java - Mahout - 简单的分类问题

Question

我正在尝试构建一个简单的模型，可以将点分类为2D 空间的 2 个分区：

我通过指定几个点和它们所属的分区来训练模型。
我使用模型来预测测试点可能落入的组（分类）。

不幸的是，我没有得到预期的答案。我在我的代码中遗漏了什么还是我做错了什么？

public class SimpleClassifier {

    public static class Point{
        public int x;
        public int y;

        public Point(int x,int y){
            this.x = x;
            this.y = y;
        }

        @Override
        public boolean equals(Object arg0) {
            Point p = (Point)  arg0;
            return( (this.x == p.x) &&(this.y== p.y));
        }

        @Override
        public String toString() {
            // TODO Auto-generated method stub
            return  this.x + " , " + this.y ; 
        }
    }

    public static void main(String[] args) {

        Map<Point,Integer> points = new HashMap<SimpleClassifier.Point, Integer>();

        points.put(new Point(0,0), 0);
        points.put(new Point(1,1), 0);
        points.put(new Point(1,0), 0);
        points.put(new Point(0,1), 0);
        points.put(new Point(2,2), 0);


        points.put(new Point(8,8), 1);
        points.put(new Point(8,9), 1);
        points.put(new Point(9,8), 1);
        points.put(new Point(9,9), 1);


        OnlineLogisticRegression learningAlgo = new OnlineLogisticRegression();
        learningAlgo =  new OnlineLogisticRegression(2, 2, new L1());
        learningAlgo.learningRate(50);

        //learningAlgo.alpha(1).stepOffset(1000);

        System.out.println("training model  \n" );
        for(Point point : points.keySet()){
            Vector v = getVector(point);
            System.out.println(point  + " belongs to " + points.get(point));
            learningAlgo.train(points.get(point), v);
        }

        learningAlgo.close();


        //now classify real data
        Vector v = new RandomAccessSparseVector(2);
        v.set(0, 0.5);
        v.set(1, 0.5);

        Vector r = learningAlgo.classifyFull(v);
        System.out.println(r);

        System.out.println("ans = " );
        System.out.println("no of categories = " + learningAlgo.numCategories());
        System.out.println("no of features = " + learningAlgo.numFeatures());
        System.out.println("Probability of cluster 0 = " + r.get(0));
        System.out.println("Probability of cluster 1 = " + r.get(1));

    }

    public static Vector getVector(Point point){
        Vector v = new DenseVector(2);
        v.set(0, point.x);
        v.set(1, point.y);

        return v;
    }
}

输出：

ans = 
no of categories = 2
no of features = 2
Probability of cluster 0 = 3.9580985042775296E-4
Probability of cluster 1 = 0.9996041901495722

99% 的时间输出显示cluster 1. 为什么？

score 5 · Accepted Answer

问题是您没有包含偏差（截距）项，它始终为 1。您需要将偏差项（1）添加到您的点类中。

这是许多机器学习经验丰富的人犯的一个非常基本的错误。花一些时间学习理论可能是个好主意。Andrew Ng 的讲座是学习的好地方。

为了让您的代码给出预期的输出，需要更改以下内容。

添加了偏置项。
学习参数太高。改成 10

现在你会得到 0 类的 P(0)=0.9999。

这是一个给出正确结果的完整工作示例：

import java.util.HashMap;
import java.util.Map;

import org.apache.mahout.classifier.sgd.L1;
import org.apache.mahout.classifier.sgd.OnlineLogisticRegression;
import org.apache.mahout.math.DenseVector;
import org.apache.mahout.math.RandomAccessSparseVector;
import org.apache.mahout.math.Vector;


class Point{
    public int x;
    public int y;

    public Point(int x,int y){
        this.x = x;
        this.y = y;
    }

    @Override
    public boolean equals(Object arg0) {
        Point p = (Point)  arg0;
        return( (this.x == p.x) &&(this.y== p.y));
    }

    @Override
    public String toString() {
        return  this.x + " , " + this.y ; 
    }
}

public class SimpleClassifier {



    public static void main(String[] args) {

            Map<Point,Integer> points = new HashMap<Point, Integer>();

            points.put(new Point(0,0), 0);
            points.put(new Point(1,1), 0);
            points.put(new Point(1,0), 0);
            points.put(new Point(0,1), 0);
            points.put(new Point(2,2), 0);

            points.put(new Point(8,8), 1);
            points.put(new Point(8,9), 1);
            points.put(new Point(9,8), 1);
            points.put(new Point(9,9), 1);


            OnlineLogisticRegression learningAlgo = new OnlineLogisticRegression();
            learningAlgo =  new OnlineLogisticRegression(2, 3, new L1());
            learningAlgo.lambda(0.1);
            learningAlgo.learningRate(10);

            System.out.println("training model  \n" );

            for(Point point : points.keySet()){

                Vector v = getVector(point);
                System.out.println(point  + " belongs to " + points.get(point));
                learningAlgo.train(points.get(point), v);
            }

            learningAlgo.close();

