分类分析(CART算法)java实现

CART（Classification and Regression Trees）算法是一种决策树分类算法，适用于离散和连续型特征。下面是一个简单的CART算法的Java实现示例：

import java.util.*;

public class CARTAlgorithm {
    private static final int MAX_DEPTH = 10;
    private static final int MIN_SIZE = 1;

    private static class Node {
        private int featureIndex;
        private double splitValue;
        private Object classification;
        private Node left, right;

        public Node(int featureIndex, double splitValue, Object classification) {
            this.featureIndex = featureIndex;
            this.splitValue = splitValue;
            this.classification = classification;
            left = null;
            right = null;
        }

        public Node(Object classification) {
            this.classification = classification;
            left = null;
            right = null;
        }

        public boolean isLeaf() {
            return left == null && right == null;
        }
    }

    public static Node buildTree(List<double[]> data, Set<Object> classifications) {
        return buildTree(data, classifications, 0);
    }

    private static Node buildTree(List<double[]> data, Set<Object> classifications, int depth) {
        if (depth > MAX_DEPTH || data.size() <= MIN_SIZE) {
            return new Node(getMostCommonClassification(data, classifications));
        }

        int featureIndex = 0;
        double splitValue = 0;
        double lowestMSE = Double.POSITIVE_INFINITY;
        List<List<double[]>> splitData = new ArrayList<>();

        for (int i = 0; i < data.get(0).length - 1; i++) {
            List<double[]> sortedData = new ArrayList<>(data);
            sortedData.sort(Comparator.comparingDouble(a -> a[i]));

            for (int j = 1; j < sortedData.size(); j++) {
                List<double[]> leftData = sortedData.subList(0, j);
                List<double[]> rightData = sortedData.subList(j, sortedData.size());
                double mse = getMSE(leftData, rightData);

                if (mse < lowestMSE) {
                    featureIndex = i;
                    splitValue = (sortedData.get(j - 1)[i] + sortedData.get(j)[i]) / 2.0;
                    lowestMSE = mse;
                    splitData.clear();
                    splitData.add(leftData);
                    splitData.add(rightData);
                }
            }
        }

        Node node = new Node(featureIndex, splitValue, null);
        node.left = buildTree(splitData.get(0), classifications, depth + 1);
        node.right = buildTree(splitData.get(1), classifications, depth + 1);

        return node;
    }

    private static double getMSE(List<double[]> leftData, List<double[]> rightData) {
        Object leftClassification = getMostCommonClassification(leftData, new HashSet<>());
        Object rightClassification = getMostCommonClassification(rightData, new HashSet<>());
        double leftMSE = 0;
        double rightMSE = 0;

        for (double[] data : leftData) {
            leftMSE += Math.pow(data[data.length - 1] - (double) leftClassification, 2);
        }

        for (double[] data : rightData) {
            rightMSE += Math.pow(data[data.length - 1] - (double) rightClassification, 2);
        }

        return leftMSE + rightMSE;
    }

    private static Object getMostCommonClassification(List<double[]> data, Set<Object> classifications) {
        Map<Object, Integer> counts = new HashMap<>();

        for (double[] datum : data) {
            Object classification = datum[datum.length - 1];

            if (!classifications.contains(classification)) {
                classifications.add(classification);
            }

            counts.put(classification, counts.getOrDefault(classification, 0) + 1);
        }

        Object mostCommonClassification = null;
        int highestCount = Integer.MIN_VALUE;

        for (Map.Entry<Object, Integer> entry : counts.entrySet()) {
            if (entry.getValue() > highestCount) {
                mostCommonClassification = entry.getKey();
                highestCount = entry.getValue();
            }
        }

        return mostCommonClassification;
    }

    public static Object predict(Node root, double[] data) {
        while (!root.isLeaf()) {
            if (data[root.featureIndex] < root.splitValue) {
                root = root.left;
            } else {
                root = root.right;
            }
        }

        return root.classification;
    }
}

在这个示例中，我们首先定义了一个节点类，用于表示决策树中的节点。节点可以是叶节点，也可以是内部节点。内部节点包括一个特征索引和一个分割值，用于将数据划分成左右子树。叶节点包括一个分类值。

然后我们定义了一个`buildTree`方法，用于构建决策树。该方法采用递归的方式，根据数据集和分类集合构建节点。在每个节点，我们计算每个特征的最佳分割点，并为其创建一个内部节点。然后我们将数据集分成左右子集，继续构建子树。如果树的深度超过了最大深度或者数据集大小小于等于最小大小，则创建一个叶节点并返回。

我们还定义了一个`predict`方法，用于根据构建的决策树预测新的数据。该方法遍历树并返回叶节点的分类值。

最后，我们使用一些辅助方法来计算节点的最佳分割点、最常见的分类值等。这些方法包括计算均方误差（MSE）、计算出现次数最多的分类值等。

请注意，这只是一个简单的CART算法的示例。实际上，CART算法的实现要复杂得多，并且需要考虑许多细节，例如如何处理缺失值、如何处理连续型特征等。