Java PageRank 实现

PageRank 是 Google 早期用于对网页进行排名的算法，下面我将提供一个完整的 Java 实现，包括基本算法和优化版本。

基本 PageRank 实现

import java.util.*;
public class BasicPageRank {
    private Map<String, Double> pageRanks;
    private Map<String, List<String>> graph;
    private int totalNodes;
    private double dampingFactor = 0.85;
    private int maxIterations = 100;
    private double tolerance = 0.0001;
    public BasicPageRank(Map<String, List<String>> graph) {
        this.graph = graph;
        this.totalNodes = graph.size();
        this.pageRanks = new HashMap<>();
        initializePageRanks();
    }
    private void initializePageRanks() {
        double initialRank = 1.0 / totalNodes;
        for (String node : graph.keySet()) {
            pageRanks.put(node, initialRank);
        }
    }
    public void compute() {
        for (int i = 0; i < maxIterations; i++) {
            Map<String, Double> newRanks = new HashMap<>();
            double maxDiff = 0.0;
            for (String node : graph.keySet()) {
                double rank = (1 - dampingFactor) / totalNodes;
                for (Map.Entry<String, List<String>> entry : graph.entrySet()) {
                    String source = entry.getKey();
                    List<String> outgoingLinks = entry.getValue();
                    if (outgoingLinks.contains(node)) {
                        rank += dampingFactor * (pageRanks.get(source) / outgoingLinks.size());
                    }
                }
                newRanks.put(node, rank);
                maxDiff = Math.max(maxDiff, Math.abs(pageRanks.get(node) - rank));
            }
            pageRanks = newRanks;
            if (maxDiff < tolerance) {
                System.out.println("Converged after " + (i + 1) + " iterations");
                break;
            }
        }
    }
    public Map<String, Double> getPageRanks() {
        return pageRanks;
    }
    public static void main(String[] args) {
        // 示例图结构
        Map<String, List<String>> graph = new HashMap<>();
        graph.put("A", Arrays.asList("B", "C"));
        graph.put("B", Arrays.asList("C"));
        graph.put("C", Arrays.asList("A"));
        graph.put("D", Arrays.asList("C"));
        BasicPageRank pageRank = new BasicPageRank(graph);
        pageRank.compute();
        System.out.println("PageRank Results:");
        pageRank.getPageRanks().entrySet().stream()
            .sorted(Map.Entry.<String, Double>comparingByValue().reversed())
            .forEach(entry -> System.out.println(entry.getKey() + ": " + entry.getValue()));
    }
}

优化版 PageRank 实现（使用矩阵运算）

import java.util.*;
public class OptimizedPageRank {
    private Map<String, Integer> nodeToIndex;
    private List<String> indexToNode;
    private double[][] transitionMatrix;
    private double[] pageRanks;
    private int totalNodes;
    private double dampingFactor = 0.85;
    private int maxIterations = 100;
    private double tolerance = 0.0001;
    public OptimizedPageRank(Map<String, List<String>> graph) {
        this.totalNodes = graph.size();
        initializeNodeMappings(graph);
        buildTransitionMatrix(graph);
        initializePageRanks();
    }
    private void initializeNodeMappings(Map<String, List<String>> graph) {
        nodeToIndex = new HashMap<>();
        indexToNode = new ArrayList<>();
        int index = 0;
        for (String node : graph.keySet()) {
            nodeToIndex.put(node, index);
            indexToNode.add(node);
            index++;
        }
    }
    private void buildTransitionMatrix(Map<String, List<String>> graph) {
        transitionMatrix = new double[totalNodes][totalNodes];
        for (Map.Entry<String, List<String>> entry : graph.entrySet()) {
            String source = entry.getKey();
            List<String> outgoingLinks = entry.getValue();
            int sourceIndex = nodeToIndex.get(source);
            if (outgoingLinks.isEmpty()) {
                // 处理悬挂节点（没有出边的节点）
                for (int j = 0; j < totalNodes; j++) {
                    transitionMatrix[sourceIndex][j] = 1.0 / totalNodes;
                }
            } else {
                for (String target : outgoingLinks) {
                    int targetIndex = nodeToIndex.get(target);
                    transitionMatrix[sourceIndex][targetIndex] = 1.0 / outgoingLinks.size();
                }
            }
        }
    }
    private void initializePageRanks() {
        pageRanks = new double[totalNodes];
        Arrays.fill(pageRanks, 1.0 / totalNodes);
    }
    public void compute() {
        for (int i = 0; i < maxIterations; i++) {
            double[] newRanks = new double[totalNodes];
            double maxDiff = 0.0;
            for (int j = 0; j < totalNodes; j++) {
                double rank = (1 - dampingFactor) / totalNodes;
                for (int k = 0; k < totalNodes; k++) {
                    rank += dampingFactor * transitionMatrix[k][j] * pageRanks[k];
                }
                newRanks[j] = rank;
                maxDiff = Math.max(maxDiff, Math.abs(pageRanks[j] - rank));
            }
            pageRanks = newRanks;
            if (maxDiff < tolerance) {
                System.out.println("Converged after " + (i + 1) + " iterations");
                break;
            }
        }
    }
    public Map<String, Double> getPageRanks() {
        Map<String, Double> result = new HashMap<>();
        for (int i = 0; i < totalNodes; i++) {
            result.put(indexToNode.get(i), pageRanks[i]);
        }
        return result;
    }
    public static void main(String[] args) {
        // 示例图结构
        Map<String, List<String>> graph = new HashMap<>();
        graph.put("A", Arrays.asList("B", "C"));
        graph.put("B", Arrays.asList("C"));
        graph.put("C", Arrays.asList("A"));
        graph.put("D", Arrays.asList("C"));
        OptimizedPageRank pageRank = new OptimizedPageRank(graph);
        pageRank.compute();
        System.out.println("PageRank Results:");
        pageRank.getPageRanks().entrySet().stream()
            .sorted(Map.Entry.<String, Double>comparingByValue().reversed())
            .forEach(entry -> System.out.println(entry.getKey() + ": " + entry.getValue()));
    }
}

使用说明

1. 基本实现:

   • 适用于小型图结构
   • 直接使用邻接表表示图
   • 每次迭代计算所有节点的PageRank值

2. 优化实现:

   • 使用矩阵运算,适合大型图
   • 首先将节点映射到索引,构建转移矩阵
   • 处理了悬挂节点（没有出边的节点）

3. 参数说明:

   • dampingFactor: 阻尼因子，通常设为0.85
   • maxIterations: 最大迭代次数
   • tolerance: 收敛阈值

4. 运行结果:

   
   （图片来源网络，侵删）

   程序会输出每个节点的PageRank值,并按排名从高到低排序

扩展功能

如果需要进一步扩展,可以考虑：

1. 分布式实现: 使用Hadoop或Spark处理大规模图
2. 增量更新: 当图结构发生变化时，只更新受影响节点的PageRank
3. 个性化PageRank: 为不同用户计算个性化的PageRank值
4. 可视化: 添加图形化展示功能

这两个实现都提供了PageRank算法的核心功能,可以根据具体需求选择使用基本版或优化版。