📘

数据科学和机器学习（第 14 部分）：运用 Kohonen 映射在市场中寻找出路·进阶篇

Q: Kohonen 映射在外汇行情里到底靠什么逻辑把走势聚成一类的？

它用竞争学习让神经元抢着匹配输入样本，赢家节点及其邻域权重向样本靠拢，相似价格形态自然落进同一聚类。

Q: 训练日志里怎么判断 SOM 聚类已经收敛了不用再跑？

看相邻 epoch 的量化误差或邻域半径衰减曲线，若误差连续多轮不再明显下降、权重更新幅度趋零，即可认为收敛。

Q: 小布能帮我把 Kohonen 映射跑完后的聚类结果直接画成图看吗？

可以，小布能读取落盘聚类数据并生成映射曲线图，省去你手动导日志和绘图的重复劳动。

Q: SOM 训练完的权重矩阵要怎么对应回具体的行情聚类落点？

用训练后的权重做最近邻匹配，把每个样本丢回胜出神经元，该神经元坐标就是它在映射上的聚类落点。

Q: 贵金属做 Kohonen 聚类时张量收口这一步容易出什么错？

常见错是收口维度压得太狠导致聚类边界糊掉，建议保留原始特征通道、仅做轻量降维再观察映射分离度。

第 2/3 篇

本章目录

Kohonen 映射怎么靠抢赢家来聚类
训练日志里看聚类收敛过程
SOM 训练完毕后的权重与聚类落点
用张量收口聚类结果
把聚类结果从日志里读出来
把聚类落盘并用曲线图看映射

「Kohonen 映射怎么靠抢赢家来聚类」

自组织映射跟常规神经网络不一样，它不靠反向传播纠错，而是让神经元之间打擂台——谁离输入数据最近谁就是赢家，这叫竞争性学习。每个输入样本进来，都算一遍和所有神经元权重向量的相似度，欧几里得距离最小的那个胜出，成为最佳匹配单元（BMU）。赢家及其邻域会按 Kohonen 规则更新权重，朝输入向量靠拢。公式就是：新权重 = 旧权重 + 学习率 ×（输入向量 − 旧权重）。注意它只动获胜聚类的权重，不像多层感知机那样全层参与。下面这段是权重更新和 BMU 选取的核心循环，默认聚类数 m=2、学习率 alpha=0.01、 epochs=100：代码里 D[j] 存每个聚类到当前样本的欧距，D.ArgMin() 直接返回赢家下标。w_matrix.Col(min) 取出胜出聚类权重，加完增量再写回。DEBUG_MODE 下会打印距离和赢家，方便你在 MT5 里核对每一步。跑完后得到两个聚集：一个 2×2（4 个值）、一个 4×2（8 个值）。这跟 K-Means 那篇一样，聚类尺寸差太大，可视化很麻烦，所以后面得另想办法。外汇与贵金属行情用这类无监督映射做状态划分时，样本非平稳，高风险，结论仅作概率参考。

MQL5 / C++

  vector D(m); class=class="str">"cmt">//Euclidean distance btn clusters  | Remember m is the number of clusters selected
  for (class="type">class="kw">ulong i=class="num">0; i<rows; i++)
    {
      for (class="type">class="kw">ulong j=class="num">0; j<m; j++)
        {
          D[j] = Euclidean_distance(Matrix.Row(i),w_matrix.Col(j));
        }
      
      class="macro">#ifdef DEBUG_MODE  
        Print("Euc distance ",D," Winning cluster ",D.ArgMin());
      class="macro">#endif
class=class="str">"cmt">//--- weights update
  
  class="type">class="kw">ulong min = D.ArgMin(); class=class="str">"cmt">//winning cluster
  
  vector w_new = w_matrix.Col(min) + (alpha * (Matrix.Row(i) - w_matrix.Col(min)));
  
  w_matrix.Col(w_new, min);
CKohonenMaps::CKohonenMaps(matrix &matrix_, class="type">bool save_clusters=true, class="type">uint clusters=class="num">2, class="type">class="kw">double alpha=class="num">0.01, class="type">uint epochs=class="num">100)
{
  Matrix = matrix_;
  n = (class="type">uint)matrix_.Cols();
  rows = matrix_.Rows();
  m = clusters;
  cluster_tensor = new CTensors(m);
  w_matrix =matrix_utils.Random(class="num">0.0, class="num">1.0, n, m, RANDOM_STATE);
    
  vector D(m); class=class="str">"cmt">//Euclidean distance btn clusters
  
  for (class="type">uint epoch=class="num">0; epoch<epochs; epoch++)
  {
    class="type">class="kw">double epoch_start = GetMicrosecondCount()/(class="type">class="kw">double)class="num">1e6, epoch_stop=class="num">0;
    
    for (class="type">class="kw">ulong i=class="num">0; i<rows; i++)
     {
      for (class="type">class="kw">ulong j=class="num">0; j<m; j++)
        {
          D[j] = Euclidean_distance(Matrix.Row(i),w_matrix.Col(j));
        }
      
      class="macro">#ifdef DEBUG_MODE  
        Print("Euc distance ",D," Winning cluster ",D.ArgMin());
      class="macro">#endif
  class=class="str">"cmt">//--- weights update
      
      class="type">class="kw">ulong min = D.ArgMin();
        
      vector w_new = w_matrix.Col(min) + (alpha * (Matrix.Row(i) - w_matrix.Col(min)));
      
      w_matrix.Col(w_new, min);
      
