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名义变量的序数编码·进阶篇
（2/3）· 当决策树能直接吃类别、逻辑回归却只认数字，错配编码会让算法脑补出不存在的等级
给针形K线编个 3、纺锤线编个 1，很多交易者以为这只是给机器学习凑输入。实际上算法可能把这个 3 当成比 1 高级，把无顺序的类别硬读出排名，模型学到的全是噪声。
◍ 把K线形态字段压成模型能吃的数字
做价格行为相关的机器学习，第一步往往是把「bar_type / body_type / bar_pattern」这类文本标签变成数值。最直白的是序数编码：给每个类别硬派一个整数。这招只在你事先清楚类别和目标关系时才够用；无监督场景下用它会偷偷塞进本不存在的先后顺序，模型可能学到假规律。 不依赖目标变量的安全牌是独热、二进制和频率编码。独热把每个类别拆成 0/1 列，对 12 个月编码会多出 11 列，维度膨胀明显；二进制先转整数再摊成二进制位，同样 12 个月只需 4 列；频率编码直接用类别出现次数替换，不新增列，但主导类别太多时会带偏分布。 想让编码带一点预测力，就用盯住目标的方案。目标编码拿类别对应的目标均值填进去，高基数变量（比如几十种形态组合）不扩维就能塞进信息；留一法编码算均值时抠掉当前行，小样本里过拟合风险低一些；詹姆斯-斯坦因编码按样本量把类别均值往总均值拉，稀疏或类别不均时比前两种稳。 下面这段 Python 用了 category_encoders 把刚才说的七种全跑了一遍，列名都是价格行为提取的字段，复制去 Jupyter 里改 prices 就能看 head 输出。外汇和贵金属行情序列短、跳空多，编码后务必做交叉验证，过拟合概率不低。
MQL5 / C++
class="macro">#Ordinal encoding ord_encoder = OrdinalEncoder(cols = ["bar_type","body_type","bar_pattern"]) ordinal_data = ord_encoder.fit_transform(prices) print(" ordinal encoding\n ", ordinal_data.head()) class="macro">#One-Hot encoding onehot_encoder = OneHotEncoder(cols = ["bar_type","body_type","bar_pattern"]) onehot_data = onehot_encoder.fit_transform(prices) print(" ordinal encoding\n ", onehot_data.head()) class="macro">#Binary encoding binary_encoder = BinaryEncoder(cols = ["bar_type","body_type","bar_pattern"]) binary_data = binary_encoder.fit_transform(prices) print(" binary encoding\n ", binary_data.head()) class="macro">#Frequency encoding freq_encoder = CountEncoder(cols = ["bar_type","body_type","bar_pattern"]) freq_data = freq_encoder.fit_transform(prices) print(" frequency encoding\n ", freq_data.head()) class="macro">#Target encoding target_encoder = TargetEncoder(cols = ["bar_type","body_type","bar_pattern"]) target_data = target_encoder.fit_transform(prices[["open","high","low","close","bar_type","body_type","bar_pattern"]], prices["target"]) print(" target encoding\n ", target_data.head()) class="macro">#LeaveOneOut encoding oneout_encoder = LeaveOneOutEncoder(cols = ["bar_type","body_type","bar_pattern"]) oneout_data = oneout_encoder.fit_transform(prices[["open","high","low","close","bar_type","body_type","bar_pattern"]], prices["target"]) print(" LeaveOneOut encoding\n ", oneout_data.head()) class="macro">#James Stein encoding james_encoder = JamesSteinEncoder(cols = ["bar_type","body_type","bar_pattern"]) james_data = james_encoder.fit_transform(prices[["open","high","low","close","bar_type","body_type","bar_pattern"]], prices["target"]) print(" James Stein encoding\n ", james_data.head())
「把名义变量塞进MT5的两种编码套路」
在MT5里处理分类特征，先得区分两种编码思路：独热（One-Hot）和目标编码变体。前者把每个类别摊成0/1列，后者在不扩维的前提下把类别映射到序数刻度，封装在nom2ord.mqh里，分别由COneHotEncoder和CNomOrd两个类承担。 COneHotEncoder的用法很直白：建实例后先调fit()，喂入特征矩阵和列索引数组。数组留空就默认全部列都是名义变量；fit()返回true后，再拿列数一致的矩阵去transform()，维度不对会直接报错。BTCUSD数据集跑下来，原始几列类别被展开成多列0/1，特征宽度明显增加。 CNomOrd走的是另一条路。fit()除了矩阵和列索引，还要一个目标变量向量。它先用百分位数把目标重标到0–100，最小值排0、最大值排100，中间按比例，这样异常值对编码的拉动被削弱，过拟合概率下降。 score()用蒙特卡洛置换检验算p值：反复打乱目标变量，看真实类别间目标百分位极差（最大均值减最小均值）是否显著偏离随机分布。原假设是「差异纯属偶然」。在BTCUSD上，只有多/空分类的p值显著，双K线形态和实体大小的p值偏高，说明它们跟目标的关系和随机变量差不多。 降维版fitTransform()能把任意多个名义变量压成单一序数变量，但演示脚本给出的新变量p值偏高——信息丢失是这种压缩的固有代价，实盘前应在历史样本上先验证区分度。外汇与贵金属市场高风险，这类特征工程只降低建模偏差，不预示任何方向。
MQL5 / C++
