefan Bosse http://www.bsslab.de
**
** COPYRIGHT: THIS SOFTWARE, EXECUTABLE AND SOURCE CODE IS OWNED
** BY THE AUTHOR(S).
** THIS SOURCE CODE MAY NOT BE COPIED, EXTRACTED,
** MODIFIED, OR OTHERWISE USED IN A CONTEXT
** OUTSIDE OF THE SOFTWARE SYSTEM.
**
** $AUTHORS: Stefan Bosse
** $INITIAL: (C) 2006-2018 bLAB
** $CREATED: 03-03-16 by sbosse.
** $VERSION: 1.4.2
**
** $INFO:
**
** Interval Decision Tree Learner
**
** Modified ID3-based Decision Tree Algorithm that wraps all data with 2-eps intervals and uses
** interval instead single value arithmetic for entropy calculation and feature selection.
** The classification bases on a nearest-neighbourhood look-up of best matching results.
**
** Two different algorithms are supported:
**
** 1. Static (using learn), the DTI learner using attribute selection based on entropy.
** The training data must be available in advance.
** 2. Dynamic (using update), the DTI learrner using attribute selection based on significance.
** The training data is applied sequentielly (stream learning) updating the model.
**
** Though in principle the both algrotihms can be mixed (first static, then dynamic updating),
** the resulting model will have poor classification quality. Either use static or only dynamic
** (stream) learning.
**
** Portable model
**
** $ENDOFINFO
*/
var Io = Require('com/io');
var Comp = Require('com/compat');
var current=none;
var Aios=none;
var min = Comp.pervasives.min;
var max = Comp.pervasives.max;
/**
* Map of valid tree node types
* @constant
* @static
*/
var NODE_TYPES = {
RESULT: 'result',
FEATURE: 'feature',
FEATURE_VALUE: 'feature_value'
};
function Result(key) {
return {
type:NODE_TYPES.RESULT,
name:key
}
}
function Feature(name,vals) {
return {
type:NODE_TYPES.FEATURE,
name:name,
vals:vals
}
}
// A value can be a scalar or a range {a,b} object
function Value(val,child) {
return {
type:NODE_TYPES.FEATURE_VALUE,
val:val,
child:child
}
}
/** Add a new training set with optional data set merging and value interval expansion.
*
*/
function add_training_set(data,set,merge) {
if (merge) {
// Merge a data set with an existing for a specific key; create value ranges
} else
data.push(set);
}
/**
* Computes Log with base-2
* @private
*/
function log2(n) {
return Math.log(n) / Math.log(2);
}
function results(model) {
var line='',sep;
if (!model) return '';
switch (model.type) {
case NODE_TYPES.RESULT:
return model.name;
case NODE_TYPES.FEATURE:
sep='';
line='';
Comp.array.iter(model.vals,function (v) {
line += sep+results(v);
sep=',';
});
return line;
case NODE_TYPES.FEATURE_VALUE:
return results(model.child);
}
return 'result?';
}
/**
* Finds element with highest occurrence in a list
* @private
*/
function mostCommon(list) {
var elementFrequencyMap = {};
var largestFrequency = -1;
var mostCommonElement = null;
list.forEach(function(element) {
var elementFrequency = (elementFrequencyMap[element] || 0) + 1;
elementFrequencyMap[element] = elementFrequency;
if (largestFrequency < elementFrequency) {
mostCommonElement = element;
largestFrequency = elementFrequency;
}
});
return mostCommonElement;
}
function addVal(v1,v2) {
if (v1.a!=undefined) {
if (v2.a!=undefined) return {a:v1.a+v2.a,b:v1.b+v2.b};
else return {a:v1.a+v2,b:v2.b+v2};