     }
  
    epoch_stop =GetMicrosecondCount()/(class="type">class="kw">double)class="num">1e6;

训练日志里看聚类收敛过程

自组织映射（SOM）在 EURUSD H1 上跑训练时，终端会逐条吐出欧氏距离和获胜聚类编号。从日志看，第 1 轮 epoch 的 100 次迭代里，前 6 个样本欧氏距离分别落在 [2.12,1.82]、[1.43,1.10]、[5.57,5.26]、[4.37,4.00]、[8.05,7.65]、[6.97,6.50]，且全部判给 cluster 1，说明初始权重下样本被粗略推到同一侧。到后面 epoch 临近结束，同一毫秒（04:13:26.622）输出的距离开始出现分化：例如 [0.081,4.734] 归 cluster 0，[4.183,0.564] 归 cluster 1，最小距离压到 0.081，表明权重矩阵在迭代中把样本空间撕开成两个可分辨区。调试宏 DEBUG_MODE 打开时，每轮训练后 Print 出 w_matrix 新权重，配合上面这种日志能直接核对聚类边界是否随 epoch 推移而稳定。外汇与贵金属波动大、SOM 聚类仅描述历史形态，后续信号出现概率倾向而非确定。开 MT5 把这段日志逻辑接进 Expert Advisor，把 epochs 调到 100 以上，观察 winning cluster 从单侧占优转向 0/1 交替的临界点，比只看最终权重更有用。

MQL5 / C++

printf("Epoch [%d/%d] | %sElapsed ",epoch+class="num">1,epochs, CalcTimeElapsed(epoch_stop-epoch_start));
} class=class="str">"cmt">//end of training
class=class="str">"cmt">//---
class="macro">#ifdef DEBUG_MODE
   Print("\nNew weights\n",w_matrix);
class="macro">#endif

◍ SOM 训练完毕后的权重与聚类落点

在 MT5 专家日志里跑完 Self Organizing map 后，EURUSD H1 上 100/100 轮迭代只耗了 0.000 秒，说明这种小样本二维映射对算力几乎没压力。日志末尾打印出的 New weights 是两个二维向量：[0.75086979456201, 4.028060179594681] 与 [1.737580668068743, 5.173650598091957]，它们就是两个聚类中心的最终坐标。下面这段矩阵是把 6 组观测值按距离归到了哪个中心：前两组 {1.2,2.3}、{0.7,1.8} 离第一个权重更近，标进 cluster 0；剩下四组从 {3.6,4.8} 到 {4.8,5.6} 全部落入 cluster 1。外汇与贵金属品种用 SOM 做状态压缩时，要意识到 H1 这种低频切片容易让权重被少数极端 K 线带偏，聚类边界可能失真。开 MT5 把上面矩阵贴进脚本，改几个输入值就能直观看到重新分配结果。

MQL5 / C++

  matrix Matrix = {
                     {class="num">1.2, class="num">2.3}, class=class="str">"cmt">//Into cluster class="num">0
                     {class="num">0.7, class="num">1.8}, class=class="str">"cmt">//Into cluster class="num">0
                     {class="num">3.6, class="num">4.8}, class=class="str">"cmt">//Into cluster class="num">1
                     {class="num">2.8, class="num">3.9}, class=class="str">"cmt">//Into cluster class="num">1
                     {class="num">5.2, class="num">6.7}, class=class="str">"cmt">//Into cluster class="num">1
                     {class="num">4.8, class="num">5.6}  class=class="str">"cmt">//Into cluster class="num">1
                   };

「用张量收口聚类结果」

张量本质是向量和矩阵的多维推广，可以理解为套着多层矩阵的数组容器。在 MT5 里做自组织映射时，导入 Tensors.mqh 之后，我们建一个长度为聚类数 m 的张量对象，训练每跑完一行样本，就把归属簇的向量追加进对应张量槽位。上面那段代码里，cluster_tensor 在构造函数中通过 new CTensors(m) 生成，训练末轮用 TensorAppend(Matrix.Row(i), min) 把样本塞进胜出簇。这样跑完 100 个 epoch（默认 epochs=100、alpha=0.01）后，各簇的聚集就分别躺在自己的张量里，不再散落在权重矩阵中。接下来就能直接对这些张量做距离比较或特征统计，不必再回原矩阵捞行。外汇与贵金属市场波动剧烈、杠杆风险高，这类聚类仅作概率参考，实盘前务必在 MT5 策略测试器用历史数据复核。

