commons-math-neuralnet/src/main/java/org/apache/commons/math4/neuralnet/Network.java - commons-math - Git at Google

 /*
  * 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.
  */

 package org.apache.commons.math4.neuralnet;

 import java.io.Serializable;
 import java.io.ObjectInputStream;
 import java.util.NoSuchElementException;
 import java.util.List;
 import java.util.ArrayList;
 import java.util.Set;
 import java.util.HashSet;
 import java.util.Collection;
 import java.util.Iterator;
 import java.util.Comparator;
 import java.util.Collections;
 import java.util.Map;
 import java.util.concurrent.ConcurrentHashMap;
 import java.util.concurrent.atomic.AtomicLong;
 import java.util.stream.Collectors;

 import org.apache.commons.math4.neuralnet.internal.NeuralNetException;

 /**
  * Neural network, composed of {@link Neuron} instances and the links
  * between them.
  *
  * Although updating a neuron's state is thread-safe, modifying the
  * network's topology (adding or removing links) is not.
  *
  * @since 3.3
  */
 public class Network
     implements Iterable<Neuron>,
                Serializable {
     /** Serializable. */
     private static final long serialVersionUID = 20130207L;
     /** Neurons. */
     private final ConcurrentHashMap<Long, Neuron> neuronMap
         = new ConcurrentHashMap<>();
     /** Next available neuron identifier. */
     private final AtomicLong nextId;
     /** Neuron's features set size. */
     private final int featureSize;
     /** Links. */
     private final ConcurrentHashMap<Long, Set<Long>> linkMap
         = new ConcurrentHashMap<>();

     /**
      * Comparator that prescribes an order of the neurons according
      * to the increasing order of their identifier.
      */
     public static class NeuronIdentifierComparator
         implements Comparator<Neuron>,
                    Serializable {
         /** Version identifier. */
         private static final long serialVersionUID = 20130207L;

         /** {@inheritDoc} */
         @Override
         public int compare(Neuron a,
                            Neuron b) {
             final long aId = a.getIdentifier();
             final long bId = b.getIdentifier();
             return aId < bId ? -1 :
                 aId > bId ? 1 : 0;
         }
     }

     /**
      * Constructor with restricted access, solely used for deserialization.
      *
      * @param nextId Next available identifier.
      * @param featureSize Number of features.
      * @param neuronList Neurons.
      * @param neighbourIdList Links associated to each of the neurons in
      * {@code neuronList}.
      * @throws IllegalStateException if an inconsistency is detected
      * (which probably means that the serialized form has been corrupted).
      */
     Network(long nextId,
             int featureSize,
             Neuron[] neuronList,
             long[][] neighbourIdList) {
         final int numNeurons = neuronList.length;
         if (numNeurons != neighbourIdList.length) {
             throw new IllegalStateException();
         }

         for (int i = 0; i < numNeurons; i++) {
             final Neuron n = neuronList[i];
             final long id = n.getIdentifier();
             if (id >= nextId) {
                 throw new IllegalStateException();
             }
             neuronMap.put(id, n);
             linkMap.put(id, new HashSet<Long>());
         }

         for (int i = 0; i < numNeurons; i++) {
             final long aId = neuronList[i].getIdentifier();
             final Set<Long> aLinks = linkMap.get(aId);
             for (final Long bId : neighbourIdList[i]) {
                 if (neuronMap.get(bId) == null) {
                     throw new IllegalStateException();
                 }
                 addLinkToLinkSet(aLinks, bId);
             }
         }

         this.nextId = new AtomicLong(nextId);
         this.featureSize = featureSize;
     }

     /**
      * @param initialIdentifier Identifier for the first neuron that
      * will be added to this network.
      * @param featureSize Size of the neuron's features.
      */
     public Network(long initialIdentifier,
                    int featureSize) {
         nextId = new AtomicLong(initialIdentifier);
         this.featureSize = featureSize;
     }