} else if (v2.a!=undefined) return {a:v2.a+v1,b:v2.b+v1};
else return v1+v2;
}
function lowerBound(v) {
if (v.a==undefined) return v; else return v.a;
}
function upperBound(v) {
if (v.b==undefined) return v; else return v.b;
}
function equal(v1,v2) {
return (v1==v2 ||
(upperBound(v1) == upperBound(v2) &&
(lowerBound(v1) == lowerBound(v2))))
}
function overlap(v1,v2) {
return (upperBound(v1) >= lowerBound(v2) && upperBound(v1) <= upperBound(v2)) ||
(upperBound(v2) >= lowerBound(v1) && upperBound(v2) <= upperBound(v1))
}
function containsVal(vl,v) {
for (var i in vl) {
var v2=vl[i];
if (overlap(v,v2)) return true;
}
return false;
}
function centerVal(v) {
if (v.a==undefined) return v; else return (v.a+v.b)/2;
}
function distanceVal (v1,v2) {
return Math.abs(centerVal(v1)-centerVal(v2));
}
function Bounds(vl,v) {
if (vl.length==0) return {a:v,b:v};
else if (v==undefined) return {a:Min(vl),b:Max(vl)};
else return {a:Min([Min(vl),v]),b:Max([Max(vl),v])};
}
function Min(vals) {
var min=none;
Comp.array.iter(vals, function (val) {
if (min==none) min=(val.a==undefined?val:val.a);
else min=val.a==undefined?(val<min?val:min):(val.a<min?val.a:min);
});
return min;
}
function Max(vals) {
var max=none;
Comp.array.iter(vals,function (val) {
if (max==none) max=(val.b==undefined?val:val.b);
else max=(val.b==undefined?(val>max?val:max):(val.b>max?val.a:max));
});
return max;
}
// Return interval of a value x with a<=x_center-eps, b>=x_center+eps
function epsVal(x,eps) {
if (x.a == undefined) return {a:x-eps,b:x+eps};
else if ((x.b-x.a) < 2*eps) return {a:centerVal(x)-eps,b:centerVal(x)+eps};
else return x;
}
/** Filter out unique values that are spaced at least by eps
*
*/
function uniqueEps(data,eps) {
var results=[];
Comp.array.iter(data,function (x) {
var found;
if (!results.length) results.push(x);
else {
Comp.array.iter(results,function (y,i) {
if (found) return;
found = Math.abs(centerVal(x)-centerVal(y))<eps;
if (found) // create new overlapping value with +-eps extensions
results[i]={a:Min([x,y])-eps,b:Max([x,y])+eps}
});
if (!found) results.push(x);
}
});
return results;
}
/** Compact tree, merge nodes and intervals.
** adjust=true: Adjust overlapping feature variable value intervals!!!
*/
function compactTree(model,adjust) {
var i,j,vi,vj,_vals,merged;
function target(model) {
var line;
switch (model.type) {
case NODE_TYPES.RESULT:
return model.name;
case NODE_TYPES.FEATURE:
line = model.name+'?'+target;
Comp.array.iter(model.vals,function (v) {
line += target(v);
});
return line;
case NODE_TYPES.FEATURE_VALUE:
line='='+(model.val.a==undefined?model.val:'['+model.val.a+','+model.val.b+']')+NL;
return line+target(model.child);
}
}
if (!model) return model;
switch (model.type) {
case NODE_TYPES.RESULT:
return model;
break;
case NODE_TYPES.FEATURE:
_vals=[];
// 1. Merge
for (i in model.vals) {
vi=model.vals[i];
assert((vi.type==NODE_TYPES.FEATURE_VALUE)||'vi.type==NODE_TYPES.FEATURE_VALUE');
merged=false;
loopj: for(j in _vals) {
vj=_vals[j];
if (target(vi.child)==target(vj.child)) {
merged=true;
vj.val={a:Min([vi.val,vj.val]),b:Max([vi.val,vj.val])}
break loopj;
}
}
if (!merged) {
_vals.push(vi);
vi.child=compactTree(vi.child);
}
}
// 2. Adjust overlapping value intervals!
