用Java实现MVPtree——MVPtree核心算法代码的搭建

　　项目需要，需要把MVPtree这种冷门的数据结构写入Java，然网上没有成形的Java实现，虽说C++看惯了不过对C++实现复杂结构也是看得蒙蔽，幸好客户给了个github上job什么的人用Java写的VPtree，大体结构可以嵌入MVPtree。

　　对于MVPtree的其他信息请左转百度= =本文只讲述算法实现。

　　点查找树结构主要需解决的问题有2个：如何减少非必要点的搜索，以及如何减少距离计算次数。前者的解决方法比较容易想到，把点集分割为左右对称的两半长方形，或者脑洞大点的，通过距离切分（效率很高，因为所有查询都是基于点距离的）成为圆和圆环。后者适用面不是很广，优化思路通常是预先计算与基准点的距离，查询点时筛点。

　　VPtree就是使用距离划分点集的例子。每个结点一个点集，随意定个点作为基准点，然后把点集根据与基准点距离分成数量相等的2个子集，这2个子集再分别进入此结点的子结点，用点查找出点集的过程如出一辙，但是没有对第2点进行优化，这个结构适合于距离函数是曼哈顿距离或者欧几里得距离的情况。

　　MVPtree继承了VPtree用距离划分的特点，只不过一个结点会划分4个点集，同时通过path数组限制距离函数运行次数。划分为4个点集而不是2个点集，可以分割得细一些，减少无效点；使用一定数量的基准点限制，可以在查询频繁的情况下减少距离计算次数，并且这些基准点通常被切分得很散，大片大片的无效区域被排除了，效果拔群。这个结构适合于距离函数是计算次数过高的切比雪夫函数之流。

　　接下来就是代码的实现了。

　　MVPtree与VPtree的点有个不同之处，就是MVPtree的点还附上了与基准点的距离数组，这里就需要使用特别的点数据结构：MVPtree用点

　　核心代码如下：

public class MVPTreePoint<P> {

    private ArrayList<Double> path;

    private P point;

    private final int maxLevel;

    public MVPTreePoint(final P point, final int maxLevel) {
        this.point = point;
        this.maxLevel = maxLevel;
        this.path = new ArrayList<>();
    }

    public void addDistanceToSelf(final MVPTreePoint<P> vantagePointElement, final DistanceFunction<P> distanceFunction) {
        if(this.path.size() < this.maxLevel)
            this.path.add(distanceFunction.getDistance(this.point, vantagePointElement.point));
    }

    public void addDistanceToSelf(final P vantagePoint, final DistanceFunction<P> distanceFunction) {
        if(this.path.size() < this.maxLevel)
            this.path.add(distanceFunction.getDistance(this.point, vantagePoint));
    }

    public void addDistanceToSelf(final double distance) {
        if(this.path.size() < this.maxLevel) {
            this.path.add(distance);
        }
    }

    public void removeDistanceToSelf(final int position) {
        if(position < this.path.size()) {
            this.path.remove(position);
        }
    }

    public double getDistanceToSelf(int i) {
        return this.path.get(i);
    }

    public int size() {
        return this.path.size();
    }

    public void clearPath() {
        this.path.clear();
    }

    public P getPoint() {
        return this.point;
    }

    @SuppressWarnings("unchecked")
    public boolean equals(Object o){
        MVPTreePoint<P> t = (MVPTreePoint<P>) o;
        return this.point.equals(t.point);
    }
}

MVPTreePoint

　　把距离数组写到点类上而不是集成到树结点类上，结构会清晰一些，并且从点里取出距离也方便。

　　MVPtree与VPtree有好多不同的地方，但是好多都只是改一下类名，把P,E改成MVPTreePoint<P>,MVPTreePoint<E>，这里主讲核心算法——初始化树和点查询。