     /**
      * Performs a deep copy of this instance.
      * Upon return, the copied and original instances will be independent:
      * Updating one will not affect the other.
      *
      * @return a new instance with the same state as this instance.
      * @since 3.6
      */
     public synchronized Network copy() {
         final Network copy = new Network(nextId.get(),
                                          featureSize);


         for (final Map.Entry<Long, Neuron> e : neuronMap.entrySet()) {
             copy.neuronMap.put(e.getKey(), e.getValue().copy());
         }

         for (final Map.Entry<Long, Set<Long>> e : linkMap.entrySet()) {
             copy.linkMap.put(e.getKey(), new HashSet<>(e.getValue()));
         }

         return copy;
     }

     /**
      * {@inheritDoc}
      */
     @Override
     public Iterator<Neuron> iterator() {
         return neuronMap.values().iterator();
     }

     /**
      * Creates a list of the neurons, sorted in a custom order.
      *
      * @param comparator {@link Comparator} used for sorting the neurons.
      * @return a list of neurons, sorted in the order prescribed by the
      * given {@code comparator}.
      * @see NeuronIdentifierComparator
      */
     public Collection<Neuron> getNeurons(Comparator<Neuron> comparator) {
         final List<Neuron> neurons = new ArrayList<>(neuronMap.values());

         Collections.sort(neurons, comparator);

         return neurons;
     }

     /**
      * Creates a neuron and assigns it a unique identifier.
      *
      * @param features Initial values for the neuron's features.
      * @return the neuron's identifier.
      * @throws IllegalArgumentException if the length of {@code features}
      * is different from the expected size (as set by the
      * {@link #Network(long,int) constructor}).
      */
     public long createNeuron(double[] features) {
         if (features.length != featureSize) {
             throw new NeuralNetException(NeuralNetException.SIZE_MISMATCH,
                                          features.length, featureSize);
         }

         final long id = createNextId();
         neuronMap.put(id, new Neuron(id, features));
         linkMap.put(id, new HashSet<Long>());
         return id;
     }

     /**
      * Deletes a neuron.
      * Links from all neighbours to the removed neuron will also be
      * {@link #deleteLink(Neuron,Neuron) deleted}.
      *
      * @param neuron Neuron to be removed from this network.
      * @throws NoSuchElementException if {@code n} does not belong to
      * this network.
      */
     public void deleteNeuron(Neuron neuron) {
         // Delete links to from neighbours.
         getNeighbours(neuron).forEach(neighbour -> deleteLink(neighbour, neuron));

         // Remove neuron.
         neuronMap.remove(neuron.getIdentifier());
     }

     /**
      * Gets the size of the neurons' features set.
      *
      * @return the size of the features set.
      */
     public int getFeaturesSize() {
         return featureSize;
     }

     /**
      * Adds a link from neuron {@code a} to neuron {@code b}.
      * Note: the link is not bi-directional; if a bi-directional link is
      * required, an additional call must be made with {@code a} and
      * {@code b} exchanged in the argument list.
      *
      * @param a Neuron.
      * @param b Neuron.
      * @throws NoSuchElementException if the neurons do not exist in the
      * network.
      */
     public void addLink(Neuron a,
                         Neuron b) {
         // Check that the neurons belong to this network.
         final long aId = a.getIdentifier();
         if (a != getNeuron(aId)) {
             throw new NoSuchElementException(Long.toString(aId));
         }
         final long bId = b.getIdentifier();
         if (b != getNeuron(bId)) {
             throw new NoSuchElementException(Long.toString(bId));
         }

         // Add link from "a" to "b".
         addLinkToLinkSet(linkMap.get(aId), bId);
     }

     /**
      * Adds a link to neuron {@code id} in given {@code linkSet}.
      * Note: no check verifies that the identifier indeed belongs
      * to this network.
      *
      * @param linkSet Neuron identifier.
      * @param id Neuron identifier.
      */
     private void addLinkToLinkSet(Set<Long> linkSet,
                                   long id) {
         linkSet.add(id);
     }

