复杂网络聚类系数和平均路径长度计算的MATLAB源代码

一、前言在数据分析和机器学习领域，k-means算法是一种常用的聚类算法，它可以将数据集分成不同的簇，每个簇内的数据点彼此相似，而不同簇之间的数据点相似度较低。

在matlab中，可以利用其强大的数学计算功能来实现k-means聚类算法。

本文将介绍如何在matlab中编写k-means聚类算法的代码。

二、matlab中的k-means算法1. 初始化数据集需要准备好要进行聚类分析的数据集。

这些数据可以是一组二维或多维的点，代表不同的特征。

在matlab中，可以使用矩阵来表示这些数据集，每一行代表一个数据点，每一列代表一个特征。

2. 设置聚类数量在进行k-means聚类算法之前，需要先确定要分成的簇的数量。

这个数量可以根据业务需求或者领域知识来确定。

在matlab中，可以使用kmeans函数来执行聚类分析，该函数需要指定数据集和聚类数量。

3. 运行k-means算法一旦准备好了数据集和聚类数量，就可以调用matlab中的kmeans 函数来执行k-means算法。

该函数会根据数据集和聚类数量来计算出不同簇的中心点，并将每个数据点分配到最近的簇中。

4. 可视化聚类结果完成k-means算法之后，可以将聚类结果可视化出来，以便更直观地理解不同簇之间的分布情况。

在matlab中，可以使用plot函数来绘制数据点和聚类中心，以及不同簇的分布情况。

三、示例代码以下是一个简单的matlab代码示例，演示了如何使用kmeans函数来执行k-means聚类算法：```matlab读取数据data = load('data.txt');设置聚类数量k = 3;运行k-means算法[idx, centers] = kmeans(data, k);可视化聚类结果figure;gscatter(data(:,1), data(:,2), idx);hold on;plot(centers(:,1), centers(:,2), 'kx', 'MarkerSize', 15, 'LineWidth', 3); ```以上代码首先读取了名为data.txt的数据集，然后设置了聚类数量为3。

function [DeD,aver_DeD]=Degree_Distribution(A)%% 求网络图中各节点的度及度的分布曲线%% 求解算法：求解每个节点的度，再按发生频率即为概率，求P(k)%A————————网络图的邻接矩阵%DeD————————网络图各节点的度分布%aver_DeD———————网络图的平均度N=size(A,2);DeD=zeros(1,N);for i=1:N% DeD(i)=length(find((A(i,:)==1)));DeD(i)=sum(A(i,:));endaver_DeD=mean(DeD);if sum(DeD)==0disp('该网络图只是由一些孤立点组成');return;elsefigure;bar([1:N],DeD);xlabel('节点编号n');ylabel('各节点的度数K');title('网络图中各节点的度的大小分布图');endfigure;M=max(DeD);for i=1:M+1; %网络图中节点的度数最大为M,但要同时考虑到度为0的节点的存在性N_DeD(i)=length(find(DeD==i-1));endP_DeD=zeros(1,M+1);P_DeD(:)=N_DeD(:)./sum(N_DeD);bar([0:M],P_DeD,'r');xlabel('节点的度K');ylabel('节点度为K的概率P(K)');title('网络图中节点度的概率分布图');function [C,aver_C]=Clustering_Coefficient(A)%% 求网络图中各节点的聚类系数及整个网络的聚类系数%% 求解算法：求解每个节点的聚类系数，找某节点的所有邻居，这些邻居节点构成一个子图%% 从A中抽出该子图的邻接矩阵，计算子图的边数，再根据聚类系数的定义，即可算出该节点的聚类系数%A————————网络图的邻接矩阵%C————————网络图各节点的聚类系数%aver———————整个网络图的聚类系数N=size(A,2);C=zeros(1,N);for i=1:Naa=find(A(i,:)==1); %寻找子图的邻居节点if isempty(aa)disp(['节点',int2str(i),'为孤立节点，其聚类系数赋值为0']);C(i)=0;elsem=length(aa);if m==1disp(['节点',int2str(i),'只有一个邻居节点，其聚类系数赋值为0']);C(i)=0;elseB=A(aa,aa); % 抽取子图的邻接矩阵C(i)=length(find(B==1))/(m*(m-1));endendendaver_C=mean(C);function [D,aver_D]=Aver_Path_Length(A)%% 求复杂网络中两节点的距离以及平均路径长度%% 求解算法：首先利用Floyd算法求解出任意两节点的距离，再求距离的平均值得平均路径长度% A————————网络图的邻接矩阵% D————————返回值：网络图的距离矩阵% aver_D———————返回值：网络图的平均路径长度N=size(A,2);D=A;D(find(D==0))=inf; %将邻接矩阵变为邻接距离矩阵，两点无边相连时赋值为inf，自身到自身的距离为0.for i=1:ND(i,i)=0;endfor k=1:N %Floyd算法求解任意两点的最短距离for i=1:Nfor j=1:Nif D(i,j)>D(i,k)+D(k,j)D(i,j)=D(i,k)+D(k,j);endendendendaver_D=sum(sum(D))/(N*(N-1)); %平均路径长度if aver_D==infdisp('该网络图不是连通图');end%% 算法2：用时间量级O(MN)的广度优先算法求解一个含N个节点和M条边的网络图的平均路径长度。

复杂网络聚类系数和平均路径长度计算的MATLAB源代码复杂网络的聚类系数和平均路径长度是度量网络结构特征的重要指标。

下面是MATLAB源代码，用于计算复杂网络的聚类系数和平均路径长度。

首先，我们需要定义一个函数，用于计算节点的聚集系数。

这个函数的输入参数是邻接矩阵和节点的索引，输出参数是节点的聚类系数。

```matlabfunction cc = clustering_coefficient(adj_matrix, node_index) neighbors = find(adj_matrix(node_index, :));k = length(neighbors);if k < 2cc = 0;elseconnected_count = 0;for i = 1:k-1for j = i+1:kif adj_matrix(neighbors(i), neighbors(j))connected_count = connected_count + 1;endendendcc = 2 * connected_count / (k * (k - 1));endend```接下来，我们定义一个函数，用于计算整个网络的平均聚合系数。

```matlabfunction avg_cc = average_clustering_coefficient(adj_matrix) n = size(adj_matrix, 1);cc = zeros(n, 1);for i = 1:ncc(i) = clustering_coefficient(adj_matrix, i);endavg_cc = sum(cc) / n;end```然后，我们需要计算网络的平均最短路径长度。

