链路预测（Link Prediction）MATLAB 实现

一、问题定义（先统一接口）

给定一个无向网络 ( G = (V, E) )：

• ( V )：节点集合
• ( E )：已有连边集合
• 目标：预测 ( T ) 时刻尚未连接的节点对中，哪些将来会连接

---

二、 MATLAB 源码（主程序 + 算法）

2.1 主程序：link_prediction_main.m

%% 链路预测主程序
clear; clc; close all;

%% 1. 加载网络（示例：用 Zachary Karate Club）
load karate.mat;  % 包含 adjacency matrix A (34×34)
A = adjacency;    % 邻接矩阵（0/1）
N = size(A, 1);   % 节点数

%% 2. 划分训练集 / 测试集（90% 训练，10% 测试）
ratio = 0.1;
[A_train, test_edges] = split_network(A, ratio);

%% 3. 计算链路预测得分
fprintf('计算链路预测得分...\n');

% 3.1 基于相似度的方法
S_CN  = common_neighbors(A_train);
S_Jac = jaccard(A_train);
S_AA  = adamic_adar(A_train);
S_RA  = resource_allocation(A_train);

% 3.2 基于概率的方法
S_PA  = preferential_attachment(A_train);

% 3.3 基于机器学习的方法（特征拼接）
features = cat(3, S_CN, S_Jac, S_AA);
S_ML = ml_link_prediction(A_train, features);

%% 4. 评估性能
methods = {'CN','Jaccard','AA','RA','PA','ML'};
scores = {S_CN, S_Jac, S_AA, S_RA, S_PA, S_ML};

for i = 1:length(methods)
    auc = evaluate_auc(A_train, scores{i}, test_edges);
    fprintf('方法: %-10s AUC = %.4f\n', methods{i}, auc);
end

%% 5. 可视化 Top-K 预测结果
K = 10;
[~, idx] = sort(S_AA(:), 'descend');
[pred_i, pred_j] = ind2sub([N N], idx);

fprintf('\nTop %d 预测链路:\n', K);
for k = 1:K
    if A(pred_i(k), pred_j(k)) == 0
        fprintf('%2d: 节点 %2d --- 节点 %2d (得分 = %.4f)\n', ...
                k, pred_i(k), pred_j(k), S_AA(pred_i(k), pred_j(k)));
    end
end

---

2.2 网络划分：split_network.m

function [A_train, test_edges] = split_network(A, ratio)
% 随机移除一定比例边作为测试集
edges = find(triu(A,1));
N_edge = length(edges);
N_remove = round(N_edge * ratio);

remove_idx = randperm(N_edge, N_remove);
A_train = A;
A_train(edges(remove_idx)) = 0;
A_train = A_train + A_train';  % 保持对称

test_edges = edges(remove_idx);
end

---

2.3 相似度算法（核心）

（1）共同邻居 CN

function S = common_neighbors(A)
N = size(A,1);
S = zeros(N);
for i = 1:N
    for j = i+1:N
        S(i,j) = sum(A(i,:) .* A(j,:));
    end
end
S = S + S';
end

（2）Jaccard 系数

function S = jaccard(A)
N = size(A,1);
S = zeros(N);
for i = 1:N
    for j = i+1:N
        inter = sum(A(i,:) .* A(j,:));
        union = sum(A(i,:) + A(j,:)) - inter;
        S(i,j) = inter / (union + eps);
    end
end
S = S + S';
end

（3）Adamic--Adar 指数

function S = adamic_adar(A)
N = size(A,1);
deg = sum(A);
S = zeros(N);
for i = 1:N
    for j = i+1:N
        common = find(A(i,:) .* A(j,:));
        S(i,j) = sum(1 ./ log(deg(common) + eps));
    end
end
S = S + S';
end

（4）资源分配 RA

function S = resource_allocation(A)
N = size(A,1);
deg = sum(A);
S = zeros(N);
for i = 1:N
    for j = i+1:N
        common = find(A(i,:) .* A(j,:));
        S(i,j) = sum(1 ./ deg(common));
    end
end
S = S + S';
end

（5）优先连接 PA

function S = preferential_attachment(A)
deg = sum(A);
S = deg * deg';
end

---

2.4 机器学习方法（逻辑回归 / 随机森林）

function S = ml_link_prediction(A, features)
% features: [N×N×F] 特征张量
[N, ~, F] = size(features);

% 构造训练样本
pos = find(triu(A,1));
neg = find(triu(1-A,1) .* triu(ones(N),1));
neg = neg(randperm(length(neg), length(pos)));

X = zeros(length(pos)+length(neg), F);
Y = zeros(length(pos)+length(neg), 1);

for k = 1:length(pos)
    [i,j] = ind2sub([N N], pos(k));
    X(k,:) = squeeze(features(i,j,:))';
    Y(k) = 1;
end

for k = 1:length(neg)
    [i,j] = ind2sub([N N], neg(k));
    X(length(pos)+k,:) = squeeze(features(i,j,:))';
    Y(length(pos)+k) = 0;
end

% 训练逻辑回归
mdl = fitglm(X, Y, 'Distribution', 'binomial');
S = predict(mdl, reshape(features,[],F));
S = reshape(S, [N N]);
end

---

2.5 评估函数（AUC）

function auc = evaluate_auc(A_train, S, test_edges)
% 正样本得分
pos_scores = S(sub2ind(size(S), test_edges(:,1), test_edges(:,2)));

% 负样本得分（随机采样）
neg_edges = find(triu(1-A_train,1) .* triu(ones(size(S)),1));
neg_edges = neg_edges(randperm(length(neg_edges), length(test_edges)));
neg_scores = S(sub2ind(size(S), neg_edges(:,1), neg_edges(:,2)));

% 计算 AUC
scores = [pos_scores; neg_scores];
labels = [ones(length(pos_scores),1); zeros(length(neg_scores),1)];
[~, ~, auc] = perfcurve(labels, scores, 1);
end

参考代码 链路预测matlab源码 www.youwenfan.com/contentcsv/79333.html

三、示例网络数据（Karate Club）

% karate.mat
adjacency = [
 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0;
 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0;
 ...
];

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四、结果解读

方法	特点	适用场景
CN	最简单，速度快	小规模网络
AA / RA	抑制枢纽节点，效果好	无标度网络 ✅
Jaccard	归一化，抗密度差异	社区结构明显
PA	偏向高 degree	纯幂律网络
ML	精度最高	数据充足时 ✅