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:

1. 我通过指定几个点和它们所属的分区来训练模型.
2. 我使用该模型来预测组(分类),其中,测试点可能落在.

不幸的是,我没有得到预期的答案.我在代码中遗漏了什么,或者我做错了什么？

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%的输出显示出更多的概率cluster 1.为什么？

Answer 1

问题是你没有包含偏差(截距)项,它始终为1.你需要在你的点类中加入偏差项(1).

这是许多有经验的人在机器学习中犯下的一个非常基本的错误.在学习理论上投入一些时间可能是个好主意.Andrew Ng的讲座是一个值得学习的好地方.

要使代码得到预期的输出,需要更改以下内容.

1. 偏见增加.
2. 学习参数太高了.将其更改为10

现在你将得到0级的P(0)= 0.9999.

这是一个完整的工作示例,可以给出正确的结果:

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类之外定义了类Point,但这只是为了使代码更具可读性并且不是必需的.

看看改变学习率时会发生什么.阅读有关交叉验证的说明,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:

1. 运行随机梯度下降是常见的,因为我们通过以固定学习速率α开始,通过在算法运行时缓慢地让学习速率α减小到零,也可以确保参数将收敛到全局最小而不是仅仅围绕最小值振荡.
2. 在这种情况下,当我们使用常数α时,您可以进行初始选择,运行梯度下降和观察成本函数,并相应地调整学习率.这里解释一下