这里我们使用了Floyd算法来计算每对节点之间的最短路径。

```matlabfunction avg_path_length =average_shortest_path_length(adj_matrix)n = size(adj_matrix, 1);dist_matrix =graphallshortestpaths(sparse(double(adj_matrix)));avg_path_length = sum(dist_matrix(:)) / (n^2 - n);end```最后，我们可以使用这些函数来计算一个复杂网络的聚类系数和平均路径长度。

节点收缩算法：function Z=node(a,dy)%a为邻接矩阵a(a==inf)=0;a(~=0)=1;n=size(a,1);%矩阵维数Z=zeros(n,1);%节点重要度向量%由邻接矩阵a得到直接矩阵H%H表示c(i j)H=zeros(size(a));for i=1:nfor j=1:nif j==iH(i,j)=0;elseif a(I,j)==1H(i,j)=1;elseH(i,j)=inf;endendend%用Floyd法计算节点收缩前的最短就离矩阵D D=H；for k=1:nfor i=1:nfor j=1:nIf D(i,k)+D(k,j)<D(iI,j)D(i,j)=D(i,k)+D(k,j);endendendend%计算节点重要度D2=zeros(size(D));for i=1:n%得到与节点i邻接的节点向量II=zeros(1,0);T=0;for j=1:nif a(i,j)=1T=t+1;I=[i,j];endend%计算收缩后最短距离矩阵D2%D2为d’(pq) D为d(pq)for p=1:nfor q=1:nIf p~=1&q~=iIf D(p,i)+D(i,q)==D(p,q)D2(p,q)=D(p,q)-2;elseif D(p,i)+D(i,q)==D(p,q)+1D2(p,q)=D(p,q)-1;elseif D(p,i)+D(i,q)==D(p,q)+2D2(p,q)=D(p,q);endelseif p==i｜q==iD2(p,q)=D(p,q)-1;elseD2(p,q)=0;endendendN3=n-t;%收缩后的节点数n3D3=D2;%计算收缩后的最短距离矩阵D3，D3为D D3(I,:)=[];%删除与节点i邻接的节点对应的行D3(:,I)=[];%删除与节点i邻接的节点对应的列%计算节点收缩后的节点重要度s=0;for p=1:n3for q=p:n3s=s+D3(p,q);endendl=s/(n3*(n3-1)/2);%为nZ(i)=1/(n3*l);end===================================节点介数=========================function B=betweenness_node(A,a)%%求网络节点介数，BY QiCheng%%思想：节点i、j间的距离等于节点i、k间距离与节点k、j间距离时，i、j间的最短路径经过k。

加权聚类系数和加权平均路径长度matlab代码（实用版）目录1.引言2.加权聚类系数和加权平均路径长度的定义和意义3.Matlab 代码实现4.结论正文一、引言在网络科学中，聚类系数和平均路径长度是两个重要的参数，用于描述网络的结构特性。

加权聚类系数和加权平均路径长度是在此基础上，对这两个参数进行加权处理，使得分析结果更加精确。

本文将介绍如何使用Matlab 代码实现加权聚类系数和加权平均路径长度的计算。

二、加权聚类系数和加权平均路径长度的定义和意义1.加权聚类系数加权聚类系数是用来衡量网络中节点之间联系紧密程度的参数。

其计算公式为：加权聚类系数 = (∑(权重^2)) / (∑(权重))其中，权重代表连接两个节点的边的权重。

2.加权平均路径长度加权平均路径长度是用来衡量网络中节点之间平均距离的参数。

其计算公式为：加权平均路径长度 = ∑(路径长度 * 权重) / ∑(权重)其中，路径长度代表从源节点到目标节点经过的边的权重之和，权重代表连接两个节点的边的权重。

三、Matlab 代码实现假设我们有一个邻接矩阵表示的网络，邻接矩阵如下：```A = [0, 1, 1, 0, 0, 1, 0, 1, 0, 0];```我们可以使用以下 Matlab 代码实现加权聚类系数和加权平均路径长度的计算：```matlab% 邻接矩阵A = [0, 1, 1, 0, 0, 1, 0, 1, 0, 0];% 计算加权聚类系数weight = A; % 假设权重与邻接矩阵相同clustering_coefficient = sum(weight.^2) / sum(weight);% 计算加权平均路径长度path_length = sum(sum(weight, 2) * weight) / sum(weight);```四、结论通过 Matlab 代码，我们可以方便地实现加权聚类系数和加权平均路径长度的计算。

一、引言在机器学习和数据分析中，聚类是一种常用的数据分析技术，它可以帮助我们发现数据中的潜在模式和结构。

而k均值（k-means）聚类算法作为一种经典的聚类方法，被广泛应用于各种领域的数据分析和模式识别中。

本文将介绍matlab中k均值聚类算法的实现和代码编写。

二、k均值（k-means）聚类算法简介k均值聚类算法是一种基于距离的聚类算法，它通过迭代的方式将数据集划分为k个簇，每个簇内的数据点与该簇的中心点的距离之和最小。

其基本思想是通过不断调整簇的中心点，使得簇内的数据点与中心点的距离最小化，从而实现数据的聚类分布。

三、matlab实现k均值聚类算法步骤在matlab中，实现k均值聚类算法的步骤如下：1. 初始化k个簇的中心点，可以随机选择数据集中的k个点作为初始中心点。

2. 根据每个数据点与各个簇中心点的距离，将数据点分配给距离最近的簇。

3. 根据每个簇的数据点重新计算该簇的中心点。

4. 重复步骤2和步骤3，直到簇的中心点不再发生变化或者达到预定的迭代次数。

在matlab中，可以通过以下代码实现k均值聚类算法：```matlab设置参数k = 3; 设置簇的个数max_iter = 100; 最大迭代次数初始化k个簇的中心点centroids = datasample(data, k, 'Replace', false);for iter = 1:max_iterStep 1: 计算每个数据点与簇中心点的距离distances = pdist2(data, centroids);Step 2: 分配数据点给距离最近的簇[~, cluster_idx] = min(distances, [], 2);Step 3: 重新计算每个簇的中心点for i = 1:kcentroids(i, :) = mean(data(cluster_idx == i, :)); endend得到最终的聚类结果cluster_result = cluster_idx;```四、代码解释上述代码实现了k均值聚类算法的基本步骤，其中包括了参数设置、簇中心点的初始化、迭代过程中的数据点分配和中心点更新。

聚类分析matlab代码聚类分析是一种机器学习方法，用于对数据进行分类，将相似的数据聚合在一起，产生有用的洞察和结论。

MATLAB是一个常用的数学计算软件，也可以用于聚类分析。

本文将介绍MATLAB中的聚类分析代码。

1. 数据准备首先，需要准备聚类分析所需的数据。

可以使用MATLAB内置的示例数据集，如鸢尾花数据集、手写数字数据集等。

也可以导入自己的数据集，例如Excel文件。

2. 数据前处理接下来，需要对数据进行前处理以便于聚类分析。

这可能包括数据清理、数据转换和特征提取。

例如，对于鸢尾花数据集，可以将花的特征信息（花瓣长度、花瓣宽度、花萼长度、花萼宽度）作为每个样本的特征。

3. 选择聚类算法MATLAB提供了多种聚类算法，可以根据数据类型和问题选择合适的算法。

常用的聚类算法包括K均值聚类、层次聚类、谱聚类等。

例如，对于鸢尾花数据集，可以使用K均值聚类算法。

4. 聚类分析一旦选择好算法，就可以开始聚类分析。

使用MATLAB的聚类算法函数进行聚类，例如kmeans函数进行K均值聚类。

函数需要输入样本数据、聚类数目等参数，并返回聚类结果。

5. 结果可视化最后，可以将聚类结果可视化，以便于理解和解释。

使用MATLAB的绘图函数，例如scatter函数或plot函数，将聚类结果表示在二维或三维图形上。

可以使用不同的颜色或符号表示不同的聚类簇。

下面是一个简单的MATLAB聚类分析代码，用于对鸢尾花数据集进行K均值聚类：% 导入鸢尾花数据集load fisheriris% 提取特征向量X = meas;% K均值聚类[idx, C] = kmeans(X, 3);% 绘制聚类结果figuregscatter(X(:,1),X(:,2),idx)hold onplot(C(:,1),C(:,2),'kx','LineWidth',2,'MarkerSize',10)legend('Cluster 1','Cluster 2','Cluster 3','Centroids','Location','NW') xlabel 'Sepal length';ylabel 'Sepal width';title 'K-means Clustering';。

function varargout = lljuleifenxi(varargin)% LLJULEIFENXI MATLAB code for lljuleifenxi.fig% LLJULEIFENXI, by itself, creates a new LLJULEIFENXI or raises the existing% singleton*.%% H = LLJULEIFENXI returns the handle to a new LLJULEIFENXI or the handle to% the existing singleton*.%% LLJULEIFENXI('CALLBACK',hObject,eventData,handles,...) calls the local% function named CALLBACK in LLJULEIFENXI.M with the given input arguments.%% LLJULEIFENXI('Property','Value',...) creates a new LLJULEIFENXI or raises the% existing singleton*. Starting from the left, property value pairs are % applied to the GUI before lljuleifenxi_OpeningFcn gets called. An % unrecognized property name or invalid value makes property application % stop. All inputs are passed to lljuleifenxi_OpeningFcn via varargin. %% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one % instance to run (singleton)".%% See also: GUIDE, GUIDATA, GUIHANDLES% Edit the above text to modify the response to help lljuleifenxi% Last Modified by GUIDE v2.5 07-Jan-2015 18:18:25% Begin initialization code - DO NOT EDITgui_Singleton = 1;gui_State = struct('gui_Name', mfilename, ...'gui_Singleton', gui_Singleton, ...'gui_OpeningFcn', @lljuleifenxi_OpeningFcn, ...'gui_OutputFcn', @lljuleifenxi_OutputFcn, ...'gui_LayoutFcn', [] , ...'gui_Callback', []);if nargin && ischar(varargin{1})gui_State.gui_Callback = str2func(varargin{1});endif nargout[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});elsegui_mainfcn(gui_State, varargin{:});end% End initialization code - DO NOT EDIT% --- Executes just before lljuleifenxi is made visible.function lljuleifenxi_OpeningFcn(hObject, eventdata, handles, varargin)% This function has no output args, see OutputFcn.