if (adjust) {
// TODO: approach too simple!!!!
for (i in _vals) {
i=Comp.pervasives.int_of_string(i);
if (_vals[i+1]) {
if (upperBound(_vals[i].val) > lowerBound(_vals[i+1].val)) {
if (_vals[i].val.b) _vals[i].val.b=lowerBound(_vals[i+1].val)-1;
else _vals[i+1].val.a=upperBound(_vals[i].val)+1;
}
}
}
}
model.vals=_vals;
return model;
break;
case NODE_TYPES.FEATURE_VALUE:
return model;
break;
}
}
/** Creates a new tree from training data (data)
*
* data is {x1:v1,x2:v2,..,y:vn} []
* target is classification key name
* features is ['x1','x2,',..] w/o target variable
* eps is interval applied to all data values
*
*/
function createTree(data, target, features, options) {
var _newS,child_node,bounds;
var targets = Comp.array.unique(Comp.array.pluck(data, target));
// console.log(targets)
if (options.maxdepth==undefined) options.maxdepth=1;
if (options.maxdepth==0) return Result('-');
// console.log(data);
// console.log(features);
//Aios.aios.log('createTree:'+targets.length);
//try {Aios.aios.CP();} catch (e) {throw 'DTI.createTree: '+options.maxdepth };
if (Aios) Aios.aios.CP();
if (targets.length == 1) return Result(targets[0]);
if (features.length == 0) {
var topTarget = mostCommon(targets);
return Result(topTarget)
}
var bestFeatures = getBestFeatures(data, target, features, options.eps);
var bestFeature = bestFeatures[0];
var remainingFeatures = Comp.array.filtermap(bestFeatures,function (feat) {
if (feat.name!=bestFeature.name) return feat.name;
else return none;
});
/*
var possibleValues = Comp.array.sort(Comp.array.pluck(data, bestFeature.name), function (x,y) {
if (upperBound(x) < lowerBound(y)) return -1; else return 1; // increasing value order
});
*/
var possibleValues = getPossibleVals(data,bestFeature.name);
var vals=[];
//console.log(bestFeatures);
//console.log(possibleValues);
var partitions=partitionVals(possibleValues,options.eps);
// Aios.aios.log(partitions);
//console.log(bestFeatures);
//console.log(possibleValues);
if (partitions.length==1) {
// no further 2*eps separation possible, find best feature by largest distance
// resort best feature list with respect to value deviation
bestFeatures.sort(function (ef1,ef2) {
if (ef1.d > ef2.d) return -1; else return 1;
});
bestFeature = bestFeatures[0];
possibleValues = getPossibleVals(data,bestFeature.name);
Comp.array.iter(mergeVals(possibleValues),function (val,i) {
_newS = data.filter(function(x) {
// console.log(x[bestFeature.name],val,overlap(val,x[bestFeature.name]))
return overlap(val,x[bestFeature.name]);
});
child_node = Value(val);
options.maxdepth--;
child_node.child = createTree(_newS, target, remainingFeatures, options);
//console.log(_newS);
vals.push(child_node);
})
} else Comp.array.iter(partitions,function (partition,i) {
_newS = data.filter(function(x) {
// console.log(x[bestFeature.name],v,overlap(x[bestFeature.name],v))
return containsVal(partition,x[bestFeature.name]);
});
bounds = Bounds(partition);
child_node = Value(options.eps==0?{a:bounds.a,b:bounds.b}:{a:bounds.a-options.eps,b:bounds.b+options.eps});
options.maxdepth--;
child_node.child = createTree(_newS, target, remainingFeatures, options);
//console.log(_newS);
vals.push(child_node);
});
return Feature(bestFeature.name,vals);