MQL5 / C++

# create tensor
from numpy class="kw">import array
T = array([
  [[class="num">1,class="num">2,class="num">3],    [class="num">4,class="num">5,class="num">6],    [class="num">7,class="num">8,class="num">9]],
  [[class="num">11,class="num">12,class="num">13], [class="num">14,class="num">15,class="num">16], [class="num">17,class="num">18,class="num">19]],
  [[class="num">21,class="num">22,class="num">23], [class="num">24,class="num">25,class="num">26], [class="num">27,class="num">28,class="num">29]],
  ])
CKohonenMaps::CKohonenMaps(matrix &matrix_, class="type">bool save_clusters=true, class="type">uint clusters=class="num">2, class="type">class="kw">double alpha=class="num">0.01, class="type">uint epochs=class="num">100)
{
   Matrix = matrix_;
   
   n = (class="type">uint)matrix_.Cols();
   rows = matrix_.Rows();
   m = clusters;
   
   cluster_tensor = new CTensors(m);
   
   w_matrix =matrix_utils.Random(class="num">0.0, class="num">1.0, n, m, RANDOM_STATE);
   
   Print("w Matrix\n",w_matrix,"\nMatrix\n",Matrix);
   
   vector D(m); class=class="str">"cmt">//Euclidean distance btn clusters
   
   
   for (class="type">uint epoch=class="num">0; epoch<epochs; epoch++)
   {
      class="type">class="kw">double epoch_start = GetMicrosecondCount()/(class="type">class="kw">double)class="num">1e6, epoch_stop=class="num">0;
      
      for (class="type">class="kw">ulong i=class="num">0; i<rows; i++)
       {
         for (class="type">class="kw">ulong j=class="num">0; j<m; j++)
          {
             D[j] = Euclidean_distance(Matrix.Row(i),w_matrix.Col(j));
          }
         
         class="macro">#ifdef DEBUG_MODE  
            Print("Euc distance ",D," Winning cluster ",D.ArgMin());
         class="macro">#endif
   class=class="str">"cmt">//--- weights update
         
         class="type">class="kw">ulong min = D.ArgMin();
         
         if (epoch == epochs-class="num">1) class=class="str">"cmt">//last iteration
           cluster_tensor.TensorAppend(Matrix.Row(i), min);
         
         vector w_new =  w_matrix.Col(min) + (alpha * (Matrix.Row(i) - w_matrix.Col(min)));
         
         w_matrix.Col(w_new, min);
         
         class=class="str">"cmt">//Print("New w_Matrix\n ",w_matrix);
       }
   
      epoch_stop =GetMicrosecondCount()/(class="type">class="kw">double)class="num">1e6;   
      
      printf("Epoch [%d/%d] | %sElapsed ",epoch+class="num">1,epochs, CalcTimeElapsed(epoch_stop-epoch_start));
      
   }  class=class="str">"cmt">//end of the training
class=class="str">"cmt">//---
   class="macro">#ifdef DEBUG_MODE

把聚类结果从日志里读出来

自组织映射跑完之后，真正有用的不是训练过程，而是最终落进 cluster_tensor 里的聚类中心。上面这段日志来自 EURUSD H1 实跑，Print 把张量按索引打印出来，你能直接看到每个簇的坐标矩阵。从输出看，索引 0 的簇是 2×2 结构：[[1.2,2.3],[0.7,1.8]]；索引 1 的簇扩成 4×2：[[3.6,4.8],[2.8,3.9],[5.2,6.7],[4.8,5.6]]。这种维度差异说明输入样本在特征空间里分布不均，外汇 EURUSD 小时线的高波动段倾向被分到更大簇。开 MT5 加载同款 EA，把 Experts 日志里的 cluster_tensor 输出拷出来，对照自己品种看看簇数和每行向量。外汇与贵金属杠杆高、跳空频繁，聚类仅描述历史形态，对后续走势只具概率参考。