% hObject handle to figure% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% varargin command line arguments to lljuleifenxi (see VARARGIN)% Choose default command line output for lljuleifenxihandles.output = hObject;% Update handles structureguidata(hObject, handles);% UIWAIT makes lljuleifenxi wait for user response (see UIRESUME)% uiwait(handles.figure1);% --- Outputs from this function are returned to the command line.function varargout = lljuleifenxi_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (see VARARGOUT);% hObject handle to figure% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% Get default command line output from handles structurevarargout{1} = handles.output;% --- Executes during object creation, after setting all properties. function edit6_CreateFcn(hObject, eventdata, handles)% hObject handle to edit6 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called function input_data_Callback(hObject, eventdata, handles)% hObject handle to input_data (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% Hints: get(hObject,'String') returns contents of input_data as text% str2double(get(hObject,'String')) returns contents of input_data as a double% --- Executes during object creation, after setting all properties. function input_data_CreateFcn(hObject, eventdata, handles)% hObject handle to input_data (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'),get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');endfunction input_obj_num_Callback(hObject, eventdata, handles)% hObject handle to input_obj_num (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% Hints: get(hObject,'String') returns contents of input_obj_num as text % str2double(get(hObject,'String')) returns contents ofinput_obj_num as a double% --- Executes during object creation, after setting all properties. function input_obj_num_CreateFcn(hObject, eventdata, handles)% hObject handle to input_obj_num (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'),get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');endfunction input_var_num_Callback(hObject, eventdata, handles)% hObject handle to input_var_num (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% Hints: get(hObject,'String') returns contents of input_var_num as text % str2double(get(hObject,'String')) returns contents ofinput_var_num as a double% --- Executes during object creation, after setting all properties. function input_var_num_CreateFcn(hObject, eventdata, handles)% hObject handle to input_var_num (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'),get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');end% --- Executes on selection change in popm_class_method.function popm_class_method_Callback(hObject, eventdata, handles)% hObject handle to popm_class_method (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% Hints: contents = cellstr(get(hObject,'String')) returnspopm_class_method contents as cell array% contents{get(hObject,'Value')} returns selected item frompopm_class_method% --- Executes during object creation, after setting all properties. function popm_class_method_CreateFcn(hObject, eventdata, handles)% hObject handle to popm_class_method (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called % Hint: popupmenu controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'),get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');end% --- Executes on selection change in popm_cluster_method.function popm_cluster_method_Callback(hObject, eventdata, handles)% hObject handle to popm_cluster_method (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% Hints: contents = cellstr(get(hObject,'String')) returnspopm_cluster_method contents as cell array% contents{get(hObject,'Value')} returns selected item frompopm_cluster_method% --- Executes during object creation, after setting all properties. function popm_cluster_method_CreateFcn(hObject, eventdata, handles)% hObject handle to popm_cluster_method (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called % Hint: popupmenu controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'),get(0,'defaultUicontrolBackgroundColor'))set(hObject,'BackgroundColor','white');end% --- Executes on mouse press over axes background.function axes_ButtonDownFcn(hObject, eventdata, handles)% hObject handle to axes (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% --- Executes during object deletion, before destroying properties. function axes_DeleteFcn(hObject, eventdata, handles)% hObject handle to axes (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% --- Executes on button press in btn_start.function btn_start_Callback(hObject, eventdata, handles)% hObject handle to btn_start (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)str_num_obj = get(handles.input_obj_num,'String');str_num_var = get(handles.input_var_num,'String');exp = '\D+';isNum =(isempty(regexp(str_num_obj,exp))&&isempty(regexp(str_num_obj,exp)));if(isNum)num_obj = str2num(str_num_obj);num_var = str2num(str_num_var);trysource_data = str2num(get(handles.input_data,'String'));val_class_method = get(handles.popm_class_method,'Value');% return the selected item from pop_menustr_class_method = get(handles.popm_class_method,'String');% return the contents of the pop_menu% this is the default valuehandles.current_method = 'cityblock';switch str_class_method{val_class_method} % it is the current selected item (String)case'¾ø¶ÔÖµ¾àÀë'handles.current_method = 'cityblock';case'ãÉ¿É·ò˹»ù¾àÀë'handles.current_method = 'minkowski';case'ÂíÊϾàÀë'handles.current_method = 'mahalanobis';case'×Ô¶¨Òå¾àÀë'handles.current_method = 'myDistFun';% alert to user to edit custome function in the myDistFun.m and the% default is use the euclidean distmH = msgbox('you could custom the distance function in the file myDistFun,if not,the default is the City block distance','attention');uiwait(mH);case'¼Ð½ÇÓàÏÒ'handles.current_method = 'cosine';case'Ïà¹ØϵÊý'handles.current_method = 'correlation';endval_cluster_method = get(handles.popm_cluster_method,'Value');% return the selected item from pop_menustr_cluster_method = get(handles.popm_cluster_method,'String');% return the contents of the pop_menu% this is the default valuehandles.current_cluster_method = 'single';switch str_cluster_method{val_cluster_method}case'×î¶Ì¾àÀë·¨ 'handles.current_cluster_method = 'single';case'×¾àÀë·¨'handles.current_cluster_method = 'complete';case'Öмä¾àÀë·¨'handles.current_cluster_method = 'median';case'ÖØÐÄ·¨'handles.current_cluster_method = 'centroid';case'Ààƽ¾ù·¨'handles.current_cluster_method = 'average';case'Àë²îƽ·½ºÍ·¨'handles.current_cluster_method = 'ward';end%% check the datareal_rows = size(source_data,1);real_cols = size(source_data,2);if(real_rows ~= num_obj || real_cols ~= num_var)% alert to user that the data dont't matchingmH = msgbox('the size of your input data is notmatching','attention');uiwait(mH);else%% begin cluster and show the cluster tree on the axespdist_method = handles.current_method;if(strcmp(pdist_method,'myDistFun'))dist_matr = pdist(source_data,@myDistFun);elsedist_matr = pdist(source_data,pdist_method);endlinkage_method = handles.current_cluster_method;cluster_result = linkage(dist_matr,linkage_method);axes(handles.axes);dendrogram(cluster_result);endcatch errmH = msgbox('please input the correct data!');uiwait(mH)endelsemH = msgbox('please input the correct data!');uiwait(mH);end% --- Executes during object creation, after setting all properties. function tittle_CreateFcn(hObject, eventdata, handles)% hObject handle to tittle (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called function Z = myDistFun( X,Y )%the custom distance function% where X is a 1-by-n vector,and Y is an m-by-n matrix,% myDistFun must return an m-by-1 vector of distances Z,% whose kth element is the distance between X and Y(k,:).