}
/** Return the depth of the tree
*
*/
function depth(model) {
switch (model.type) {
case NODE_TYPES.RESULT: return 0;
case NODE_TYPES.FEATURE:
return 1+Comp.array.max(model.vals,function (val) {
return depth(val);
});
case NODE_TYPES.FEATURE_VALUE:
return depth(model.child);
}
return 0;
}
/** Computes entropy of a list with 2-epsilon intervals
*
*/
function entropyEps(vals,eps) {
// TODO: overlapping value intervals
var uniqueVals = Comp.array.unique(vals);
var probs = uniqueVals.map(function(x) {
return probEps(x, vals, eps)
});
var logVals = probs.map(function(p) {
return -p * log2(p)
});
return logVals.reduce(function(a, b) {
return a + b
}, 0);
}
function entropyEps2(vals,eps) {
// TODO: overlapping value intervals
var uniqueVals = uniqueEps(vals,eps);
var probs = uniqueVals.map(function(x) {
return probEps2(x, vals, eps)
});
var logVals = probs.map(function(p) {
return -p * log2(p)
});
return logVals.reduce(function(a, b) {
return a + b
}, 0);
}
function getBestFeatures(data,target,features,eps) {
var bestfeatures=[];
function deviation(vals) {
var n = vals.length;
var mu=Comp.array.sum(vals,function (val) {
return (lowerBound(val)+upperBound(val))/2;
})/n;
var dev=Comp.array.sum(vals,function (val) {
return Math.pow(((lowerBound(val)+upperBound(val))/2)-mu,2);
})/n;
return dev;
}
for (var feature in features) {
if (features[feature]==undefined) throw 'DTI.getBestFeatures: invalid feature vector';
var vals=Comp.array.pluck(data, features[feature]).map(function (val) {return val==undefined?0:val});
var e = entropyEps(vals,eps);
var d = deviation(vals);
var min = Min(vals);
var max = Max(vals);
bestfeatures.push({e:e,d:d,range:{a:min,b:max},name:features[feature]});
}
bestfeatures.sort(function (ef1,ef2) {
if (ef1.e > ef2.e) return -1; else return 1;
});
return bestfeatures;
}
/** Find in one data set the most significant feature variable (i.e., with highest value)
*/
function getSignificantFeature(data,features) {
var f,sig;
for (f in features) {
if (sig==undefined || sig.val < data[features[f]]) sig={name:features[f],val:data[features[f]]};
}
return sig;
}
function getPossibleVals(data,feature) {
return Comp.array.sort(Comp.array.pluck(data, feature), function (x,y) {
if (upperBound(x) < lowerBound(y)) return -1; else return 1; // increasing value order
});
}
/** Merge values and intervals
*/
function mergeVals(vals) {
var _vals,
merged,i,j;
for (i in vals) {
var vi = vals[i];
if (!_vals) _vals=[vi];
else {
// Find overlapping values and merge
merged=false;
loopj: for (j in _vals) {
var vj = _vals[j];
if (equal(vi,vj)) {
merged=true;
break loopj;
}
else if (overlap(vi,vj)) {
merged=true;
_vals[j]={a:Min([vi,vj]),b:Max([vi,vj])};
break loopj;
}
}
if (!merged) _vals.push(vi);
}
}
//Aios.aios.log(_vals);
return _vals||[];
}
/**
* Predicts class for sample
*/
function nearestVal(vals,sample,fun) {
var best=none;
for (var v in vals) {
var d=fun?distanceVal(fun(vals[v]),sample):distanceVal(vals[v],sample);
if (best==none)
best={v:vals[v],d:d};
else if (best.d > d)
best={v:vals[v],d:d};
}
if (best) return best.v;
else return none;
}
/** Parttition an ordered set of values
* Each partition of values has at least 2*eps distance to the next partition.