            Vector v = new RandomAccessSparseVector(3);
            v.set(0, 0.5);
            v.set(1, 0.5);
            v.set(2, 1);

            Vector r = learningAlgo.classifyFull(v);
            System.out.println(r);

            System.out.println("ans = " );
            System.out.println("no of categories = " + learningAlgo.numCategories());
            System.out.println("no of features = " + learningAlgo.numFeatures());
            System.out.println("Probability of cluster 0 = " + r.get(0));
            System.out.println("Probability of cluster 1 = " + r.get(1));

    }

    public static Vector getVector(Point point){
        Vector v = new DenseVector(3);
        v.set(0, point.x);
        v.set(1, point.y);
        v.set(2, 1);
        return v;
    }
}

输出：

2 , 2 belongs to 0
1 , 0 belongs to 0
9 , 8 belongs to 1
8 , 8 belongs to 1
0 , 1 belongs to 0
0 , 0 belongs to 0
1 , 1 belongs to 0
9 , 9 belongs to 1
8 , 9 belongs to 1
{0:2.470723149516907E-6,1:0.9999975292768505}
ans = 
no of categories = 2
no of features = 3
Probability of cluster 0 = 2.470723149516907E-6
Probability of cluster 1 = 0.9999975292768505

请注意，我在 SimpleClassifier 类之外定义了 Point 类，但这只是为了使代码更具可读性，并不是必需的。

看看当你改变学习率时会发生什么。阅读有关交叉验证的说明，以了解如何选择学习率。

Learning Rate => Probability of cluster 0
0.001 => 0.4991116089
0.01 => 0.492481585
0.1 => 0.469961472
1 => 0.5327745322
10 => 0.9745740393
100 => 0
1000 => 0

选择学习率：

运行随机梯度下降是很常见的，就像我们从一个固定的学习率 α 开始一样，通过在算法运行时让学习率 α 慢慢降低到零，也可以确保参数收敛到全局最小值，而不是仅仅围绕最小值振荡。
在这种情况下，当我们使用常数 α 时，您可以进行初始选择，运行梯度下降并观察成本函数，并相应地调整学习率。这里解释

score 1 · Accepted Answer

我想我认为这是您的分类示例的潜在问题：

使用OnlineLogisticRegression训练的默认值（learningRate等...）
引入恒定偏差（它只是另一个具有恒定值的预测变量1）
将训练数据打乱（不要先提供第一个集群对应的训练数据，然后再提供给第二个集群的数据）
显着增加训练数据量

有关此潜在问题的更多详细信息，请参阅Mahout in Action一书。

“修复”潜在问题后的结果
：测试点<0.5, 0.5>被分类为cluster 0概率为 ca。0.89在多次运行中始终如一。
这听起来像是一个合理的输出，因为原点附近的其他点（用于训练模型）也属于cluster 0.

代码

public class SimpleClassifier {

    public static class Point {
        public int x;
        public int y;

        public Point(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public boolean equals(Object arg0) {
            Point p = (Point) arg0;
            return ((this.x == p.x) && (this.y == p.y));
        }

        @Override
        public String toString() {
            // TODO Auto-generated method stub
            return this.x + " , " + this.y;
        }
    }

    public static void main(String[] args) {

        Map<Point, Integer> points = new HashMap<Point, Integer>();

        points.put(new Point(0, 0), 0);
        points.put(new Point(1, 1), 0);
        points.put(new Point(1, 0), 0);
        points.put(new Point(0, 1), 0);
        points.put(new Point(2, 2), 0);


        points.put(new Point(8, 8), 1);
        points.put(new Point(8, 9), 1);
        points.put(new Point(9, 8), 1);
        points.put(new Point(9, 9), 1);


        OnlineLogisticRegression learningAlgo = new OnlineLogisticRegression(2, 3, new L1());

        System.out.println("training model  \n");
        for (int i=0; i<100; i++) {
            List<Point> randomPoints = new ArrayList<>(points.keySet());
            Collections.shuffle(randomPoints);
            for (Point point : randomPoints) {
                Vector v = getVector(point);
                System.out.println(point + " belongs to " + points.get(point));
                learningAlgo.train(points.get(point), v);
            }
        }
        learningAlgo.close();


        //now classify real data
        Vector v = new RandomAccessSparseVector(3);
        v.set(0, 0.5);
        v.set(1, 0.5);
        v.set(2, 1);

        Vector r = learningAlgo.classify(v);
        System.out.println(r);

        System.out.println("ans = ");
        System.out.println("no of categories = " + learningAlgo.numCategories());
        System.out.println("no of features = " + learningAlgo.numFeatures());
        System.out.println("Probability of cluster 0 = " + (1.0d - r.get(0)));
        System.out.println("Probability of cluster 1 = " + r.get(0));

    }

    public static Vector getVector(Point point) {
        Vector v = new DenseVector(3);
        v.set(0, point.x);
        v.set(1, point.y);
        v.set(2, 1);

        return v;
    }
}

java - Mahout - 简单的分类问题

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