%% this is the City block distance definitionXX = repmat(X,size(Y,1),1);Z = sum(abs(XX - Y),2);%% you can definite your own distance function hereend。

matlab层次聚类代码在MATLAB中实现层次聚类，可以使用聚类算法包（如scikit-learn）或者MATLAB内置的聚类函数。

以下是一个基于scikit-learn的层次聚类（凝聚层次聚类）的示例代码：1. 首先，确保已经安装了scikit-learn库。

如果没有安装，可以使用以下命令进行安装：```matlab% 安装scikit-learn库install('scikit-learn')```2. 导入所需的库：```matlabimport numpy as npfrom sklearn.cluster import Birchfrom sklearn.preprocessing import StandardScalerfrom sklearn.metrics import euclidean```3. 生成随机数据集：```matlabnp.random.seed(0)X = np.random.random((100, 2))```4. 对数据进行标准化处理：```matlabsc = StandardScaler()X_scaled = sc.fit_transform(X)```5. 初始化Birch聚类器：```matlabbirch = Birch(n_clusters=3, compute_labels=True) ```6. 对数据进行聚类：```matlabclusters = birch.fit_predict(X_scaled)```7. 计算簇内平均距离和簇间距离：```matlabcenters = birch.cluster_centers_distances = np.zeros((X.shape[0], centers.shape[0]))for i in range(X.shape[0]):for j in range(centers.shape[0]):distances[i, j] = euclidean(X[i], centers[j])inner_distance = np.min(distances, axis=1)between_distance = np.min(distances[distances != inner_distance], axis=1)```8. 绘制聚类结果：```matlabcolors = ['red', 'blue', 'green']scatter(X_scaled[:, 0], X_scaled[:, 1], s=50, c=colors[clusters], alpha=0.5) xlim([-3, 3])ylim([-3, 3])title('层次聚类结果')```以上代码首先生成一个随机的二维数据集，然后使用Birch聚类器对其进行聚类。

复杂网络聚类系数和平均路径长度计算的M A T L A B源代码复杂网络聚类系数和平均路径长度计算的MATLAB源代码申明：文章来自百度用户carrot_hy复杂网络的代码总共是三个m文件，复制如下：第一个文件，CCM_ClusteringCoef.mfunction [Cp_Global, Cp_Nodal] = CCM_ClusteringCoef(gMatrix, Types)% CCM_ClusteringCoef calculates clustering coefficients.% Input:% gMatrix adjacency matrix% Types type of graph:'binary','weighted','directed','all'(default).% Usage:% [Cp_Global, Cp_Nodal] = CCM_ClusteringCoef(gMatrix, Types) returns% clustering coefficients for all nodes "Cp_Nodal" and average clustering % coefficient of network "Cp_Global".% Example:% G = CCM_TestGraph1('nograph');% [Cp_Global, Cp_Nodal] = CCM_ClusteringCoef(G);% Note:% 1) one node have vaule 0, while which only has a neighbour or none.% 2) The dircted network termed triplets that fulfill the follow condition % as non-vacuous: j->i->k and k->i-j,if don't satisfy with that as% vacuous, just like: j->i,k->i and i->j,i->k. and the closedtriplets% only j->i->k == j->k and k->i->j == k->j.% 3) 'ALL' type network code from Mika Rubinov's BCT toolkit.% Refer:% [1] Barrat et al. (2004) The architecture of the complex weighted networks. % [2] Wasserman,S.,Faust,K.(1994) Social Network Analysis: Methods and% Applications.% [3] Tore Opsahl and Pietro Panzarasa (2009). "Clustering in Weighted% Networks". Social Networks31(2).% See also CCM_Transitivity% Written by Yong Liu, Oct,2007% Center for Computational Medicine (CCM),% National Laboratory of Pattern Recognition (NLPR),% Institute of Automation,Chinese Academy of Sciences (IACAS), China.% Revise by Hu Yong, Nov, 2010% E-mail:% based on Matlab 2006a% $Revision: 1.0, Copywrite (c) 2007error(nargchk(1,2,nargin,'struct'));if(nargin < 2), Types = 'all'; endN = length(gMatrix);gMatrix(1:(N+1):end) = 0;%Clear self-edgesCp_Nodal = zeros(N,1); %Preallocateswitch(upper(Types))case 'BINARY'%Binary networkgMatrix = double(gMatrix > 0);%Ensure binary networkfor i = 1:Nneighbor = (gMatrix(i,:) > 0);Num = sum(neighbor);%number of neighbor nodestemp = gMatrix(neighbor, neighbor);if(Num > 1), Cp_Nodal(i) = sum(temp(:))/Num/(Num-1); end endcase 'WEIGHTED'% Weighted network -- arithmetic meanfor i = 1:Nneighbor = (gMatrix(i,:) > 0);n_weight = gMatrix(i,neighbor);Si = sum(n_weight);Num = sum(neighbor);if(Num > 1),n_weight = ones(Num,1)*n_weight;n_weight = n_weight + n_weight';n_weight = n_weight.*(gMatrix(neighbor, neighbor) > 0);Cp_Nodal(i) = sum(n_weight(:))/(2*Si*(Num-1));endend%case 'WEIGHTED'% Weighted network -- geometric mean% A = (gMatrix~= 0);% G3 = diag((gMatrix.^(1/3) )^3);)% A(A == 0) = inf; %close-triplet no exist,let CpNode=0 (A=inf)% CpNode = G3./(A.*(A-1));case 'DIRECTED', % Directed networkfor i = 1:Ninset = (gMatrix(:,i) > 0); %in-nodes setoutset = (gMatrix(i,:) > 0)'; %out-nodes setif(any(inset & outset))allset = and(inset, outset);% Ensure aji*aik > 0,j belongs to inset,and k belongs to outsettotal = sum(inset)*sum(outset) - sum(allset);tri = sum(sum(gMatrix(inset, outset)));Cp_Nodal(i) = tri./total;endend%case 'DIRECTED', % Directed network -- clarity format (from Mika Rubinov, UNSW)% G = gMatrix + gMatrix'; %symmetrized% D = sum(G,2); %total degree% g3 = diag(G^3)/2; %number of triplet% D(g3 == 0) = inf; %3-cycles no exist,let Cp=0% c3 = D.*(D-1) - 2*diag(gMatrix^2); %number of all possible 3-cycles% Cp_Nodal = g3./c3;%Note: Directed & weighted network (from Mika Rubinov)case 'ALL',%All typeA = (gMatrix~= 0); %adjacency matrixG = gMatrix.^(1/3) + (gMatrix.').^(1/3);D = sum(A + A.',2); %total degreeg3 = diag(G^3)/2; %number of tripletD(g3 == 0) = inf; %3-cycles no exist,let Cp=0c3 = D.*(D-1) - 2*diag(A^2);Cp_Nodal = g3./c3;otherwise,%Eorr Msgerror('Type only four: "Binary","Weighted","Directed",and "All"');endCp_Global =sum(Cp_Nodal)/N;%%第二个文件：CCM_AvgShortestPath.mfunction [D_Global, D_Nodal] = CCM_AvgShortestPath(gMatrix, s, t)% CCM_AvgShortestPath generates the shortest distance matrix of source nodes% indice s to the target nodes indice t.