*
*/
function partitionVals(vals,eps) {
var last=none;
var partitions=[];
var partition=[];
for(var i in vals) {
var val0=vals[i];
var val1=vals[i-1];
if (val1==undefined) partition.push(val0);
else if ( upperBound(val0) < upperBound(addVal(val1,2*eps))) partition.push(val0);
else {
partitions.push(partition);
partition=[val0];
}
}
if (partition.length>0) partitions.push(partition);
return partitions;
}
/** Make a predicition with sample data
*
*/
function predict(model,sample) {
var root = model;
while (root && root.type !== NODE_TYPES.RESULT) {
var attr = root.name;
var sampleVal = sample[attr];
var childNode = nearestVal(root.vals,sampleVal,function (node) {
return node.val;
});
if (childNode){
root = childNode.child;
} else {
root = none;
}
}
if (root) return root.name||root.val;
else return none;
};
/** Print the tree
*
*/
function print(model,indent, compact) {
var line='',sep;
if (compact) return results(model);
if (indent==undefined) indent=0;
if (!model) return '';
var sp = function () {return Comp.string.create(indent);};
switch (model.type) {
case NODE_TYPES.RESULT:
return sp()+'-> '+model.name+NL;
case NODE_TYPES.FEATURE:
line=sp()+'$'+model.name+'?'+NL;
Comp.array.iter(model.vals,function (v) {
line += print(v,indent+2);
});
return line;
case NODE_TYPES.FEATURE_VALUE:
line=sp()+'='+(model.val.a==undefined?model.val:'['+model.val.a+','+model.val.b+']')+NL;
return line+print(model.child,indent+2);
}
return 'model?';
}
/**
* Computes probability of of a given value existing in a given list
* with additional 2*epsilon interval, only applicable to numerical values.
*/
function probEps(value, list, eps) {
// TODO: ranges
var occurrences = Comp.array.filter(list, function(element) {
return (element >= (value-eps)) && (element <= (value+eps));
});
var numOccurrences = occurrences.length;
var numElements = list.length;
return numOccurrences / numElements;
}
function probEps2(value, list, eps) {
// TODO: ranges
var occurrences = Comp.array.filter(list, function(element) {
return overlap(epsVal(value), epsVal(element));
});
var numOccurrences = occurrences.length;
var numElements = list.length;
return numOccurrences / numElements;
}
/** Incremental update of the model with new training set(s). Can be executed with an empty model.
* The current tree can be week for a new training set (new target).
* This can result in a classification of the new target with insignificant variables.
* Therefore, the last tree node must be exapnded with an additional strong (most significant)
* variable of the new data set (but it is still a heuristic for future updates).
*/
function updateTree(model,data, target, features, options) {
var eps = options.eps,
maxdepth = options.maxdepth,
verbose = options.verbose;
var featuresINm={}, // All current tree feature variables and their value interval
results=[], // All current tree result leafs
set,i,v,feature,remainingFeatures,exists,sigFeature;
// 1. Analysis of existing model
var analyze = function (model,feature) {
var feature2;
if (!model) return;
switch (model.type) {
case NODE_TYPES.RESULT:
if (!Comp.array.contains(results,model.name)) results.push(model.name);
break;
case NODE_TYPES.FEATURE:
feature2={name:model.name};
if (!featuresINm[model.name]) featuresINm[model.name]=feature2;
Comp.array.iter(model.vals,function (v) { analyze(v,featuresINm[model.name]) });
break;
case NODE_TYPES.FEATURE_VALUE:
if (!feature.val) feature.val={
a:(model.val.a==undefined?model.val:model.val.a),
b:(model.val.a==undefined?model.val:model.val.b)
}; else {
feature.val.a=min(feature.val.a,
(model.val.a==undefined?model.val:model.val.a));
feature.val.b=max(feature.val.b,
(model.val.a==undefined?model.val:model.val.b));
}
analyze(model.child);