　　初始化MVPtree不仅要多选出一个基准点，多切分2次数组，还要把基准点到每个点的距离都分别储存起来。

　　capacity就是叶子结点的容量，要设中间一些，根据数据规模定吧。

　　原论文把基准点从点集取出来放到单独的位置上，但是实际编写程序时，把基准点仅仅当作一个基准点，基准点还是作为点集的一部分初始化。这样，数据结构仅仅是多出quantityOfPoint/capacity个点，但是程序编写方便了很多。

public MVPTreeNode(
            final Collection<MVPTreePoint<E>> pointNodes,
            final DistanceFunction<P> distanceFunction,
            final MVPThresholdSelectionStrategy<P, E> thresholdSelectionStrategy,
            final int capacity, final int maxLevel) {

        if (capacity < 1) {
            throw new IllegalArgumentException("Capacity must be positive.");
        }

        if (pointNodes.isEmpty()) {
            throw new IllegalArgumentException(
                    "Cannot create a MVPTreeNode with an empty list of points.");
        }

        this.capacity = capacity;
        this.maxLevel = maxLevel;
        this.distanceFunction = distanceFunction;
        this.thresholdSelectionStrategy = thresholdSelectionStrategy;
        this.pointNodes = new ArrayList<>(pointNodes);
        this.children = new MVPTreeNode[2][2];
        this.vantagePoint = (E[]) new Object[2];
        this.secondThreshold = new double[2];

        this.anneal();
    }

    protected void anneal() {
        if (this.pointNodes == null) {
            int childrenSize[][] = new int[2][2];
            for (int i = 0; i < 2; i++) {
                for (int j = 0; j < 2; j++) {
                    childrenSize[i][j] = this.children[i][j].size();
                }
            }

            if (childrenSize[0][0] == 0 || childrenSize[0][1] == 0
                    || childrenSize[1][0] == 0 || childrenSize[1][1] == 0) {
                // One of the child nodes has become empty, and needs to be
                // pruned.
                this.pointNodes = new ArrayList<>(childrenSize[0][0]
                        + childrenSize[0][1] + childrenSize[1][0]
                        + childrenSize[1][1]);
                this.addAllPointsToCollection(this.pointNodes);
                for (MVPTreePoint<E> pointNode : this.pointNodes) {
                    pointNode.clearPath();
                }
                for (int i = 0; i < 2; i++) {
                    for (int j = 0; j < 2; j++) {
                        this.children[i][j] = null;
                    }
                }
                this.anneal();
            } else {
                for (int i = 0; i < 2; i++) {
                    for (int j = 0; j < 2; j++) {
                        this.children[i][j].anneal();
                    }
                }
            }
        } else {
            int firstVantagePointIndex = new Random().nextInt(this.pointNodes
                    .size());
            this.vantagePoint[0] = this.pointNodes.get(firstVantagePointIndex)
                    .getPoint();
            this.firstThreshold = this.thresholdSelectionStrategy
                    .selectThreshold(this.pointNodes, this.vantagePoint[0],
                            this.distanceFunction);
            int firstIndexPastThreshold;
            try {
                firstIndexPastThreshold = MVPTreeNode.partitionPoints(
                        this.pointNodes, this.vantagePoint[0],
                        this.firstThreshold, this.distanceFunction);

            } catch (final PartitionException e) {
                this.storeInOneNode();
                return;
            }

            if (this.pointNodes.size() > this.capacity) {
                List<MVPTreePoint<E>> subTreeList[] = new List[2];

                subTreeList[0] = this.pointNodes.subList(0,
                        firstIndexPastThreshold);
                subTreeList[1] = this.pointNodes.subList(
                        firstIndexPastThreshold, this.pointNodes.size());