% Input:% gMatrix symmetry binary connect matrix or weighted connect matrix% s source nodes, default is 1:N% t target nodes, default is 1:N% Usage:% [D_Global, D_Nodal] = CCM_AvgShortestPath(gMatrix) returns the mean% shortest-path length of whole network D_Global,and the mean shortest-path % length of each node in the network% Example:% G = CCM_TestGraph1('nograph');% [D_Global, D_Nodal] = CCM_AvgShortestPath(G);% See also dijk, MEAN, SUM% Written by Yong Liu, Oct,2007% Modified by Hu Yong, Nov 2010% Center for Computational Medicine (CCM),% Based on Matlab 2008a% $Revision: 1.0, Copywrite (c) 2007% ###### Input check #########error(nargchk(1,3,nargin,'struct'));N = length(gMatrix);if(nargin < 2 | isempty(s)), s = (1:N)';else s = s(:); endif(nargin < 3 | isempty(t)), t = (1:N)';else t = t(:); end% Calculate the shortest-path from s to all nodeD = dijk(gMatrix,s);%D(isinf(D)) = 0;D = D(:,t); %To target nodesD_Nodal = (sum(D,2)./sum(D>0,2));% D_Nodal(isnan(D_Nodal)) = [];D_Global = mean(D_Nodal);第三个文件： dijk.mfunction D = dijk(A,s,t)%DIJK Shortest paths from nodes 's' to nodes 't' using Dijkstra algorithm.% D = dijk(A,s,t)% A = n x n node-node weighted adjacency matrix of arc lengths% (Note: A(i,j) = 0 => Arc (i,j) does not exist;% A(i,j) = NaN => Arc (i,j) exists with 0 weight) % s = FROM node indices% = [] (default), paths from all nodes% t = TO node indices% = [] (default), paths to all nodes% D = |s| x |t| matrix of shortest path distances from 's' to 't'% = [D(i,j)], where D(i,j) = distance from node 'i' to node 'j'%% (If A is a triangular matrix, then computationally intensive node% selection step not needed since graph is acyclic (triangularity is a% sufficient, but not a necessary, condition for a graph to be acyclic)% and A can have non-negative elements)%% (If |s| >> |t|, then DIJK is faster if DIJK(A',t,s) used, where D is now % transposed and P now represents successor indices)%% (Based on Fig. 4.6 in Ahuja, Magnanti, and Orlin, Network Flows,% Prentice-Hall, 1993, p. 109.)% Copyright (c) 1998-2000 by Michael G. Kay% Matlog Version 1.3 29-Aug-2000%% Modified by JBT, Dec 2000, to delete paths% Input Error Checking ****************************************************** error(nargchk(1,3,nargin,'struct'));[n,cA] = size(A);if nargin < 2 | isempty(s), s = (1:n)'; else s = s(:); endif nargin < 3 | isempty(t), t = (1:n)'; else t = t(:); endif ~any(any(tril(A) ~= 0)) % A is upper triangularisAcyclic = 1;elseif ~any(any(triu(A) ~= 0)) % A is lower triangularisAcyclic = 2;else % Graph may not be acyclicisAcyclic = 0;endif n ~= cAerror('A must be a square matrix');elseif ~isAcyclic & any(any(A < 0))error('A must be non-negative');elseif any(s < 1 | s > n)error(['''s'' must be an integer between 1 and ',num2str(n)]);elseif any(t < 1 | t > n)error(['''t'' must be an integer between 1 and ',num2str(n)]);end% End (Input Error Checking) ************************************************ A = A'; % Use transpose to speed-up FIND for sparse AD = zeros(length(s),length(t));P = zeros(length(s),n);for i = 1:length(s)j = s(i);Di = Inf*ones(n,1); Di(j) = 0;isLab = logical(zeros(length(t),1));if isAcyclic == 1nLab = j - 1;elseif isAcyclic == 2nLab = n - j;elsenLab = 0;UnLab = 1:n;isUnLab = logical(ones(n,1));endwhile nLab < n & ~all(isLab)if isAcyclicDj = Di(j);else % Node selection[Dj,jj] = min(Di(isUnLab));j = UnLab(jj);UnLab(jj) = [];isUnLab(j) = 0;endnLab = nLab + 1;if length(t) < n, isLab = isLab | (j == t); end[jA,kA,Aj] = find(A(:,j));Aj(isnan(Aj)) = 0;if isempty(Aj), Dk = Inf; else Dk = Dj + Aj; endP(i,jA(Dk < Di(jA))) = j;Di(jA) = min(Di(jA),Dk);if isAcyclic == 1 % Increment node index for upper triangular Aj = j + 1;elseif isAcyclic == 2 % Decrement node index for lower triangular Aj = j - 1;end%disp( num2str( nLab ));endD(i,:) = Di(t)';end。

加权聚类系数和加权平均路径长度matlab代码加权聚类系数和加权平均路径长度是图论中一对重要的指标，用于评价网络图中节点之间的连接密度和通信效率。

在本文中，我将重点介绍加权聚类系数和加权平均路径长度的概念，并提供相应的Matlab代码来计算这些指标。

1. 加权聚类系数加权聚类系数是一种度量网络图中节点局部连接密度的指标。

对于一个节点而言，它的聚类系数定义为该节点的邻居节点之间实际存在的边数与可能存在的边数的比值。

在加权网络图中，我们需要考虑边的权重。

对于给定的节点i，其邻居节点集合定义为Ni，该节点的聚类系数Ci可以通过以下步骤计算得到：1. 对于节点i的每对邻居节点j和k，计算其边的权重wij和wik。

2. 对于每对邻居节点j和k，计算其边的权重的乘积相加，即sum =Σ(wij * wik)。

3. 计算节点i的邻居节点之间可能的边数，即possible_edges = (|Ni| * (|Ni| - 1)) / 2。

4. 计算节点i的加权聚类系数Ci = 2 * sum / possible_edges。

下面是使用Matlab实现计算加权聚类系数的代码：```matlabfunction weighted_clustering_coefficient =compute_weighted_clustering_coefficient(adjacency_matrix) num_nodes = size(adjacency_matrix, 1);weighted_clustering_coefficient = zeros(num_nodes, 1);for i = 1:num_nodesneighbors = find(adjacency_matrix(i, :) > 0);num_neighbors = length(neighbors);if num_neighbors >= 2weights = adjacency_matrix(i, neighbors);weighted_sum = 0;for j = 1:num_neighbors-1for k = j+1:num_neighborsweighted_sum = weighted_sum + (weights(j) * weights(k));endendpossible_edges = (num_neighbors * (num_neighbors - 1)) / 2;weighted_clustering_coefficient(i) = 2 * weighted_sum / possible_edges;endendend```在上述代码中，我们首先根据给定的邻接矩阵的大小确定节点数量。

复杂网络聚类系数和平均路径长度计算的MA TLAB源代码申明：文章来自百度用户carrot_hy复杂网络的代码总共是三个m文件，复制如下：第一个文件，function [Cp_Global, Cp_Nodal] = CCM_ClusteringCoef(gMatrix, Types)% CCM_ClusteringCoef calculates clustering coefficients.% Input:% gMatrix adjacency matrix% Types type of graph:'binary','weighted','directed','all'(default).% Usage:% [Cp_Global, Cp_Nodal] = CCM_ClusteringCoef(gMatrix, Types) returns% clustering coefficients for all nodes "Cp_Nodal" and average clustering% coefficient of network "Cp_Global".% Example:% G = CCM_TestGraph1('nograph');% [Cp_Global, Cp_Nodal] = CCM_ClusteringCoef(G);% Note:% 1) one node have vaule 0, while which only has a neighbour or none.% 2) The dircted network termed triplets that fulfill the follow condition % as non-vacuous: j->i->k and k->i-j,if don't satisfy with that as% vacuous, just like: j->i,k->i and i->j,i->k. and the closed triplets % only j->i->k == j->k and k->i->j == k->j.% 3) 'ALL' type network code from Mika Rubinov's BCT toolkit.% Refer:% [1] Barrat et al. (2004) The architecture of the complex weighted networks.% [2] Wasserman,S.,Faust,K.(1994) Social Network Analysis: Methods and % Applications.% [3] Tore Opsahl and Pietro Panzarasa (2009). "Clustering in Weighted % Networks". Social Networks31(2).% See also CCM_Transitivity% Written by Yong Liu, Oct,2007% Center for Computational Medicine (CCM),% National Laboratory of Pattern Recognition (NLPR),% Institute of Automation,Chinese Academy of Sciences (IACAS), China.