break;
}
}
analyze(model);
// console.log(featuresINm);
// console.log(results);
exists=Comp.array.contains(results,data[target]);
// 2a. Empty model, add first training set with two significant feature variable nodes
function init(set) {
set=data[i];
sigFeature1=getSignificantFeature(set,features);
remainingFeatures=Comp.array.filter(features,function (feat) {
return sigFeature1.name!=feat;
});
sigFeature2=getSignificantFeature(set,remainingFeatures);
featuresINm[sigFeature1.name]={name:sigFeature1.name,
val:{a:sigFeature1.val-eps,b:sigFeature1.val+eps}};
featuresINm[sigFeature2.name]={name:sigFeature2.name,
val:{a:sigFeature2.val-eps,b:sigFeature2.val+eps}};
results.push(set[target]);
model=Feature(sigFeature1.name,[
Value({a:set[sigFeature1.name]-eps,b:set[sigFeature1.name]+eps},
Feature(sigFeature2.name,[
Value({a:sigFeature2.val-eps,b:sigFeature2.val+eps},
Result(set[target]))
]))]);
return model;
}
remainingFeatures=Comp.array.filter(features,function (feat) {
return !featuresINm[feat];
});
// 2b. Update the tree with the new training set
var update = function (model,set,feature) {
var feature2,p;
if (!model) return;
switch (model.type) {
case NODE_TYPES.RESULT:
if (model.name != set[target] && verbose)
console.log('Cannot insert new training set '+set[target]+' in tree. No more separating variables!');
break;
case NODE_TYPES.FEATURE:
// console.log(set[target]+': '+ model.name+'='+set[model.name]);
if (set[model.name]<(featuresINm[model.name].val.a-eps) ||
set[model.name]>(featuresINm[model.name].val.b+eps)) {
// add new training set; done
// the current decision tree can be week, thus add another strong variable node, too!
sigFeature=getSignificantFeature(set,remainingFeatures);
featuresINm[sigFeature.name]={name:sigFeature.name,
val:{a:sigFeature.val-eps,b:sigFeature.val+eps}};
featuresINm[model.name].val.a=min(featuresINm[model.name].val.a,set[model.name]-eps);
featuresINm[model.name].val.b=max(featuresINm[model.name].val.b,set[model.name]+eps);
if (!Comp.array.contains(results,set[target])) results.push(set[target]);
model.vals.push(Value({a:set[model.name]-eps,b:set[model.name]+eps},
Feature(sigFeature.name,[
Value({a:sigFeature.val-eps,b:sigFeature.val+eps},
Result(set[target]))
])));
model.vals=Comp.array.sort(model.vals,function (v1,v2) {return (lowerBound(v1.val)<lowerBound(v2.val))?-1:1});
} else {
// go deeper, but extend the interval of the best matching child node with new data variable
Comp.array.iter_break(model.vals,function (fv) {
// console.log(model.name,fv.val,overlap(fv.val,{a:set[model.name]-eps,b:set[model.name]+eps}))
if (overlap(fv.val,{a:set[model.name]-eps,b:set[model.name]+eps})) {
fv.val.a=min(lowerBound(fv.val),set[model.name]-eps);
fv.val.b=max(upperBound(fv.val),set[model.name]+eps);
update(fv,set,model.name);
return true;
} else return false;
});
}
break;
case NODE_TYPES.FEATURE_VALUE:
update(model.child,set);
break;
}
}
for (i in data) {
set=data[i];
if (model==undefined || model.type==undefined)
model=init(set);
else
update(model,set);
}
return model;
}
module.exports = {
NODE_TYPES:NODE_TYPES,
compactTree:compactTree,
create:function (options) {
// type options = {data number [][], target:string, features: string [], eps;number, maxdepth}
return createTree(options.data,options.target,options.features,options)
},
depth:depth,
entropy:entropyEps,
evaluate:function evaluate(model,target,samples){},
predict:predict,
print:print,
results:results,
update:function (model,options) {
// type options = {data number [][], target:string, features: string [], eps:number, maxdepth}
return updateTree(model,options.data,options.target,options.features,options)
},
current:function (module) { current=module.current; Aios=module;}
};