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# "Learning Algorithm that can handle complex input relationships?"

Member Posts: 60 Contributor II
edited May 2019 in Help
Is there a learning algorithm that can handle complicated input relationships?  For example, say I feed in 7 signals and it turns out that the difference between two of the signals perfectly explains the output signal.  Or what if the output is equal to 2 times one of the inputs, but only if another input is equal to 3, otherwise, the output is equal to some kind of function of the other inputs.  Is there a learning algorithm that can learn those types of inputs?
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Member Posts: 849 Maven
Hi there!

Indeed there is, check out the 'Generate Function Set' operator, and there is an example of how to use it here...

http://www.myexperiment.org/workflows/1321.html

You'll need to provide the data as indicated..

Have fun.

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Member Posts: 60 Contributor II
So that's basically a pre-processing step based on a genetic algorithm for combining operators.  There's no off-the-shelf learning algorithm which can analyze inputs as I described and come up with some relation.  I did read about one open-source project called Eureqa which can discover such relationships, but it also uses a pre-defined list of operations.  It's not fully generic so you have to have some idea of what you are searching for.
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Member Posts: 849 Maven
Hi there,

When you say..
 So that's basically a pre-processing step based on a genetic algorithm for combining operators.
What are you referring to, the operator ' Generate Function Set ', or the example I pointed to? The reason I ask is that the source of the operator is like this ...
`/* *  RapidMiner * *  Copyright (C) 2001-2010 by Rapid-I and the contributors * *  Complete list of developers available at our web site: * *       http://rapid-i.com * *  This program is free software: you can redistribute it and/or modify *  it under the terms of the GNU Affero General Public License as published by *  the Free Software Foundation, either version 3 of the License, or *  (at your option) any later version. * *  This program is distributed in the hope that it will be useful, *  but WITHOUT ANY WARRANTY; without even the implied warranty of *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the *  GNU Affero General Public License for more details. * *  You should have received a copy of the GNU Affero General Public License *  along with this program.  If not, see http://www.gnu.org/licenses/. */package com.rapidminer.operator.features.construction;import java.util.ArrayList;import java.util.Iterator;import java.util.LinkedList;import java.util.List;import com.rapidminer.example.Attribute;import com.rapidminer.example.ExampleSet;import com.rapidminer.generator.AbsoluteValueGenerator;import com.rapidminer.generator.BasicArithmeticOperationGenerator;import com.rapidminer.generator.ExponentialFunctionGenerator;import com.rapidminer.generator.FeatureGenerator;import com.rapidminer.generator.FloorCeilGenerator;import com.rapidminer.generator.MinMaxGenerator;import com.rapidminer.generator.PowerGenerator;import com.rapidminer.generator.ReciprocalValueGenerator;import com.rapidminer.generator.SquareRootGenerator;import com.rapidminer.generator.TrigonometricFunctionGenerator;import com.rapidminer.operator.OperatorDescription;import com.rapidminer.operator.OperatorException;import com.rapidminer.operator.ports.metadata.AttributeMetaData;import com.rapidminer.operator.ports.metadata.ExampleSetMetaData;import com.rapidminer.operator.ports.metadata.MetaData;import com.rapidminer.parameter.ParameterType;import com.rapidminer.parameter.ParameterTypeBoolean;import com.rapidminer.parameter.UndefinedParameterError;import com.rapidminer.tools.Ontology;import com.rapidminer.tools.math.MathFunctions;/** * This operator applies a set of functions on all features of the input example set. Applicable functions include +, -, * *, /, norm, sin, cos, tan, atan, exp, log, min, max, floor, ceil, round, sqrt, abs, and pow. Features with two * arguments will be applied on all pairs. Non commutative functions will also be applied on all permutations. *  * @see com.rapidminer.generator.FeatureGenerator * @author Ingo Mierswa */public class CompleteFeatureGenerationOperator extends AbstractFeatureConstruction {	/**	 * The parameter name for &quot;If set to true, all the original attributes are kept, otherwise they are removed	 * from the example set.