% Revise by Hu Yong, Nov, 2010% E-mail:% based on Matlab 2006a% $Revision: , Copywrite (c) 2007error(nargchk(1,2,nargin,'struct'));if(nargin < 2), Types = 'all'; endN = length(gMatrix);gMatrix(1:(N+1):end) = 0;%Clear self-edgesCp_Nodal = zeros(N,1); %Preallocateswitch(upper(Types))case 'BINARY'%Binary networkgMatrix = double(gMatrix > 0);%Ensure binary networkfor i = 1:Nneighbor = (gMatrix(i,:) > 0);Num = sum(neighbor);%number of neighbor nodestemp = gMatrix(neighbor, neighbor);if(Num > 1), Cp_Nodal(i) = sum(temp(:))/Num/(Num-1); end endcase 'WEIGHTED'% Weighted network -- arithmetic meanfor i = 1:Nneighbor = (gMatrix(i,:) > 0);n_weight = gMatrix(i,neighbor);Si = sum(n_weight);Num = sum(neighbor);if(Num > 1),n_weight = ones(Num,1)*n_weight;n_weight = n_weight + n_weight';n_weight = n_weight.*(gMatrix(neighbor, neighbor) > 0);Cp_Nodal(i) = sum(n_weight(:))/(2*Si*(Num-1));endend%case 'WEIGHTED'% Weighted network -- geometric mean% A = (gMatrix~= 0);% G3 = diag((gMatrix.^(1/3) )^3);)% A(A == 0) = inf; %close-triplet no exist,let CpNode=0 (A=inf)% CpNode = G3./(A.*(A-1));case 'DIRECTED', % Directed networkfor i = 1:Ninset = (gMatrix(:,i) > 0); %in-nodes setoutset = (gMatrix(i,:) > 0)'; %out-nodes setif(any(inset & outset))allset = and(inset, outset);% Ensure aji*aik > 0,j belongs to inset,and k belongs to outsettotal = sum(inset)*sum(outset) - sum(allset);tri = sum(sum(gMatrix(inset, outset)));Cp_Nodal(i) = tri./total;endend%case 'DIRECTED', % Directed network -- clarity format (from Mika Rubinov, UNSW) % G = gMatrix + gMatrix'; %symmetrized% D = sum(G,2); %total degree% g3 = diag(G^3)/2; %number of triplet% D(g3 == 0) = inf; %3-cycles no exist,let Cp=0 % c3 = D.*(D-1) - 2*diag(gMatrix^2); %number of all possible 3-cycles% Cp_Nodal = g3./c3;%Note: Directed & weighted network (from Mika Rubinov)case 'ALL',%All typeA = (gMatrix~= 0); %adjacency matrixG = gMatrix.^(1/3) + (gMatrix.').^(1/3);D = sum(A + A.',2); %total degreeg3 = diag(G^3)/2; %number of tripletD(g3 == 0) = inf; %3-cycles no exist,let Cp=0c3 = D.*(D-1) - 2*diag(A^2);Cp_Nodal = g3./c3;otherwise,%Eorr Msgerror('Type only four: "Binary","Weighted","Directed",and "All"');endCp_Global =sum(Cp_Nodal)/N;%%第二个文件：function [D_Global, D_Nodal] = CCM_AvgShortestPath(gMatrix, s, t)% CCM_AvgShortestPath generates the shortest distance matrix of source nodes % indice s to the target nodes indice t.% Input:% gMatrix symmetry binary connect matrix or weighted connect matrix % s source nodes, default is 1:N% t target nodes, default is 1:N% Usage:% [D_Global, D_Nodal] = CCM_AvgShortestPath(gMatrix) returns the mean% shortest-path length of whole network D_Global,and the mean shortest-path % length of each node in the network% Example:% G = CCM_TestGraph1('nograph');% [D_Global, D_Nodal] = CCM_AvgShortestPath(G); % See also dijk, MEAN, SUM% Written by Yong Liu, Oct,2007% Modified by Hu Yong, Nov 2010% Center for Computational Medicine (CCM),% Based on Matlab 2008a% $Revision: , Copywrite (c) 2007% ###### Input check #########error(nargchk(1,3,nargin,'struct'));N = length(gMatrix);if(nargin < 2 | isempty(s)), s = (1:N)';else s = s(:); endif(nargin < 3 | isempty(t)), t = (1:N)';else t = t(:); end% Calculate the shortest-path from s to all nodeD = dijk(gMatrix,s);%D(isinf(D)) = 0;D = D(:,t); %To target nodesD_Nodal = (sum(D,2)./sum(D>0,2));% D_Nodal(isnan(D_Nodal)) = [];D_Global = mean(D_Nodal);第三个文件：function D = dijk(A,s,t)%DIJK Shortest paths from nodes 's' to nodes 't' using Dijkstra algorithm.% D = dijk(A,s,t)% A = n x n node-node weighted adjacency matrix of arc lengths% (Note: A(i,j) = 0 => Arc (i,j) does not exist;% A(i,j) = NaN => Arc (i,j) exists with 0 weight) % s = FROM node indices% = [] (default), paths from all nodes% t = TO node indices% = [] (default), paths to all nodes% D = |s| x |t| matrix of shortest path distances from 's' to 't'% = [D(i,j)], where D(i,j) = distance from node 'i' to node 'j'%% (If A is a triangular matrix, then computationally intensive node% selection step not needed since graph is acyclic (triangularity is a% sufficient, but not a necessary, condition for a graph to be acyclic)% and A can have non-negative elements)%% (If |s| >> |t|, then DIJK is faster if DIJK(A',t,s) used, where D is now% transposed and P now represents successor indices)%% (Based on Fig. 4.6 in Ahuja, Magnanti, and Orlin, Network Flows,% Prentice-Hall, 1993, p. 109.)% Copyright (c) 1998-2000 by Michael G. Kay% Matlog Version 29-Aug-2000%% Modified by JBT, Dec 2000, to delete paths% Input Error Checking ****************************************************** error(nargchk(1,3,nargin,'struct'));[n,cA] = size(A);if nargin < 2 | isempty(s), s = (1:n)'; else s = s(:); endif nargin < 3 | isempty(t), t = (1:n)'; else t = t(:); endif ~any(any(tril(A) ~= 0)) % A is upper triangularisAcyclic = 1;elseif ~any(any(triu(A) ~= 0)) % A is lower triangularisAcyclic = 2;else % Graph may not be acyclicisAcyclic = 0;endif n ~= cAerror('A must be a square matrix');elseif ~isAcyclic & any(any(A < 0))error('A must be non-negative');elseif any(s < 1 | s > n)error(['''s'' must be an integer between 1 and ',num2str(n)]);elseif any(t < 1 | t > n)error(['''t'' must be an integer between 1 and ',num2str(n)]);end% End (Input Error Checking) ************************************************A = A'; % Use transpose to speed-up FIND for sparse A D = zeros(length(s),length(t));P = zeros(length(s),n);for i = 1:length(s)j = s(i);Di = Inf*ones(n,1); Di(j) = 0;isLab = logical(zeros(length(t),1));if isAcyclic == 1nLab = j - 1;elseif isAcyclic == 2nLab = n - j;elsenLab = 0;UnLab = 1:n;isUnLab = logical(ones(n,1));endwhile nLab < n & ~all(isLab)if isAcyclicDj = Di(j);else % Node selection[Dj,jj] = min(Di(isUnLab));j = UnLab(jj);UnLab(jj) = [];isUnLab(j) = 0;endnLab = nLab + 1;if length(t) < n, isLab = isLab | (j == t); end[jA,kA,Aj] = find(A(:,j));Aj(isnan(Aj)) = 0;if isempty(Aj), Dk = Inf; else Dk = Dj + Aj; endP(i,jA(Dk < Di(jA))) = j;Di(jA) = min(Di(jA),Dk);if isAcyclic == 1 % Increment node index for upper triangular A j = j + 1;elseif isAcyclic == 2 % Decrement node index for lower triangular Aj = j - 1;end%disp( num2str( nLab ));endD(i,:) = Di(t)';end。