     /**
      * Deletes the link between neurons {@code a} and {@code b}.
      *
      * @param a Neuron.
      * @param b Neuron.
      * @throws NoSuchElementException if the neurons do not exist in the
      * network.
      */
     public void deleteLink(Neuron a,
                            Neuron b) {
         // Check that the neurons belong to this network.
         final long aId = a.getIdentifier();
         if (a != getNeuron(aId)) {
             throw new NoSuchElementException(Long.toString(aId));
         }
         final long bId = b.getIdentifier();
         if (b != getNeuron(bId)) {
             throw new NoSuchElementException(Long.toString(bId));
         }

         // Delete link from "a" to "b".
         deleteLinkFromLinkSet(linkMap.get(aId), bId);
     }

     /**
      * Deletes a link to neuron {@code id} in given {@code linkSet}.
      * Note: no check verifies that the identifier indeed belongs
      * to this network.
      *
      * @param linkSet Neuron identifier.
      * @param id Neuron identifier.
      */
     private void deleteLinkFromLinkSet(Set<Long> linkSet,
                                        long id) {
         linkSet.remove(id);
     }

     /**
      * Retrieves the neuron with the given (unique) {@code id}.
      *
      * @param id Identifier.
      * @return the neuron associated with the given {@code id}.
      * @throws NoSuchElementException if the neuron does not exist in the
      * network.
      */
     public Neuron getNeuron(long id) {
         final Neuron n = neuronMap.get(id);
         if (n == null) {
             throw new NoSuchElementException(Long.toString(id));
         }
         return n;
     }

     /**
      * Retrieves the neurons in the neighbourhood of any neuron in the
      * {@code neurons} list.
      * @param neurons Neurons for which to retrieve the neighbours.
      * @return the list of neighbours.
      * @see #getNeighbours(Iterable,Iterable)
      */
     public Collection<Neuron> getNeighbours(Iterable<Neuron> neurons) {
         return getNeighbours(neurons, null);
     }

     /**
      * Retrieves the neurons in the neighbourhood of any neuron in the
      * {@code neurons} list.
      * The {@code exclude} list allows to retrieve the "concentric"
      * neighbourhoods by removing the neurons that belong to the inner
      * "circles".
      *
      * @param neurons Neurons for which to retrieve the neighbours.
      * @param exclude Neurons to exclude from the returned list.
      * Can be {@code null}.
      * @return the list of neighbours.
      */
     public Collection<Neuron> getNeighbours(Iterable<Neuron> neurons,
                                             Iterable<Neuron> exclude) {
         final Set<Long> idList = new HashSet<>();
         neurons.forEach(n -> idList.addAll(linkMap.get(n.getIdentifier())));

         if (exclude != null) {
             exclude.forEach(n -> idList.remove(n.getIdentifier()));
         }

         return idList.stream().map(this::getNeuron).collect(Collectors.toList());
     }

     /**
      * Retrieves the neighbours of the given neuron.
      *
      * @param neuron Neuron for which to retrieve the neighbours.
      * @return the list of neighbours.
      * @see #getNeighbours(Neuron,Iterable)
      */
     public Collection<Neuron> getNeighbours(Neuron neuron) {
         return getNeighbours(neuron, null);
     }

     /**
      * Retrieves the neighbours of the given neuron.
      *
      * @param neuron Neuron for which to retrieve the neighbours.
      * @param exclude Neurons to exclude from the returned list.
      * Can be {@code null}.
      * @return the list of neighbours.
      */
     public Collection<Neuron> getNeighbours(Neuron neuron,
                                             Iterable<Neuron> exclude) {
         final Set<Long> idList = linkMap.get(neuron.getIdentifier());
         if (exclude != null) {
             for (final Neuron n : exclude) {
                 idList.remove(n.getIdentifier());
             }
         }

         final List<Neuron> neuronList = new ArrayList<>();
         for (final Long id : idList) {
             neuronList.add(getNeuron(id));
         }

         return neuronList;
     }

     /**
      * Creates a neuron identifier.
      *
      * @return a value that will serve as a unique identifier.
      */
     private Long createNextId() {
         return nextId.getAndIncrement();
     }

