【数据聚类】基于和谐搜索实现数据集聚类附matlab代码

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⛄ 内容介绍

Portfolio selection is one of the major capital allocation and budgeting issues in financial management, and a variety of models have been presented for optimal selection. Semi-variance is usually considered as a risk factor in drawing up an efficient frontier and the optimal portfolio. Since semi-variance offers a better estimation of the actual risk portfolio, it was used as a measure to approximate the risk of investment in this work. The optimal portfolio selection is one of the non-deterministic polynomial(NP)-hard problems that have not been presented in an exact algorithm, which can solve this problem in a polynomial time. Meta-heuristic algorithms are usually used to solve such problems. A novel hybrid harmony search and artificial bee colony algorithm and its application were introduced in order to draw efficient frontier portfolios. Computational results show that this algorithm is more successful than the harmony search method and genetic algorithm. In addition, it is more accurate in finding optimal solutions at all levels of risk and return.

⛄ 部分代码

 is a simple demo version implementing the basic Harmony Search      %

% algorithm for clustering problem without fine-tuning the parameters.     %

% Though this demo works very well, it is expected that this illustration  %  

% is much less efficient than the work reported in paper:                  %

% (Citation details):                                                      % 

% J. Senthilnath, Sushant Kulkarni, Raghuram, D.R., Sudhindra, M.,         %

% Omkar, S.N., Das, V. and Mani, V (2016) "A novel harmony search      %

% based approach for clustering problems", Int. J. Swarm Intelligence,     %

%  Vol. 2, No. 1, pp.66 ?86, 2016.                                           %

%%-------------------------------------------------------------------------%function [BestGen] = Harmony_Search(traindat,limits,attr)

    % Harmony search on illustrative dataset 

    % traindat----> matrix containing dataset without class labels (nxp)

    % UL ----> matrix with upper and lower limits for "p" attributes (px2)

    % HMCR---> Harmony Memory Consideration Rate [HMCR_max HMCR_min]

    % HMS----> Harmony Memory Size or population size

    % NVAR---> Number of attributes (p)

    % PAR---> Pitch Adjustment Rate [PAR_max PAR_min]

    

   global   ULB  HMS HMCR PAR_max PAR_min BW_min BW_max tem ;

   global   BestFit WorstFit BestGen BW HM fitness;

   global  counter BestIndex WorstIndex attributes;

   ULB = limits;                      

   BestGen =[];                             % Store the best fitness

   HMS = 5;                                 % Size of population

   NATTR = attr;                            % No. of attributes in datase              

   MaxIter = 5000;                          % Maximum no. of iterations

   

   HMCR_max = 0.95;      HMCR_min = 0.06;                  

   PAR_max = 0.95;       PAR_min = 0.35;                                                 

   BW_max = 0.01;        BW_min=0.1;                   

  

   % Initialize Matrices

   BW = zeros(1,NATTR);                     % Bandwidth values [1xp]            

   HM = zeros(HMS,NATTR) ;                  % Size of Harmony Memory (HMSxp)

   fitness = zeros(1,HMS);                  % Fitness of each population

   attributes = zeros(1,NATTR) ;     

   tem = zeros(2,NATTR) ;     

  HarmonySearch;

  

   % plot the final optimal cluster center

   plot(BestGen(1),BestGen(2),'k*', 'LineWidth',3) 

   legend('Agents','Agents Movement','Location','NorthEastOutside')

   xlabel('X'); ylabel('Y'); xlim([0 30]); ylim([0 35]);

   text(35,30,'* Cluster Centers', 'FontName','Times','Fontsize',12)

%    plot(BestGen(1),BestGen(2),'g*') % plot the final optimal cluster center

 % /***********************************************************************/

function objective = f(x)

    

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    % OBJECTIVE FUNCTION - Evaluation of fitness value of each solution vector

    % x receives the matrix containing the pseudo optimal cluster centres to be evaluated

    % Optimisation of Clustering Criteria by Reformulation

    % Refer Equation (4) in paper: "Optimisation of Clustering Criteria by Reformulation

    % Note: your own objective function can be written here

    % when using your own function, remember to change limits/bounds

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    

    objective = sum(pdist2(x,traindat)); 