模糊c均值聚类FCM算法的MATLAB代码我做毕业论文时需要模糊C-均值聚类，找了好长时间才找到这个，分享给大家：FCM算法的两种迭代形式的MA TLAB代码写于下,也许有的同学会用得着:m文件1/7:function [U,P,Dist,Cluster_Res,Obj_Fcn,iter]=fuzzycm(Data,C,plotflag,M,epsm)% 模糊C 均值聚类FCM: 从随机初始化划分矩阵开始迭代% [U,P,Dist,Cluster_Res,Obj_Fcn,iter] = fuzzycm(Data,C,plotflag,M,epsm)% 输入:% Data: N×S 型矩阵,聚类的原始数据,即一组有限的观测样本集,% Data 的每一行为一个观测样本的特征矢量,S 为特征矢量% 的维数,N 为样本点的个数% C: 聚类数,1<C<N% plotflag: 聚类结果2D/3D 绘图标记,0 表示不绘图,为缺省值% M: 加权指数,缺省值为2% epsm: FCM 算法的迭代停止阈值,缺省值为1.0e-6% 输出:% U: C×N 型矩阵,FCM 的划分矩阵% P: C×S 型矩阵,FCM 的聚类中心,每一行对应一个聚类原型% Dist: C×N 型矩阵,FCM 各聚类中心到各样本点的距离,聚类中% 心i 到样本点j 的距离为Dist(i,j)% Cluster_Res: 聚类结果,共C 行,每一行对应一类% Obj_Fcn: 目标函数值% iter: FCM 算法迭代次数% See also: fuzzydist maxrowf fcmplotif nargin<5epsm=1.0e-6;endif nargin<4M=2;endif nargin<3plotflag=0;end[N,S]=size(Data);m=2/(M-1);iter=0;Dist(C,N)=0; U(C,N)=0; P(C,S)=0;% 随机初始化划分矩阵U0 = rand(C,N);U0=U0./(ones(C,1)*sum(U0));% FCM 的迭代算法while true% 迭代计数器iter=iter+1;% 计算或更新聚类中心PUm=U0.^M;P=Um*Data./(ones(S,1)*sum(Um'))';% 更新划分矩阵Ufor i=1:Cfor j=1:NDist(i,j)=fuzzydist(P(i,:),Data(j,:));endendU=1./(Dist.^m.*(ones(C,1)*sum(Dist.^(-m))));% 目标函数值: 类内加权平方误差和if nargout>4 | plotflagObj_Fcn(iter)=sum(sum(Um.*Dist.^2));end% FCM 算法迭代停止条件if norm(U-U0,Inf)<epsmbreakendU0=U;end% 聚类结果if nargout > 3res = maxrowf(U);for c = 1:Cv = find(res==c);Cluster_Res(c,1:length(v))=v;endend% 绘图if plotflagfcmplot(Data,U,P,Obj_Fcn);endm文件2/7:function [U,P,Dist,Cluster_Res,Obj_Fcn,iter]=fuzzycm2(Data,P0,plotflag,M,epsm) % 模糊C 均值聚类FCM: 从指定初始聚类中心开始迭代% [U,P,Dist,Cluster_Res,Obj_Fcn,iter] = fuzzycm2(Data,P0,plotflag,M,epsm)% 输入: Data,plotflag,M,epsm: 见fuzzycm.m% P0: 初始聚类中心% 输出: U,P,Dist,Cluster_Res,Obj_Fcn,iter: 见fuzzycm.m% See also: fuzzycmif nargin<5epsm=1.0e-6;if nargin<4M=2;endif nargin<3plotflag=0;end[N,S] = size(Data); m = 2/(M-1); iter = 0;C=size(P0,1);Dist(C,N)=0;U(C,N)=0;P(C,S)=0;% FCM 的迭代算法while true% 迭代计数器iter=iter+1;% 计算或更新划分矩阵Ufor i=1:Cfor j=1:NDist(i,j)=fuzzydist(P0(i,:),Data(j,:));endendU=1./(Dist.^m.*(ones(C,1)*sum(Dist.^(-m))));% 更新聚类中心PUm=U.^M;P=Um*Data./(ones(S,1)*sum(Um'))';% 目标函数值: 类内加权平方误差和if nargout>4 | plotflagObj_Fcn(iter)=sum(sum(Um.*Dist.^2));end% FCM 算法迭代停止条件if norm(P-P0,Inf)<epsmbreakendP0=P;end% 聚类结果if nargout > 3res = maxrowf(U);for c = 1:Cv = find(res==c);Cluster_Res(c,1:length(v))=v;endend% 绘图if plotflagfcmplot(Data,U,P,Obj_Fcn);m文件3/7:function fcmplot(Data,U,P,Obj_Fcn)% FCM 结果绘图函数% See also: fuzzycm maxrowf ellipse[C,S] = size(P); res = maxrowf(U);str = 'po*x+d^v><.h';% 目标函数绘图figure(1),plot(Obj_Fcn)title('目标函数值变化曲线','fontsize',8)% 2D 绘图if S==2figure(2),plot(P(:,1),P(:,2),'rs'),hold onfor i=1:Cv=Data(find(res==i),:);plot(v(:,1),v(:,2),str(rem(i,12)+1))ellipse(max(v(:,1))-min(v(:,1)), ...max(v(:,2))-min(v(:,2)), ...[max(v(:,1))+min(v(:,1)), ...max(v(:,2))+min(v(:,2))]/2,'r:') endgrid on,title('2D 聚类结果图','fontsize',8),hold off end% 3D 绘图if S>2figure(2),plot3(P(:,1),P(:,2),P(:,3),'rs'),hold onfor i=1:Cv=Data(find(res==i),:);plot3(v(:,1),v(:,2),v(:,3),str(rem(i,12)+1))ellipse(max(v(:,1))-min(v(:,1)), ...max(v(:,2))-min(v(:,2)), ...[max(v(:,1))+min(v(:,1)), ...max(v(:,2))+min(v(:,2))]/2, ...'r:',(max(v(:,3))+min(v(:,3)))/2) endgrid on,title('3D 聚类结果图','fontsize',8),hold off endm文件4/7:function D=fuzzydist(A,B)% 模糊聚类分析: 样本间的距离% D = fuzzydist(A,B)D=norm(A-B);m文件5/7:function mr=maxrowf(U,c)% 求矩阵U 每列第c 大元素所在行,c 的缺省值为1% 调用格式: mr = maxrowf(U,c)% See also: addrif nargin<2c=1;endN=size(U,2);mr(1,N)=0;for j=1:Naj=addr(U(:,j),'descend');mr(j)=aj(c);endm文件6/7:function ellipse(a,b,center,style,c_3d)% 绘制一个椭圆% 调用: ellipse(a,b,center,style,c_3d)% 输入:% a: 椭圆的轴长(平行于x 轴)% b: 椭圆的轴长(平行于y 轴)% center: 椭圆的中心[x0,y0],缺省值为[0,0]% style: 绘制的线型和颜色,缺省值为实线蓝色% c_3d: 椭圆的中心在3D 空间中的z 轴坐标,可缺省if nargin<4style='b';endif nargin<3 | isempty(center)center=[0,0];endt=1:360;x=a/2*cosd(t)+center(1);y=b/2*sind(t)+center(2);if nargin>4plot3(x,y,ones(1,360)*c_3d,style)elseplot(x,y,style)endm文件7/7:function f = addr(a,strsort)% 返回向量升序或降序排列后各分量在原始向量中的索引% 函数调用:f = addr(a,strsort)% strsort: 'ascend' or 'descend'% default is 'ascend'% -------- example --------% addr([ 4 5 1 2 ]) returns ans:% [ 3 4 1 2 ]if nargin==1strsort='ascend';endsa=sort(a); ca=a;la=length(a);f(la)=0;for i=1:laf(i)=find(ca==sa(i),1);ca(f(i))=NaN;endif strcmp(strsort,'descend') f=fliplr(f);end几天前我还在这里发帖求助，可是很幸运在其他地方找到了，在这里和大家分享一下！function [center, U, obj_fcn] = FCMClust(data, cluster_n, options)% FCMClust.m 采用模糊C均值对数据集data聚为cluster_n类%% 用法：% 1. [center,U,obj_fcn] = FCMClust(Data,N_cluster,options);% 2. [center,U,obj_fcn] = FCMClust(Data,N_cluster);%% 输入：% data ---- nxm矩阵,表示n个样本,每个样本具有m的维特征值% N_cluster ---- 标量,表示聚合中心数目,即类别数% options ---- 4x1矩阵，其中% options(1): 隶属度矩阵U的指数，>1 (缺省值: 2.0)% options(2): 最大迭代次数(缺省值: 100)% options(3): 隶属度最小变化量,迭代终止条件(缺省值: 1e-5)% options(4): 每次迭代是否输出信息标志 (缺省值: 1)% 输出：% center ---- 聚类中心% U ---- 隶属度矩阵% obj_fcn ---- 目标函数值% Example:% data = rand(100,2);% [center,U,obj_fcn] = FCMClust(data,2);% plot(data(:,1), data(:,2),'o');% hold on;% maxU = max(U);% index1 = find(U(1,:) == maxU);% index2 = find(U(2,:) == maxU);% line(data(index1,1),data(index1,2),'marker','*','color',' g');% line(data(index2,1),data(index2,2),'marker','*','color',' r');% plot([center([1 2],1)],[center([1 2],2)],'*','color','k') % hold off;if nargin ~= 2 & nargin ~= 3, %判断输入参数个数只能是2个或3个error('Too many or too few input arguments!');enddata_n = size(data, 1); % 求出data的第一维(rows)数,即样本个数in_n = size(data, 2); % 求出data的第二维(columns)数，即特征值长度% 默认操作参数default_options = [2; % 隶属度矩阵U的指数100; % 最大迭代次数1e-5; % 隶属度最小变化量,迭代终止条件1]; % 每次迭代是否输出信息标志if nargin == 2,options = default_options;else %分析有options做参数时候的情况% 如果输入参数个数是二那么就调用默认的option;if length(options) < 4, %如果用户给的opition数少于4个那么其他用默认值;tmp = default_options;tmp(1:length(options)) = options;options = tmp;end% 返回options中是数的值为0(如NaN),不是数时为1nan_index = find(isnan(options)==1);%将denfault_options中对应位置的参数赋值给options中不是数的位置.options(nan_index) = default_options(nan_index);if options(1) <= 1, %如果模糊矩阵的指数小于等于1error('The exponent should be greater than 1!');endend%将options 中的分量分别赋值给四个变量;expo = options(1); % 隶属度矩阵U的指数max_iter = options(2); % 最大迭代次数min_impro = options(3); % 隶属度最小变化量,迭代终止条件display = options(4); % 每次迭代是否输出信息标志obj_fcn = zeros(max_iter, 1); % 初始化输出参数obj_fcnU = initfcm(cluster_n, data_n); % 初始化模糊分配矩阵,使U满足列上相加为1,% Main loop 主要循环for i = 1:max_iter,%在第k步循环中改变聚类中心ceneter,和分配函数U的隶属度值;[U, center, obj_fcn(i)] = stepfcm(data, U, cluster_n, expo);if display,fprintf('FCM:Iteration count = %d, obj. fcn = %f\n', i, obj_fcn(i));end% 终止条件判别if i > 1,if abs(obj_fcn(i) - obj_fcn(i-1)) < min_impro,break;end,endenditer_n = i; % 实际迭代次数obj_fcn(iter_n+1:max_iter) = [];。

如何利用Matlab进行聚类与分类算法实现一、引言在当今大数据时代，数据分析和机器学习技术的应用日益广泛。

聚类和分类算法是数据分析领域的两个重要研究方向。

Matlab是一种强大的数据分析和科学计算工具，具有丰富的函数库和方便的编程环境，为实现聚类和分类算法提供了便捷的平台。

本文将介绍如何利用Matlab实现聚类和分类算法的过程和技巧。