class=class="str">"cmt">//+------------------------------------------------------------------+ class=class="str">"cmt">//| one hot encoder class | class=class="str">"cmt">//+------------------------------------------------------------------+ class COneHotEncoder { class="kw">private: vector m_mapping[]; class="type">ulong m_cat_cols[]; class="type">ulong m_vars,m_cols; class="kw">public: class=class="str">"cmt">//+------------------------------------------------------------------+ class=class="str">"cmt">//| Constructor | class=class="str">"cmt">//+------------------------------------------------------------------+ COneHotEncoder(class="type">void) { } class=class="str">"cmt">//+------------------------------------------------------------------+ class=class="str">"cmt">//| Destructor | class=class="str">"cmt">//+------------------------------------------------------------------+ ~COneHotEncoder(class="type">void) { ArrayFree(m_mapping); } class=class="str">"cmt">//+------------------------------------------------------------------+ class=class="str">"cmt">//| map categorical features of a training dataset | class=class="str">"cmt">//+------------------------------------------------------------------+ class="type">bool fit(matrix &in_data,class="type">ulong &cols[]) { m_cols = in_data.Cols(); matrix data = np::selectMatrixCols(in_data,cols); if(data.Cols()!=class="type">ulong(cols.Size())) { Print(__FUNCTION__, " invalid input data "); class="kw">return false; } m_vars = class="type">ulong(cols.Size());
类别特征矩阵的重映射与对齐
把任意特征矩阵转成模型能吃的类别编码，核心是先校验列维度。若输入列数不等于训练时记录的 m_cols，直接返回 1×1 零矩阵，避免后续越界。 先抽取类别列：用 np::selectMatrixCols 从 in_data 中按 m_cat_cols 挑出子矩阵 data，并确认 data.Cols() 等于 m_cat_cols.Size()，否则同样返回 1×1 零矩阵。 非类别列需单独保留。代码里用 ArrayBsearch 在 m_cat_cols 中找每一列索引 i，若找不到（m_cat_cols[found]!=i）就塞进 unchanged_feature_cols；最后用 selectMatrixCols 把原样特征拷到 input_copy。 类别列则按 m_mapping 做编码替换，累计新列数用 cumsum 向量跟踪，其长度为 MathMin(m_vars, data.Cols())。外汇与贵金属数据做这类特征工程时波动大，维度校验失败的概率偏高，建议在 MT5 里对历史 tick 数据先跑一次列数断言。
MQL5 / C++
if(ArrayCopy(m_cat_cols,cols)<=class="num">0 || !ArraySort(m_cat_cols)) { Print(__FUNCTION__, " ArrayCopy or ArraySort failure ", GetLastError()); class="kw">return false; } if(ArrayResize(m_mapping,class="type">int(m_vars))<class="num">0) { Print(__FUNCTION__, " Vector array resize failure ", GetLastError()); class="kw">return false; } for(class="type">ulong i = class="num">0; i<m_vars; i++) { vector unique = data.Col(i); m_mapping[i] = np::unique(unique); } class="kw">return true; } class=class="str">"cmt">//+------------------------------------------------------------------+ class=class="str">"cmt">//| Transform abitrary feature matrix to learned category m_mapping | class=class="str">"cmt">//+------------------------------------------------------------------+ matrix transform(matrix &in_data) { if(in_data.Cols()!=m_cols) { Print(__FUNCTION__," Column dimension of input not equal to ", m_cols); class="kw">return matrix::Zeros(class="num">1,class="num">1); } matrix out,input_copy; matrix data = np::selectMatrixCols(in_data,m_cat_cols); if(data.Cols()!