     /**
      * Prevents proxy bypass.
      *
      * @param in Input stream.
      */
     private void readObject(ObjectInputStream in) {
         throw new IllegalStateException();
     }

     /**
      * Custom serialization.
      *
      * @return the proxy instance that will be actually serialized.
      */
     private Object writeReplace() {
         final Neuron[] neuronList = neuronMap.values().toArray(new Neuron[0]);
         final long[][] neighbourIdList = new long[neuronList.length][];

         for (int i = 0; i < neuronList.length; i++) {
             final Collection<Neuron> neighbours = getNeighbours(neuronList[i]);
             final long[] neighboursId = new long[neighbours.size()];
             int count = 0;
             for (final Neuron n : neighbours) {
                 neighboursId[count] = n.getIdentifier();
                 ++count;
             }
             neighbourIdList[i] = neighboursId;
         }

         return new SerializationProxy(nextId.get(),
                                       featureSize,
                                       neuronList,
                                       neighbourIdList);
     }

     /**
      * Serialization.
      */
     private static class SerializationProxy implements Serializable {
         /** Serializable. */
         private static final long serialVersionUID = 20130207L;
         /** Next identifier. */
         private final long nextId;
         /** Number of features. */
         private final int featureSize;
         /** Neurons. */
         private final Neuron[] neuronList;
         /** Links. */
         private final long[][] neighbourIdList;

         /**
          * @param nextId Next available identifier.
          * @param featureSize Number of features.
          * @param neuronList Neurons.
          * @param neighbourIdList Links associated to each of the neurons in
          * {@code neuronList}.
          */
         SerializationProxy(long nextId,
                            int featureSize,
                            Neuron[] neuronList,
                            long[][] neighbourIdList) {
             this.nextId = nextId;
             this.featureSize = featureSize;
             this.neuronList = neuronList;
             this.neighbourIdList = neighbourIdList;
         }

         /**
          * Custom serialization.
          *
          * @return the {@link Network} for which this instance is the proxy.
          */
         private Object readResolve() {
             return new Network(nextId,
                                featureSize,
                                neuronList,
                                neighbourIdList);
         }
     }
 }
	/*
	* 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.
	*/

	package org.apache.commons.math4.neuralnet;

	import java.io.Serializable;
	import java.io.ObjectInputStream;
	import java.util.NoSuchElementException;
	import java.util.List;
	import java.util.ArrayList;
	import java.util.Set;
	import java.util.HashSet;
	import java.util.Collection;
	import java.util.Iterator;
	import java.util.Comparator;
	import java.util.Collections;
	import java.util.Map;
	import java.util.concurrent.ConcurrentHashMap;
	import java.util.concurrent.atomic.AtomicLong;
	import java.util.stream.Collectors;

	import org.apache.commons.math4.neuralnet.internal.NeuralNetException;

	/**
	* Neural network, composed of {@link Neuron} instances and the links
	* between them.
	*
	* Although updating a neuron's state is thread-safe, modifying the
	* network's topology (adding or removing links) is not.
	*
	* @since 3.3
	*/
	public class Network
	implements Iterable<Neuron>,
	Serializable {
	/** Serializable. */
	private static final long serialVersionUID = 20130207L;
	/** Neurons. */
	private final ConcurrentHashMap<Long, Neuron> neuronMap
	= new ConcurrentHashMap<>();
	/** Next available neuron identifier. */
	private final AtomicLong nextId;
	/** Neuron's features set size. */
	private final int featureSize;
	/** Links. */
	private final ConcurrentHashMap<Long, Set<Long>> linkMap
	= new ConcurrentHashMap<>();

	/**
	* Comparator that prescribes an order of the neurons according
	* to the increasing order of their identifier.
	*/
	public static class NeuronIdentifierComparator
	implements Comparator<Neuron>,
	Serializable {
	/** Version identifier. */
	private static final long serialVersionUID = 20130207L;

	/** {@inheritDoc} */
	@Override
	public int compare(Neuron a,
	Neuron b) {
	final long aId = a.getIdentifier();
	final long bId = b.getIdentifier();
	return aId < bId ? -1 :
	aId > bId ? 1 : 0;
	}
	}