                // if points can be divided into 2 parts, find second vantage
                // point and try to split point array
                int secondVantagePointIndex = new Random()
                        .nextInt(subTreeList[1].size());
                this.vantagePoint[1] = subTreeList[1].get(
                        secondVantagePointIndex).getPoint();
                int splitPosition[] = new int[2];
                for (int i = 0; i < 2; i++) {
                    this.secondThreshold[i] = this.thresholdSelectionStrategy
                            .selectThreshold(subTreeList[i],
                                    this.vantagePoint[1], this.distanceFunction);
                    try {
                        splitPosition[i] = MVPTreeNode.partitionPoints(
                                subTreeList[i], this.vantagePoint[1],
                                this.secondThreshold[i], this.distanceFunction);
                    } catch (final PartitionException e) {
                        this.storeInOneNode();
                        return;
                    }
                }
                for (MVPTreePoint<E> pointNode : this.pointNodes) {
                    pointNode.addDistanceToSelf(this.distanceFunction
                            .getDistance(pointNode.getPoint(),
                                    this.vantagePoint[0]));
                    pointNode.addDistanceToSelf(this.distanceFunction
                            .getDistance(pointNode.getPoint(),
                                    this.vantagePoint[1]));
                }
                for (int i = 0; i < 2; i++) {
                    this.children[i][0] = new MVPTreeNode<>(
                            subTreeList[i].subList(0, splitPosition[i]),
                            this.distanceFunction,
                            this.thresholdSelectionStrategy, this.capacity,
                            this.maxLevel);
                    this.children[i][1] = new MVPTreeNode<>(
                            subTreeList[i].subList(splitPosition[i],
                                    subTreeList[i].size()),
                            this.distanceFunction,
                            this.thresholdSelectionStrategy, this.capacity,
                            this.maxLevel);
                }
                this.pointNodes = null;
            } else {
                this.storeInOneNode();
            }
        }
    }

    private void storeInOneNode() {
        int maxIndex = 0;
        double maxDistance = this.distanceFunction.getDistance(this.pointNodes
                .get(0).getPoint(), this.vantagePoint[0]);
        for (int i = 1; i < this.pointNodes.size(); i++) {
            double curDistance = this.distanceFunction.getDistance(
                    this.pointNodes.get(i).getPoint(), this.vantagePoint[0]);
            if (maxDistance < curDistance) {
                maxDistance = curDistance;
                maxIndex = i;
            }
        }
        this.vantagePoint[1] = this.pointNodes.get(maxIndex).getPoint();

        for (int i = 0; i < 2; i++) {
            for (int j = 0; j < 2; j++) {
                this.children[i][j] = null;
            }
        }
    }

init MVPtree

　　原作者给出了2种查询方式：找离查询点前k近点和找离查询点不远于u点。

　　找离查询点前k点的算法可以沿用查询VPtree时的做法，先查找查询点所在的子结点，再查找其他子结点，注意要先判定收集者是否装满（没装满的话，不管是啥点都直接塞），再判定收集者与查询点的最远距离（对第二种查找方式来说是固定距离）是否小于点/点集与查询点的最近距离（在树结点和叶子结点都有用处）。

public void collectNearestNeighbors(
            final NearestNeighborCollector<P, E> collector, int depth) {
        if (this.pointNodes == null) {
            // O1-Q
            final double distanceFromFirstVantagePointToQueryPoint = this.distanceFunction
                .getDistance(this.vantagePoint[0],
                    collector.getQueryPoint().getPoint());

            // O2-Q
            final double distanceFromSecondVantagePointToQueryPoint = this.distanceFunction
                .getDistance(this.vantagePoint[1],
                    collector.getQueryPoint().getPoint());

            collector.getQueryPoint().addDistanceToSelf(
                    distanceFromFirstVantagePointToQueryPoint);
            collector.getQueryPoint().addDistanceToSelf(
                    distanceFromSecondVantagePointToQueryPoint);

            final MVPTreeNode<P, E> index = this
                    .getChildNodeForPoint(collector.getQueryPoint().getPoint());
            index.collectNearestNeighbors(collector, depth + 1);