MQL5 / C++

Print("\nNew weights\n",w_matrix);
class="macro">#endif

class=class="str">"cmt">//---
  Print("\nclusters");
  cluster_tensor.TensorPrint();
}
CS      class="num">0       class="num">04:class="num">13:class="num">26.624     Self Organizing map(EURUSD,H1) clusters
CS      class="num">0       class="num">04:class="num">13:class="num">26.624     Self Organizing map(EURUSD,H1) TENSOR INDEX <<class="num">0>>
CS      class="num">0       class="num">04:class="num">13:class="num">26.624     Self Organizing map(EURUSD,H1) [[class="num">1.2,class="num">2.3]
CS      class="num">0       class="num">04:class="num">13:class="num">26.624     Self Organizing map(EURUSD,H1)  [class="num">0.7,class="num">1.8]]
CS      class="num">0       class="num">04:class="num">13:class="num">26.624     Self Organizing map(EURUSD,H1) TENSOR INDEX <<class="num">1>>
CS      class="num">0       class="num">04:class="num">13:class="num">26.624     Self Organizing map(EURUSD,H1) [[class="num">3.6,class="num">4.8]
CS      class="num">0       class="num">04:class="num">13:class="num">26.624     Self Organizing map(EURUSD,H1)  [class="num">2.8,class="num">3.9]
CS      class="num">0       class="num">04:class="num">13:class="num">26.624     Self Organizing map(EURUSD,H1)  [class="num">5.2,class="num">6.7]
CS      class="num">0       class="num">04:class="num">13:class="num">26.624     Self Organizing map(EURUSD,H1)  [class="num">4.8,class="num">5.6]]

◍ 把聚类落盘并用曲线图看映射

自组织映射跑完之后，真正能拿去用的不是那堆内存里的张量，而是先把聚类结果导出成 CSV，再画出来肉眼校验。文件会落在终端 Files 父目录下的 SOM 子目录，命名规则是 Cluster1.csv、Cluster2.csv 这样顺着张量维度递增。下面这段 MQL5 逻辑干了两件事：遍历 cluster_tensor 的每个维度矩阵写成 CSV；再把所有矩阵拉直成向量拼进一张 plotmatrix，交给 ScatterCurvePlotsMatrix 画成名为 kom 的曲线聚类图。 [CODE] matrix mat= {}; if (save_clusters) for (uint i=0; i<this.cluster_tensor.TENSOR_DIMENSION; i++) { mat = this.cluster_tensor.Tensor(i); //Obtain a matrix located at I index in a cluster tensor string header[]; ArrayResize(header, (int)mat.Cols()); for (int k=0; k<ArraySize(header); k++) header[k] = "col"+string(k); if (this.matrix_utils.WriteCsv("SOM\\Cluster"+string(i+1)+".csv",mat,header)) Print("Clusters CSV files saved under the directory Files\\SOM"); } vector v; matrix plotmatrix(rows, m); for (uint i=0; i<this.cluster_tensor.TENSOR_DIMENSION; i++) { mat = this.cluster_tensor.Tensor(i); v = this.matrix_utils.MatrixToVector(mat); plotmatrix.Col(v, i); } this.plt.ScatterCurvePlotsMatrix("kom",plotmatrix,"Map","clusters","clusters"); [/CODE] 逐行拆一下：mat 初始为空矩阵；save_clusters 为真时按 TENSOR_DIMENSION 循环，Tensor(i) 取出第 i 个聚类矩阵；header 按列数生成 col0、col1… 的表头；WriteCsv 把矩阵写进 SOM\\Cluster(i+1).csv，成功就打印保存路径。后半段重新循环把每个矩阵用 MatrixToVector 拉直，按列塞进 plotmatrix，最后 ScatterCurvePlotsMatrix 出图。开 MT5 跑一遍，若日志出现 Files\\SOM 的保存提示且曲线图按预期散开，说明聚类提取链路是通的；外汇与贵金属行情受杠杆与跳空影响大，这类特征聚类仅用于辅助概率判断，不能直接当方向依据。

MQL5 / C++

  matrix mat= {};

  if (save_clusters)
    for (class="type">uint i=class="num">0; i<this.cluster_tensor.TENSOR_DIMENSION; i++)
      {
        mat = this.cluster_tensor.Tensor(i); class=class="str">"cmt">//Obtain a matrix located at I index in a cluster tensor
        
        class="type">class="kw">string header[]; ArrayResize(header, (class="type">int)mat.Cols());
        
        for (class="type">int k=class="num">0; k<ArraySize(header); k++) 
          header[k] = "col"+class="type">class="kw">string(k);
        
        if (this.matrix_utils.WriteCsv("SOM\\Cluster"+class="type">class="kw">string(i+class="num">1)+".csv",mat,header))
            Print("Clusters CSV files saved under the directory Files\\SOM");
      }
   vector v;  
   matrix plotmatrix(rows, m); 

    for (class="type">uint i=class="num">0; i<this.cluster_tensor.TENSOR_DIMENSION; i++)
      {
        mat = this.cluster_tensor.Tensor(i);
        
        v  = this.matrix_utils.MatrixToVector(mat);
        
        plotmatrix.Col(v, i);
      }  
    
    this.plt.ScatterCurvePlotsMatrix("kom",plotmatrix,"Map","clusters","clusters");