	/**
	* Constructor with restricted access, solely used for deserialization.
	*
	* @param nextId Next available identifier.
	* @param featureSize Number of features.
	* @param neuronList Neurons.
	* @param neighbourIdList Links associated to each of the neurons in
	* {@code neuronList}.
	* @throws IllegalStateException if an inconsistency is detected
	* (which probably means that the serialized form has been corrupted).
	*/
	Network(long nextId,
	int featureSize,
	Neuron[] neuronList,
	long[][] neighbourIdList) {
	final int numNeurons = neuronList.length;
	if (numNeurons != neighbourIdList.length) {
	throw new IllegalStateException();
	}

	for (int i = 0; i < numNeurons; i++) {
	final Neuron n = neuronList[i];
	final long id = n.getIdentifier();
	if (id >= nextId) {
	throw new IllegalStateException();
	}
	neuronMap.put(id, n);
	linkMap.put(id, new HashSet<Long>());
	}

	for (int i = 0; i < numNeurons; i++) {
	final long aId = neuronList[i].getIdentifier();
	final Set<Long> aLinks = linkMap.get(aId);
	for (final Long bId : neighbourIdList[i]) {
	if (neuronMap.get(bId) == null) {
	throw new IllegalStateException();
	}
	addLinkToLinkSet(aLinks, bId);
	}
	}

	this.nextId = new AtomicLong(nextId);
	this.featureSize = featureSize;
	}

	/**
	* @param initialIdentifier Identifier for the first neuron that
	* will be added to this network.
	* @param featureSize Size of the neuron's features.
	*/
	public Network(long initialIdentifier,
	int featureSize) {
	nextId = new AtomicLong(initialIdentifier);
	this.featureSize = featureSize;
	}

	/**
	* Performs a deep copy of this instance.
	* Upon return, the copied and original instances will be independent:
	* Updating one will not affect the other.
	*
	* @return a new instance with the same state as this instance.
	* @since 3.6
	*/
	public synchronized Network copy() {
	final Network copy = new Network(nextId.get(),
	featureSize);


	for (final Map.Entry<Long, Neuron> e : neuronMap.entrySet()) {
	copy.neuronMap.put(e.getKey(), e.getValue().copy());
	}

	for (final Map.Entry<Long, Set<Long>> e : linkMap.entrySet()) {
	copy.linkMap.put(e.getKey(), new HashSet<>(e.getValue()));
	}

	return copy;
	}

	/**
	* {@inheritDoc}
	*/
	@Override
	public Iterator<Neuron> iterator() {
	return neuronMap.values().iterator();
	}

	/**
	* Creates a list of the neurons, sorted in a custom order.
	*
	* @param comparator {@link Comparator} used for sorting the neurons.
	* @return a list of neurons, sorted in the order prescribed by the
	* given {@code comparator}.
	* @see NeuronIdentifierComparator
	*/
	public Collection<Neuron> getNeurons(Comparator<Neuron> comparator) {
	final List<Neuron> neurons = new ArrayList<>(neuronMap.values());

	Collections.sort(neurons, comparator);

	return neurons;
	}

	/**
	* Creates a neuron and assigns it a unique identifier.
	*
	* @param features Initial values for the neuron's features.
	* @return the neuron's identifier.
	* @throws IllegalArgumentException if the length of {@code features}
	* is different from the expected size (as set by the
	* {@link #Network(long,int) constructor}).
	*/
	public long createNeuron(double[] features) {
	if (features.length != featureSize) {
	throw new NeuralNetException(NeuralNetException.SIZE_MISMATCH,
	features.length, featureSize);
	}

	final long id = createNextId();
	neuronMap.put(id, new Neuron(id, features));
	linkMap.put(id, new HashSet<Long>());
	return id;
	}