    

end

% /***********************************************************************/

% Initialisation of Harmony Memory with random solutions between limits

        function initialize

              for i = 1:HMS

                for j = 1:NATTR

                    % Initialization of HM between upper and lower limit

                    HM(i,j) = ((ULB(j,2)-ULB(j,1))*rand(1))+ULB(j,1);   

                end

                fitness(i)= f(HM(i,:));    % evaluate fitness of each HM

              end

            % plot initial solutions for visualization 

            plot(HM(:,1),HM(:,2),'gs', 'LineWidth',1.5);

            hold on;

        end

% /***********************************************************************/

% Improvisation of Harmony Memory

        function HarmonySearch

           initialize;         % First intialize HM with random values

           counter = 0;        % Loop counter

           while counter < MaxIter

               % dynamically vary the Harmony Search parameters - PAR, HMCR, bw

               PAR=(PAR_max-PAR_min)/(MaxIter*counter)+PAR_min;

               coef=log(BW_min/BW_max)/MaxIter;

               for pp =1:NATTR

                  BW(pp)=BW_max*exp(coef*counter);

               end

               for hh = 1:NATTR

                  HMCR(hh) = HMCR_min+(((HMCR_max-HMCR_min)/MaxIter)*counter);

               end

               % improvise the solutions using parameters

               for i = 1:NATTR

                   hmcr_rnd = rand(1);

                   if hmcr_rnd <= HMCR(i)

                      index = randi([1,HMS],1);    % randomly pick one population from HM 

                      attributes(i) = HM(index,i);

                      par_rnd = rand(1); 

                      % if random number is less than PAR, tune solution

                      if par_rnd <= PAR

                         walk_rnd = rand(1);

                         temp = attributes(i);      

                         if walk_rnd<0.5 % tune i.e. add/subtract small value with 50% probabilty

                             temp = temp+rand(1)*BW(i);  

                             % check if improvised solution is within upper limit

                             if temp < ULB(i,1) 

                                attributes(i) = temp;

                             end         

                         else          

                             temp = temp-rand(1)*BW(i);

                             % check if improvised solution is within lower limit

                             if temp>ULB(i,2)

                                attributes(i) = temp;

                             end                            

                         end                     

                      end          % End of if for r2

                   else

                      % Randomisation with probability of 1-HMCR

                      attributes(i) = ((ULB(i,1)-ULB(i,2))*rand(1))+ULB(i,2);    

                   end  

               end

               value = f(attributes);         % calculate fitness of  improvised solution

               UpdateHM(value);        % Update the fitness value of the HM

               counter = counter+1;    % Increment loop counter

           end

        end

% /***********************************************************************/

% Update the Harmony Memory

        function UpdateHM( NewFit )

            % For the first iteration, find best & worst fitness solutions with index

            if(counter==0)

                [BestFit, BestIndex] = min(fitness);

                [WorstFit, WorstIndex] = max(fitness);

            end

            % for second iteration iteration onwards

               tem(1,:) = HM(WorstIndex,:);

               % replace if less than worst fitness

               if (NewFit < WorstFit)

                   % if lower than previous best fitness, update new fitness

                   % as the best fitness while discarding the worst fitness

                  if( NewFit < BestFit )

                     HM(WorstIndex,:)=attributes;

                     BestGen=attributes;

                     tem(2,:) = attributes;

                     fitness(WorstIndex)=NewFit;

                     BestIndex=WorstIndex;

                   % if only lower than worst fitness but not best fitness, then just

                   % replace worst fitness

                  else

                    HM(WorstIndex,:)=attributes;

                    tem(2,:) = attributes;

                    fitness(WorstIndex)=NewFit;

                  end

                  

                   % plot the movement of the solutions

                   pause(0.0005)  % Pause interval for tracing movements can be changed here     

                   hold on;

                   plot(tem(:,1),tem(:,2),'k:'); 

                   

                 % find the new worst solution and its index

                 [WorstFit, WorstIndex] = max(fitness);

              end % NewFit if

        end % function update

toc;

end      % end of function

⛄ 运行结果

⛄ 参考文献

[1]戈国华, 肖海波, 张敏. 基于FCM的数据聚类分析及Matlab实现[J]. 福建电脑, 2007(4):2.

[2] Seyedhosseini, S. M. , et al. "A novel hybrid algorithm based on a harmony search and artificial bee colony for solving a portfolio optimization problem using a mean-semi variance approach." Journal of Central South University (2016).​

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