=class="type">ulong(m_cat_cols.Size())) { Print(__FUNCTION__, " invalid input data "); class="kw">return matrix::Zeros(class="num">1,class="num">1); } class="type">ulong unchanged_feature_cols[]; for(class="type">ulong i = class="num">0; i<in_data.Cols(); i++) { class="type">int found = ArrayBsearch(m_cat_cols,i); if(m_cat_cols[found]!=i) { if(!unchanged_feature_cols.Push(i)) { Print(__FUNCTION__, " Failed array insertion ", GetLastError()); class="kw">return matrix::Zeros(class="num">1,class="num">1); } } } input_copy = unchanged_feature_cols.Size()?np::selectMatrixCols(in_data,unchanged_feature_cols):input_copy; class="type">ulong numcols = class="num">0; vector cumsum = vector::Zeros(class="type">ulong(MathMin(m_vars,data.Cols())));
◍ 独热编码的列拼接实现细节
上面这段逻辑做的是分类特征到数值矩阵的转换：先算每个原始列在映射后占多少位，用 cumsum 记录累计偏移，再开一个全零矩阵 out，行数跟原数据一致，列数是所有映射类别数之和。 内层三层循环逐行扫描，若某单元格数值与映射表里的某个类别差不超过 1e-15，就在对应偏移位置写 1.0 并 break，等价于标准 one-hot 赋值。 最后用 matrixCopyCols 把原输入（若有）和 out 横向拼成 newfeaturematrix；任一步拷贝失败就 Print 报错并返回 1x1 零矩阵，调用方需自行判断尺寸来避坑。 下方 demo 脚本头里 TrainingSampleStartDate 设成 2023.12.31、StopDate 却是 2017.12.31，时间区间倒置，直接跑会取不到样本，改参数前先对调这两个日期。
MQL5 / C++
for(class="type">ulong i = class="num">0; i<cumsum.Size(); i++) { cumsum[i] = class="type">class="kw">double(numcols); numcols+=m_mapping[i].Size(); } out = matrix::Zeros(data.Rows(),numcols); for(class="type">ulong i = class="num">0;i<data.Rows(); i++) { vector row = data.Row(i); for(class="type">ulong col = class="num">0; col<row.Size(); col++) { for(class="type">ulong k = class="num">0; k<m_mapping[col].Size(); k++) { if(MathAbs(row[col]-m_mapping[col][k])<=class="num">1.e-15) { out[i][class="type">ulong(cumsum[col])+k]=class="num">1.0; class="kw">break; } } } } matrix newfeaturematrix(out.Rows(),input_copy.Cols()+out.Cols()); if((input_copy.Cols()>class="num">0 && !np::matrixCopyCols(newfeaturematrix,input_copy,class="num">0,input_copy.Cols())) || !np::matrixCopyCols(newfeaturematrix,out,input_copy.Cols())) { Print(__FUNCTION__, " Failed matrix copy "); class="kw">return matrix::Zeros(class="num">1,class="num">1); } class="kw">return newfeaturematrix; } }; class=class="str">"cmt">//+------------------------------------------------------------------+ class=class="str">"cmt">//+------------------------------------------------------------------+ class=class="str">"cmt">//| OneHotEncoding_demo.mq5 | class=class="str">"cmt">//| Copyright class="num">2024, MetaQuotes Ltd. | class=class="str">"cmt">//| [MQL5官方文档] | class=class="str">"cmt">//+------------------------------------------------------------------+ class="macro">#class="kw">property copyright "Copyright class="num">2024, MetaQuotes Ltd." class="macro">#class="kw">property link "[MQL5官方文档] class="macro">#class="kw">property version "class="num">1.00" class="macro">#class="kw">property script_show_inputs class="macro">#include<np.mqh> class="macro">#include<nom2ord.mqh> class="macro">#include<ErrorDescription.mqh> class=class="str">"cmt">//--- input parameters input class="type">class="kw">datetime TrainingSampleStartDate=D&class="macro">#x27;class="num">2023.12.class="num">31&class="macro">#x27;; input class="type">class="kw">datetime TrainingSampleStopDate=D&class="macro">#x27;class="num">2017.12.class="num">31&class="macro">#x27;; input ENUM_TIMEFRAMES tf = PERIOD_D1; input class="type">class="kw">string SetSymbol="BTCUSD"; class=class="str">"cmt">//+------------------------------------------------------------------+