            // O1-Q - O1-S1
            double basicDistance = distanceFromFirstVantagePointToQueryPoint
                    - this.firstThreshold;

            for(int i = 0;i < 2;i ++){
                if (!collector.isFull() || basicDistance <= collector.getRadius()) {
                    // O2-Q - O2-S2
                    double touchDistance = distanceFromSecondVantagePointToQueryPoint
                            - this.secondThreshold[i];

                    for(int j = 0;j < 2;j ++){
                        if (index != this.children[i][j]
                                && (!collector.isFull() || touchDistance <= collector.getRadius())) {
                            this.children[i][j].collectNearestNeighbors(collector, depth + 1);
                        }
                        touchDistance *= -1;
                    }
                }
                basicDistance *= -1;
            }
            collector.getQueryPoint().removeDistanceToSelf(depth + depth + 1);
            collector.getQueryPoint().removeDistanceToSelf(depth + depth);
        } else {
            for (final MVPTreePoint<E> pointNode : this.pointNodes) {
                if(!collector.isFull() || this.isAbleToInsert(collector.getRadius(),
                                collector.getQueryPoint(), pointNode)) {
                    collector.offerPoint(pointNode.getPoint());
                }
            }
        }
    }

collectNearestNeighbors

　　找离查询点不远于u点算法就是论文里讲述的算法，执行步骤与收集第k近有相同之处，不同在于限定距离是固定值，且任何时候都必须判定，点集没有数量限制。

public void collectAllWithinDistance(final MVPTreePoint<P> queryPoint,
            final double maxDistance, final Collection<E> collection, int depth) {
        if (this.pointNodes == null) {
            final double distanceFromFirstVantagePointToQueryPoint = this.distanceFunction
                    .getDistance(this.vantagePoint[0], queryPoint.getPoint());
            final double distanceFromSecondVantagePointToQueryPoint = this.distanceFunction
                    .getDistance(this.vantagePoint[1], queryPoint.getPoint());

            queryPoint
                    .addDistanceToSelf(distanceFromFirstVantagePointToQueryPoint);
            queryPoint
                    .addDistanceToSelf(distanceFromSecondVantagePointToQueryPoint);

            // We want to search any of this node's children that intersect with
            // the query region
            if (distanceFromFirstVantagePointToQueryPoint <= this.firstThreshold
                    + maxDistance) {
                if (distanceFromSecondVantagePointToQueryPoint <= this.secondThreshold[0]
                        + maxDistance) {
                    this.children[0][0].collectAllWithinDistance(queryPoint,
                            maxDistance, collection, depth + 1);
                }

                if (distanceFromSecondVantagePointToQueryPoint + maxDistance >= this.secondThreshold[0]) {
                    this.children[0][1].collectAllWithinDistance(queryPoint,
                            maxDistance, collection, depth + 1);
                }
            }

            if (distanceFromFirstVantagePointToQueryPoint + maxDistance >= this.firstThreshold) {
                if (distanceFromSecondVantagePointToQueryPoint <= this.secondThreshold[1]
                        + maxDistance) {
                    this.children[1][0].collectAllWithinDistance(queryPoint,
                            maxDistance, collection, depth + 1);
                }

                if (distanceFromSecondVantagePointToQueryPoint + maxDistance >= this.secondThreshold[1]) {
                    this.children[1][1].collectAllWithinDistance(queryPoint,
                            maxDistance, collection, depth + 1);
                }
            }
            queryPoint.removeDistanceToSelf(depth + depth + 1);
            queryPoint.removeDistanceToSelf(depth + depth);
        } else {
            for (MVPTreePoint<E> pointNode : pointNodes) {
                if (this.isAbleToInsert(maxDistance, queryPoint, pointNode))
                    collection.add(pointNode.getPoint());
            }
        }
    }

collectAllWithinDistance

　　这两种查询方式都需要比较预先计算的距离，把这种计算合为一个函数：

public boolean isAbleToInsert(double limitDistance,
            MVPTreePoint<P> queryPoint, MVPTreePoint<E> pointNode) {

        for (int i = 0; i < queryPoint.size(); i++) {
            double disOffset = queryPoint.getDistanceToSelf(i)
                    - pointNode.getDistanceToSelf(i);

            if (Math.abs(disOffset) > limitDistance) {
                return false;
            }
        }

        return this.distanceFunction.getDistance(pointNode.getPoint(),
                queryPoint.getPoint()) <= limitDistance;
    }

isAbleToInsert

　　其他函数也需要修改，但是没有像这3个函数一样大幅度的修改结构。

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代码地址：https://coding.net/u/funcfans/p/MVPtree-for-Java/git