&quot;	 */	public static final String PARAMETER_KEEP_ALL = "keep_all";	/** The parameter name for &quot;Generate sums.&quot; */	public static final String PARAMETER_USE_PLUS = "use_plus";	/** The parameter name for &quot;Generate differences.&quot; */	public static final String PARAMETER_USE_DIFF = "use_diff";	/** The parameter name for &quot;Generate products.&quot; */	public static final String PARAMETER_USE_MULT = "use_mult";	/** The parameter name for &quot;Generate quotients.&quot; */	public static final String PARAMETER_USE_DIV = "use_div";	/** The parameter name for &quot;Generate reciprocal values.&quot; */	public static final String PARAMETER_USE_RECIPROCALS = "use_reciprocals";	/** The parameter name for &quot;Generate square root values.&quot; */	public static final String PARAMETER_USE_SQUARE_ROOTS = "use_square_roots";	/** The parameter name for &quot;Generate the power of one attribute and another.&quot; */	public static final String PARAMETER_USE_POWER_FUNCTIONS = "use_power_functions";	/** The parameter name for &quot;Generate sinus.&quot; */	public static final String PARAMETER_USE_SIN = "use_sin";	/** The parameter name for &quot;Generate cosinus.&quot; */	public static final String PARAMETER_USE_COS = "use_cos";	/** The parameter name for &quot;Generate tangens.&quot; */	public static final String PARAMETER_USE_TAN = "use_tan";	/** The parameter name for &quot;Generate arc tangens.&quot; */	public static final String PARAMETER_USE_ATAN = "use_atan";	/** The parameter name for &quot;Generate exponential functions.&quot; */	public static final String PARAMETER_USE_EXP = "use_exp";	/** The parameter name for &quot;Generate logarithmic functions.&quot; */	public static final String PARAMETER_USE_LOG = "use_log";	/** The parameter name for &quot;Generate absolute values.&quot; */	public static final String PARAMETER_USE_ABSOLUTE_VALUES = "use_absolute_values";	/** The parameter name for &quot;Generate minimum values.&quot; */	public static final String PARAMETER_USE_MIN = "use_min";	/** The parameter name for &quot;Generate maximum values.&quot; */	public static final String PARAMETER_USE_MAX = "use_max";	/** The parameter name for &quot;Generate ceil values.&quot; */	public static final String PARAMETER_USE_CEIL = "use_ceil";	/** The parameter name for &quot;Generate floor values.&quot; */	public static final String PARAMETER_USE_FLOOR = "use_floor";	/** The parameter name for &quot;Generate rounded values.&quot; */	public static final String PARAMETER_USE_ROUNDED = "use_rounded";	public CompleteFeatureGenerationOperator(OperatorDescription description) {		super(description);	}@Override	protected MetaData modifyMetaData(ExampleSetMetaData metaData) throws UndefinedParameterError {		// counting numerical attributes		int numberOfNumerical = 0;		for (AttributeMetaData amd : metaData.getAllAttributes()) {			if (amd.isNumerical() && !amd.isSpecial())				numberOfNumerical++;		}		// clear regular if needed		if (!getParameterAsBoolean(PARAMETER_KEEP_ALL))			metaData.clearRegular();		// new ones		int numberOfAdditionalAttributes = 0;		int commutativeNonSelfapplicable = MathFunctions.factorial(numberOfNumerical - 1);		int commutativeSelfapplicable = MathFunctions.factorial(numberOfNumerical);		int nonCommuatativeSelfApplicable = numberOfNumerical * numberOfNumerical;		int nonCommuatativeNonSelfApplicable = numberOfNumerical * numberOfNumerical;		if (getParameterAsBoolean(PARAMETER_USE_PLUS))			numberOfAdditionalAttributes += commutativeNonSelfapplicable;		if (getParameterAsBoolean(PARAMETER_USE_DIFF))			numberOfAdditionalAttributes += nonCommuatativeNonSelfApplicable;		if (getParameterAsBoolean(PARAMETER_USE_MULT))			numberOfAdditionalAttributes += commutativeSelfapplicable;		if (getParameterAsBoolean(PARAMETER_USE_DIV))			numberOfAdditionalAttributes += nonCommuatativeNonSelfApplicable;		if (getParameterAsBoolean(PARAMETER_USE_RECIPROCALS))			numberOfAdditionalAttributes += numberOfNumerical;		if (getParameterAsBoolean(PARAMETER_USE_SQUARE_ROOTS)) {			numberOfAdditionalAttributes += numberOfNumerical;		}		if (getParameterAsBoolean(PARAMETER_USE_POWER_FUNCTIONS)) {			numberOfAdditionalAttributes += nonCommuatativeSelfApplicable;		}		if (getParameterAsBoolean(PARAMETER_USE_SIN))			numberOfAdditionalAttributes += numberOfNumerical;		if (getParameterAsBoolean(PARAMETER_USE_COS))			numberOfAdditionalAttributes += numberOfNumerical;		if (getParameterAsBoolean(PARAMETER_USE_TAN))			numberOfAdditionalAttributes += numberOfNumerical;		if (getParameterAsBoolean(PARAMETER_USE_ATAN))			numberOfAdditionalAttributes += numberOfNumerical;		if (getParameterAsBoolean(PARAMETER_USE_EXP))			numberOfAdditionalAttributes += numberOfNumerical;		if (getParameterAsBoolean(PARAMETER_USE_LOG))			numberOfAdditionalAttributes += numberOfNumerical;		if (getParameterAsBoolean(PARAMETER_USE_ABSOLUTE_VALUES))			numberOfAdditionalAttributes += numberOfNumerical;		if (getParameterAsBoolean(PARAMETER_USE_MIN))			numberOfAdditionalAttributes += commutativeNonSelfapplicable;		if (getParameterAsBoolean(PARAMETER_USE_MAX))			numberOfAdditionalAttributes += commutativeNonSelfapplicable;		if (getParameterAsBoolean(PARAMETER_USE_CEIL))			numberOfAdditionalAttributes += numberOfNumerical;		if (getParameterAsBoolean(PARAMETER_USE_FLOOR))			numberOfAdditionalAttributes += numberOfNumerical;		if (getParameterAsBoolean(PARAMETER_USE_ROUNDED))			numberOfAdditionalAttributes += numberOfNumerical;		for (int i = 0; i < numberOfAdditionalAttributes; i++) {			if (i == 0)				metaData.addAttribute(new AttributeMetaData("gensym", Ontology.REAL));			else				metaData.addAttribute(new AttributeMetaData("gensym" + i, Ontology.REAL));		}		return metaData;	}@Override	public ExampleSet apply(ExampleSet exampleSet) throws OperatorException {		// set selection mode to restrictive mode		FeatureGenerator.setSelectionMode(FeatureGenerator.SELECTION_MODE_RESTRICTIVE);		List<FeatureGenerator> generators = getGenerators();		List<FeatureGenerator> generatorList = new LinkedList<FeatureGenerator>();		Iterator<FeatureGenerator> i = generators.iterator();		while (i.hasNext()) {			FeatureGenerator generator = i.next();			List<Attribute[]> inputAttributes = generator.getInputCandidates(exampleSet, new String[0]);			Iterator<Attribute[]> a = inputAttributes.iterator();			while (a.hasNext()) {				Attribute[] args = a.next();				FeatureGenerator newGenerator = generator.newInstance();				newGenerator.setArguments(args);				generatorList.add(newGenerator);			}		}		// generate all new attributes		if (!getParameterAsBoolean(PARAMETER_KEEP_ALL)) {			exampleSet.getAttributes().clearRegular();		}		List<Attribute> newAttributes = FeatureGenerator.generateAll(exampleSet.getExampleTable(), generatorList);		for (Attribute newAttribute : newAttributes)			exampleSet.getAttributes().addRegular(newAttribute);		return exampleSet;	}	private List<FeatureGenerator> getGenerators() {		List<FeatureGenerator> generators = new ArrayList<FeatureGenerator>();		if (getParameterAsBoolean(PARAMETER_USE_PLUS))			generators.add(new BasicArithmeticOperationGenerator(BasicArithmeticOperationGenerator.SUM));		if (getParameterAsBoolean(PARAMETER_USE_DIFF))			generators.add(new BasicArithmeticOperationGenerator(BasicArithmeticOperationGenerator.DIFFERENCE));		if (getParameterAsBoolean(PARAMETER_USE_MULT))			generators.add(new BasicArithmeticOperationGenerator(BasicArithmeticOperationGenerator.PRODUCT));		if (getParameterAsBoolean(PARAMETER_USE_DIV))			generators.add(new BasicArithmeticOperationGenerator(BasicArithmeticOperationGenerator.QUOTIENT));		if (getParameterAsBoolean(PARAMETER_USE_RECIPROCALS))			generators.add(new ReciprocalValueGenerator());		if (getParameterAsBoolean(PARAMETER_USE_SQUARE_ROOTS)) {			generators.add(new SquareRootGenerator());		}		if (getParameterAsBoolean(PARAMETER_USE_POWER_FUNCTIONS)) {			generators.add(new PowerGenerator());		}		if (getParameterAsBoolean(PARAMETER_USE_SIN))			generators.add(new TrigonometricFunctionGenerator(TrigonometricFunctionGenerator.SINUS));		if (getParameterAsBoolean(PARAMETER_USE_COS))			generators.add(new TrigonometricFunctionGenerator(TrigonometricFunctionGenerator.COSINUS));		if (getParameterAsBoolean(PARAMETER_USE_TAN))			generators.add(new TrigonometricFunctionGenerator(TrigonometricFunctionGenerator.TANGENS));		