	/**
	* Deletes a neuron.
	* Links from all neighbours to the removed neuron will also be
	* {@link #deleteLink(Neuron,Neuron) deleted}.
	*
	* @param neuron Neuron to be removed from this network.
	* @throws NoSuchElementException if {@code n} does not belong to
	* this network.
	*/
	public void deleteNeuron(Neuron neuron) {
	// Delete links to from neighbours.
	getNeighbours(neuron).forEach(neighbour -> deleteLink(neighbour, neuron));

	// Remove neuron.
	neuronMap.remove(neuron.getIdentifier());
	}

	/**
	* Gets the size of the neurons' features set.
	*
	* @return the size of the features set.
	*/
	public int getFeaturesSize() {
	return featureSize;
	}

	/**
	* Adds a link from neuron {@code a} to neuron {@code b}.
	* Note: the link is not bi-directional; if a bi-directional link is
	* required, an additional call must be made with {@code a} and
	* {@code b} exchanged in the argument list.
	*
	* @param a Neuron.
	* @param b Neuron.
	* @throws NoSuchElementException if the neurons do not exist in the
	* network.
	*/
	public void addLink(Neuron a,
	Neuron b) {
	// Check that the neurons belong to this network.
	final long aId = a.getIdentifier();
	if (a != getNeuron(aId)) {
	throw new NoSuchElementException(Long.toString(aId));
	}
	final long bId = b.getIdentifier();
	if (b != getNeuron(bId)) {
	throw new NoSuchElementException(Long.toString(bId));
	}

	// Add link from "a" to "b".
	addLinkToLinkSet(linkMap.get(aId), bId);
	}

	/**
	* Adds a link to neuron {@code id} in given {@code linkSet}.
	* Note: no check verifies that the identifier indeed belongs
	* to this network.
	*
	* @param linkSet Neuron identifier.
	* @param id Neuron identifier.
	*/
	private void addLinkToLinkSet(Set<Long> linkSet,
	long id) {
	linkSet.add(id);
	}

	/**
	* Deletes the link between neurons {@code a} and {@code b}.
	*
	* @param a Neuron.
	* @param b Neuron.
	* @throws NoSuchElementException if the neurons do not exist in the
	* network.
	*/
	public void deleteLink(Neuron a,
	Neuron b) {
	// Check that the neurons belong to this network.
	final long aId = a.getIdentifier();
	if (a != getNeuron(aId)) {
	throw new NoSuchElementException(Long.toString(aId));
	}
	final long bId = b.getIdentifier();
	if (b != getNeuron(bId)) {
	throw new NoSuchElementException(Long.toString(bId));
	}

	// Delete link from "a" to "b".
	deleteLinkFromLinkSet(linkMap.get(aId), bId);
	}

	/**
	* Deletes a link to neuron {@code id} in given {@code linkSet}.
	* Note: no check verifies that the identifier indeed belongs
	* to this network.
	*
	* @param linkSet Neuron identifier.
	* @param id Neuron identifier.
	*/
	private void deleteLinkFromLinkSet(Set<Long> linkSet,
	long id) {
	linkSet.remove(id);
	}

	/**
	* Retrieves the neuron with the given (unique) {@code id}.
	*
	* @param id Identifier.
	* @return the neuron associated with the given {@code id}.
	* @throws NoSuchElementException if the neuron does not exist in the
	* network.
	*/
	public Neuron getNeuron(long id) {
	final Neuron n = neuronMap.get(id);
	if (n == null) {
	throw new NoSuchElementException(Long.toString(id));
	}
	return n;
	}

	/**
	* Retrieves the neurons in the neighbourhood of any neuron in the
	* {@code neurons} list.
	* @param neurons Neurons for which to retrieve the neighbours.
	* @return the list of neighbours.
	* @see #getNeighbours(Iterable,Iterable)
	*/
	public Collection<Neuron> getNeighbours(Iterable<Neuron> neurons) {
	return getNeighbours(neurons, null);
	}