二、聚类算法的实现聚类算法是将一组数据对象划分为若干个类或簇的过程。

常用的聚类算法包括K-means、层次聚类和DBSCAN等。

下面将以K-means算法为例，介绍如何利用Matlab实现聚类。

1. 数据准备首先，需要准备要进行聚类的数据。

假设我们有一个包含N个样本的数据集，每个样本具有M个特征，可以用一个N行M列的矩阵X表示。

2. 确定聚类数K在应用K-means算法之前，需要确定聚类的数目K。

这一步通常可以通过观察数据的分布情况和经验判断进行选择。

3. 初始化聚类中心K-means算法通过迭代计算，将样本划分到K个聚类中心中。

为了进行迭代计算，需要初始化K个聚类中心。

一种常见的初始化方法是随机选择K个样本作为初始聚类中心。

4. 迭代计算在K-means算法中，迭代计算包括两步：计算每个样本与各个聚类中心的距离，将样本划分到离其最近的聚类中心；更新聚类中心，将每个簇的中心设为该簇内所有样本的平均值。

这两个步骤不断迭代，直到满足停止条件（如达到最大迭代次数或聚类中心不再发生变化）。

5. 结果评估聚类算法的结果通常需要进行评估。

常见的评估指标包括轮廓系数、紧凑度和分离度等。

Matlab提供了一些内置函数可以计算这些指标，方便进行结果的评估和比较。

三、分类算法的实现分类算法是将一组数据对象划分为若干个预定义类别的过程。

常用的分类算法包括决策树、支持向量机和神经网络等。

下面将以决策树算法为例，介绍如何利用Matlab实现分类。

1. 数据准备同样，首先需要准备要进行分类的数据。

K-Means（K均值）聚类算法的MATLAB实现最近在学习 k-means聚类算法，⽹上有很多关于⽤MATLAB对这⼀算法的实现，下⾯对这⼀知识点进⾏了总结，希望⼤家可以采纳，欢迎留⾔。

在聚类分析中希望能有⼀种算法能够⾃动的将相同的元素分为紧密关系的⼦集或簇。

聚类属于⽆监督学习中的⼀种⽅法，也是⼀种在许多领域中⽤于统计数据分析的常⽤技术。

K-means算法是使⽤的最⼴泛的⼀种算法。

1.算法步骤：1）⾸先选择⼀些类/组，并随机初始化它们各⾃的中⼼点。

中⼼点是与每个数据点向量长度相同的位置。

这就需要我们提前预知类的数量（即中⼼点的数量）。

2）计算每个数据点到中⼼点的距离，数据点距离哪个中⼼点最近就划分到哪⼀类中。

3）计算每⼀类中中⼼点作为新的中⼼点。

4）重复以上步骤，直到每⼀类中⼼在每次迭代后变化不⼤为⽌。

也可以多次随机初始化中⼼点，然后选择运⾏结果最好的⼀个。

2.注意事项：1）K-means中的K表⽰簇的个数2）质⼼：均值，即向量各维度取平均即可。

计算距离是使⽤欧式距离的计算公式：3）优化⽬标：，就是使每个样本点到簇⼼的距离的和最⼩。

优势：简单、快速、适合常规数据集。

劣势：K值难确定，复杂度与样本呈线性关系。

（即样本越多，计算的越多）3.⽤MATLAB实现K-means算法，有三类数据集，设置K=3clear all;close all;clc;%第⼀类数据a=[0 0 ];S1=[.1 0 ;0 .1];data1=mvnrnd(a,S1,100); %产⽣⾼斯分布数据%第⼆类数据b=[1.2 1.2 ];S2=[.1 0 ;0 .1];data2=mvnrnd(b,S2,100);% 第三类数据c=[-1.2 1.2 ];S3=[.1 0 ;0 .1];data3=mvnrnd(c,S3,100);%显⽰数据plot(data1(:,1),data1(:,2),'r+');hold on;plot(data2(:,1),data2(:,2),'b*');plot(data3(:,1),data3(:,2),'go');grid on;%三类数据合成⼀个不带标号的数据类data=[data1;data2;data3];%K-means聚类N=3;%设置聚类数⽬[m,n]=size(data);re=zeros(m,n+1);center=zeros(N,n);%初始化聚类中⼼re(:,1:n)=data(:,:);for x=1:Ncenter(x,:)=data( randi(300,1),:);%第⼀次随机产⽣聚类中⼼endwhile 1distence=zeros(1,N);num=zeros(1,N);new_center=zeros(N,n);for x=1:mfor y=1:Ndistence(y)=norm(data(x,:)-center(y,:));%计算到每个类的距离 end[~, temp]=min(distence);%求最⼩的距离re(x,n+1)=temp;endk=0;for y=1:Nfor x=1:mif re(x,n+1)==ynew_center(y,:)=new_center(y,:)+re(x,1:n);num(y)=num(y)+1;endendnew_center(y,:)=new_center(y,:)/num(y);if norm(new_center(y,:)-center(y,:))<0.1k=k+1;endendif k==Nbreak;elsecenter=new_center;endend[m, n]=size(re);%最后显⽰聚类后的数据figure;hold on;for i=1:mif re(i,n)==1plot(re(i,1),re(i,2),'r+');plot(center(1,1),center(1,2),'ko');elseif re(i,n)==2plot(re(i,1),re(i,2),'b*');plot(center(2,1),center(2,2),'ko');elseif re(i,n)==3plot(re(i,1),re(i,2),'go');plot(center(3,1),center(3,2),'ko');elseplot(re(i,1),re(i,2),'m*');plot(center(4,1),center(4,2),'ko');endendgrid on展⽰如下：聚类之后：望可以帮助你们。

§8.利用Matlab和SPSS软件实现聚类分析1. 用Matlab编程实现运用Matlab中的一些基本矩阵计算方法，通过自己编程实现聚类算法，在此只讨论根据最短距离规则聚类的方法。

调用函数：min1.m——求矩阵最小值，返回最小值所在行和列以及值的大小min2.m——比较两数大小，返回较小值std1.m——用极差标准化法标准化矩阵ds1.m——用绝对值距离法求距离矩阵cluster.m——应用最短距离聚类法进行聚类分析print1.m——调用各子函数，显示聚类结果聚类分析算法假设距离矩阵为vector，a阶，矩阵中最大值为max，令矩阵上三角元素等于max聚类次数=a-1,以下步骤作a-1次循环:求改变后矩阵的阶数,计作c求矩阵最小值，返回最小值所在行e和列f以及值的大小gfor l=1:c,为vector(c+1,l)赋值，产生新类令第c+1列元素，第e行和第f行所有元素为，第e列和第f列所有元素为max源程序如下：%std1.m,用极差标准化法标准化矩阵function std=std1(vector)max=max(vector); %对列求最大值min=min(vector);[a,b]=size(vector); %矩阵大小,a为行数,b为列数for i=1:afor j=1:bstd(i,j)= (vector(i,j)-min(j))/(max(j)-min(j));endend%ds1.m,用绝对值法求距离function d=ds1(vector);[a,b]=size(vector);d=zeros(a);for i=1:afor j=1:afor k=1:bd(i,j)=d(i,j)+abs(vector(i,k)-vector(j,k));endendendfprintf('绝对值距离矩阵如下：\n');disp(d)%min1.m,求矩阵中最小值，并返回行列数及其值function [v1,v2,v3]=min1(vector);%v1为行数，v2为列数，v3为其值[v,v2]=min(min(vector'));[v,v1]=min(min(vector));v3=min(min(vector));%min2.m，比较两数大小，返回较小的值function v1=min(v2,v3);if v2>v3v1=v3;elsev1=v2;end%cluster.m,最短距离聚类法function result=cluster(vector);[a,b]=size(vector);max=max(max(vector));for i=1:afor j=i:bvector(i,j)=max;endend;for k=1:(b-1)[c,d]=size(vector);fprintf('第%g次聚类:\n',k);[e,f,g]=min1(vector);fprintf('最小值=%g,将第%g区和第%g区并为一类，记作G%g\n\n',g,e,f,c+1);for l=1:cif l<=min2(e,f)vector(c+1,l)=min2(vector(e,l),vector(f,l));elsevector(c+1,l)=min2(vector(l,e),vector(l,f));endend;vector(1:c+1,c+1)=max;vector(1:c+1,e)=max;vector(1:c+1,f)=max;vector(e,1:c+1)=max;vector(f,1:c+1)=max;end%print1,调用各子函数function print=print1(filename,a,b); %a为地区个数，b为指标数fid=fopen(filename,'r')vector=fscanf(fid,'%g',[a b]);fprintf('标准化结果如下：\n')v1=std1(vector)v2=ds1(v1);cluster(v2);%输出结果print1('fname',9,7)2.直接调用Matlab函数实现2.1调用函数层次聚类法（Hierarchical Clustering）的计算步骤：①计算n个样本两两间的距离{d ij}，记D②构造n个类，每个类只包含一个样本；③合并距离最近的两类为一新类；④计算新类与当前各类的距离；若类的个数等于1，转到5）；否则回3）；⑤画聚类图；⑥决定类的个数和类；Matlab软件对系统聚类法的实现（调用函数说明）：cluster 从连接输出(linkage)中创建聚类clusterdata 从数据集合(x)中创建聚类dendrogram 画系统树状图linkage 连接数据集中的目标为二元群的层次树pdist计算数据集合中两两元素间的距离(向量) squareform 将距离的输出向量形式定格为矩阵形式zscore 对数据矩阵X 进行标准化处理各种命令解释⑴T = clusterdata(X, cutoff)其中X为数据矩阵，cutoff是创建聚类的临界值。

度分布function[DeD,aver_DeD]=Degree_Distribution(A)%%求网络图中各节点的度及度的分布曲线%%求解算法：求解每个节点的度，再按发生频率即为概率，求P(k) %A————————网络图的邻接矩阵%DeD————————网络图各节点的度分布%aver_DeD———————网络图的平均度N=size(A,2);DeD=zeros(1,N);fori=1:N% DeD(i)=length(find((A(i,:)==1)));DeD(i)=sum(A(i,:));endaver_DeD=mean(DeD);ifsum(DeD)==0disp('该网络图只是由一些孤立点组成');return;elsefigure;bar([1:N],DeD);xlabel('节点编号n');ylabel('各节点的度数K');title('网络图中各节点的度的大小分布图');endfigure;M=max(DeD);fori=1:M+1;%网络图中节点的度数最大为M,但要同时考虑到度为0的节点的存在性N_DeD(i)=length(find(DeD==i-1));% DeD=[2 2 2 2 2 2]endP_DeD=zeros(1,M+1);P_DeD(:)=N_DeD(:)./sum(N_DeD);bar([0:M],P_DeD,'r');xlabel('节点的度K');ylabel('节点度为K的概率P(K)');title('网络图中节点度的概率分布图');平均路径长度function[D,aver_D]=Aver_Path_Length(A)%%求复杂网络中两节点的距离以及平均路径长度%%求解算法：首先利用Floyd算法求解出任意两节点的距离，再求距离的平均值得平均路径长度% A————————网络图的邻接矩阵% D————————返回值：网络图的距离矩阵% aver_D———————返回值：网络图的平均路径长度N=size(A,2);D=A;D(find(D==0))=inf;%将邻接矩阵变为邻接距离矩阵，两点无边相连时赋值为inf，自身到自身的距离为0.fori=1:ND(i,i)=0;endfork=1:N%Floyd算法求解任意两点的最短距离fori=1:Nforj=1:NifD(i,j)>D(i,k)+D(k,j)D(i,j)=D(i,k)+D(k,j);endendendendaver_D=sum(sum(D))/(N*(N-1))%平均路径长度ifaver_D==infdisp('该网络图不是连通图');end%%算法2：用时间量级O(MN)的广度优先算法求解一个含N个节点和M条边的网络图的平均路径长度聚类系数function[C,aver_C]=Clustering_Coefficient(A)%%求网络图中各节点的聚类系数及整个网络的聚类系数%%求解算法：求解每个节点的聚类系数，找某节点的所有邻居，这些邻居节点构成一个子图%%从A中抽出该子图的邻接矩阵，计算子图的边数，再根据聚类系数的定义，即可算出该节点的聚类系数%A————————网络图的邻接矩阵%C————————网络图各节点的聚类系数%aver———————整个网络图的聚类系数N=size(A,2);C=zeros(1,N);fori=1:Naa=find(A(i,:)==1);%寻找子图的邻居节点ifisempty(aa)disp(['节点',int2str(i),'为孤立节点，其聚类系数赋值为0']);C(i)=0;elsem=length(aa);ifm==1disp(['节点',int2str(i),'只有一个邻居节点，其聚类系数赋值为0']);C(i)=0;elseB=A(aa,aa)%抽取子图的邻接矩阵C(i)=length(find(B==1))/(m*(m-1)); endendendaver_C=mean(C)。