if (getParameterAsBoolean(PARAMETER_USE_ATAN))			generators.add(new TrigonometricFunctionGenerator(TrigonometricFunctionGenerator.ARC_TANGENS));		if (getParameterAsBoolean(PARAMETER_USE_EXP))			generators.add(new ExponentialFunctionGenerator(ExponentialFunctionGenerator.EXP));		if (getParameterAsBoolean(PARAMETER_USE_LOG))			generators.add(new ExponentialFunctionGenerator(ExponentialFunctionGenerator.LOG));		if (getParameterAsBoolean(PARAMETER_USE_ABSOLUTE_VALUES))			generators.add(new AbsoluteValueGenerator());		if (getParameterAsBoolean(PARAMETER_USE_MIN))			generators.add(new MinMaxGenerator(MinMaxGenerator.MIN));		if (getParameterAsBoolean(PARAMETER_USE_MAX))			generators.add(new MinMaxGenerator(MinMaxGenerator.MAX));		if (getParameterAsBoolean(PARAMETER_USE_CEIL))			generators.add(new FloorCeilGenerator(FloorCeilGenerator.CEIL));		if (getParameterAsBoolean(PARAMETER_USE_FLOOR))			generators.add(new FloorCeilGenerator(FloorCeilGenerator.FLOOR));		if (getParameterAsBoolean(PARAMETER_USE_ROUNDED))			generators.add(new FloorCeilGenerator(FloorCeilGenerator.ROUND));		return generators;	}@Override	public List<ParameterType> getParameterTypes() {		List<ParameterType> types = super.getParameterTypes();		types.add(new ParameterTypeBoolean(PARAMETER_KEEP_ALL, "If set to true, all the original attributes are kept, otherwise they are removed from the example set.", true, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_PLUS, "Generate sums.", false, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_DIFF, "Generate differences.", false, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_MULT, "Generate products.", false, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_DIV, "Generate quotients.", false, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_RECIPROCALS, "Generate reciprocal values.", false, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_SQUARE_ROOTS, "Generate square root values.", false, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_POWER_FUNCTIONS, "Generate the power of one attribute and another.", false, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_SIN, "Generate sinus.", false, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_COS, "Generate cosinus.", false, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_TAN, "Generate tangens.", false, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_ATAN, "Generate arc tangens.", false, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_EXP, "Generate exponential functions.", false, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_LOG, "Generate logarithmic functions.", false, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_ABSOLUTE_VALUES, "Generate absolute values.", false, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_MIN, "Generate minimum values.", false, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_MAX, "Generate maximum values.", false, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_CEIL, "Generate ceil values.", false, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_FLOOR, "Generate floor values.", false, false));		types.add(new ParameterTypeBoolean(PARAMETER_USE_ROUNDED, "Generate rounded values.", false, false));		return types;	}}`
and the example XML is just a loop that keeps the best formulae in the 'Construction" column of the meta-data. So where is  the genetic algorithm hiding? Ah, Eureka! It is there! http://www.hakank.org/eureqa/

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Administrator, Moderator, Employee, RapidMiner Certified Analyst, RapidMiner Certified Expert, Community Manager, RMResearcher, Member, University Professor Posts: 1,751 RM Founder
Hi,

want to add a note (since I did a lot of research in this topic like 10 years ago):

- if you want an automatic way for creating those complex features and their interactions, you could try the operator Yagga2
- personally I think that having this automatic feature construction with a robust inner learner is much more stable than for example Genetic Programming, but of course this would also be an option for you
- if you want to read more about this, you could try some of my papers including the second part of my PhD: http://www-ai.cs.uni-dortmund.de/PERSONAL/mierswa.html

Cheers,
Ingo