	/**
	* Retrieves the neurons in the neighbourhood of any neuron in the
	* {@code neurons} list.
	* The {@code exclude} list allows to retrieve the "concentric"
	* neighbourhoods by removing the neurons that belong to the inner
	* "circles".
	*
	* @param neurons Neurons for which to retrieve the neighbours.
	* @param exclude Neurons to exclude from the returned list.
	* Can be {@code null}.
	* @return the list of neighbours.
	*/
	public Collection<Neuron> getNeighbours(Iterable<Neuron> neurons,
	Iterable<Neuron> exclude) {
	final Set<Long> idList = new HashSet<>();
	neurons.forEach(n -> idList.addAll(linkMap.get(n.getIdentifier())));

	if (exclude != null) {
	exclude.forEach(n -> idList.remove(n.getIdentifier()));
	}

	return idList.stream().map(this::getNeuron).collect(Collectors.toList());
	}

	/**
	* Retrieves the neighbours of the given neuron.
	*
	* @param neuron Neuron for which to retrieve the neighbours.
	* @return the list of neighbours.
	* @see #getNeighbours(Neuron,Iterable)
	*/
	public Collection<Neuron> getNeighbours(Neuron neuron) {
	return getNeighbours(neuron, null);
	}

	/**
	* Retrieves the neighbours of the given neuron.
	*
	* @param neuron Neuron for which to retrieve the neighbours.
	* @param exclude Neurons to exclude from the returned list.
	* Can be {@code null}.
	* @return the list of neighbours.
	*/
	public Collection<Neuron> getNeighbours(Neuron neuron,
	Iterable<Neuron> exclude) {
	final Set<Long> idList = linkMap.get(neuron.getIdentifier());
	if (exclude != null) {
	for (final Neuron n : exclude) {
	idList.remove(n.getIdentifier());
	}
	}

	final List<Neuron> neuronList = new ArrayList<>();
	for (final Long id : idList) {
	neuronList.add(getNeuron(id));
	}

	return neuronList;
	}

	/**
	* Creates a neuron identifier.
	*
	* @return a value that will serve as a unique identifier.
	*/
	private Long createNextId() {
	return nextId.getAndIncrement();
	}

	/**
	* Prevents proxy bypass.
	*
	* @param in Input stream.
	*/
	private void readObject(ObjectInputStream in) {
	throw new IllegalStateException();
	}

	/**
	* Custom serialization.
	*
	* @return the proxy instance that will be actually serialized.
	*/
	private Object writeReplace() {
	final Neuron[] neuronList = neuronMap.values().toArray(new Neuron[0]);
	final long[][] neighbourIdList = new long[neuronList.length][];

	for (int i = 0; i < neuronList.length; i++) {
	final Collection<Neuron> neighbours = getNeighbours(neuronList[i]);
	final long[] neighboursId = new long[neighbours.size()];
	int count = 0;
	for (final Neuron n : neighbours) {
	neighboursId[count] = n.getIdentifier();
	++count;
	}
	neighbourIdList[i] = neighboursId;
	}

	return new SerializationProxy(nextId.get(),
	featureSize,
	neuronList,
	neighbourIdList);
	}

	/**
	* Serialization.
	*/
	private static class SerializationProxy implements Serializable {
	/** Serializable. */
	private static final long serialVersionUID = 20130207L;
	/** Next identifier. */
	private final long nextId;
	/** Number of features. */
	private final int featureSize;
	/** Neurons. */
	private final Neuron[] neuronList;
	/** Links. */
	private final long[][] neighbourIdList;

	/**
	* @param nextId Next available identifier.
	* @param featureSize Number of features.
	* @param neuronList Neurons.
	* @param neighbourIdList Links associated to each of the neurons in
	* {@code neuronList}.
	*/
	SerializationProxy(long nextId,
	int featureSize,
	Neuron[] neuronList,
	long[][] neighbourIdList) {
	this.nextId = nextId;
	this.featureSize = featureSize;
	this.neuronList = neuronList;
	this.neighbourIdList = neighbourIdList;
	}

	/**
	* Custom serialization.
	*
	* @return the {@link Network} for which this instance is the proxy.
	*/
	private Object readResolve() {
	return new Network(nextId,
	featureSize,
	neuronList,
	neighbourIdList);
	}
	}
	}