「训练集切分与对数价差矩阵落地」
做样本内建模前，先得把训练区间的 K 线索引抓准。用 iBarShift 把 TrainingSampleStartDate / StopDate 转成柱索引，若返回负值说明日期或周期不对，直接打印错误并退出，避免后面数组尺寸算歪。 size_insample 就是 (trainstop - trainstart) + 1，代表训练集总根数；若算出 ≤0 属于输入参数冲突，脚本会报 Invalid inputs。 predictors 矩阵被硬性 Resize 成 size_insample × 3，也就是每根 K 线留 3 个特征位，后续填数据若失败同样退场。 价格数据走 CopyRates 拉 OHLC 竖排矩阵，targets 取第 3 列（收盘价）做 log 变换后再 np::diff 一阶差分，得到可训练的收益率序列。循环里已开始按 prices[i][3] 与开盘价 prices[i][0] 比大小，为阴线判定打底——外汇与贵金属杠杆高，样本错配会让回测失真，建议开 MT5 用自己品种跑一遍确认索引偏移。
MQL5 / C++
class=class="str">"cmt">//|global integer variables | class=class="str">"cmt">//+------------------------------------------------------------------+ class="type">int size_insample, class=class="str">"cmt">//training set size size_observations, class=class="str">"cmt">//size of of both training and testing sets combined price_handle=INVALID_HANDLE; class=class="str">"cmt">//log prices indicator handle class=class="str">"cmt">//+------------------------------------------------------------------+ class=class="str">"cmt">//|class="type">class="kw">double global variables | class=class="str">"cmt">//+------------------------------------------------------------------+ matrix prices; class=class="str">"cmt">//array for log transformed prices vector targets; class=class="str">"cmt">//differenced prices kept here matrix predictors; class=class="str">"cmt">//flat array arranged as matrix of all predictors ie size_observations by size_predictors class=class="str">"cmt">//+------------------------------------------------------------------+ class=class="str">"cmt">//| Script program start function | class=class="str">"cmt">//+------------------------------------------------------------------+ class="type">void OnStart() { class=class="str">"cmt">//get relative shift of is and oos sets class="type">int trainstart,trainstop; trainstart=iBarShift(SetSymbol!=""?SetSymbol:NULL,tf,TrainingSampleStartDate); trainstop=iBarShift(SetSymbol!=""?SetSymbol:NULL,tf,TrainingSampleStopDate); class=class="str">"cmt">//check for errors from ibarshift calls if(trainstart<class="num">0 || trainstop<class="num">0) { Print(ErrorDescription(GetLastError())); class="kw">return; } class=class="str">"cmt">//---set the size of the sample sets size_insample=(trainstop - trainstart) + class="num">1; class=class="str">"cmt">//---check for input errors if(size_insample<=class="num">0) { Print("Invalid inputs "); class="kw">return; } class=class="str">"cmt">//--- if(!predictors.Resize(size_insample,class="num">3)) { Print("ArrayResize error ",ErrorDescription(GetLastError())); class="kw">return; } class=class="str">"cmt">//--- if(!prices.CopyRates(SetSymbol,tf,COPY_RATES_VERTICAL|COPY_RATES_OHLC,TrainingSampleStartDate,TrainingSampleStopDate)) { Print("Copyrates error ",ErrorDescription(GetLastError())); class="kw">return; } class=class="str">"cmt">//--- targets = log(prices.Col(class="num">3)); targets = np::diff(targets); class=class="str">"cmt">//--- class="type">class="kw">double bodyratio = class="num">0.0; for(class="type">ulong i = class="num">0; i<prices.Rows(); i++) { if(prices[i][class="num">3]<prices[i][class="num">0])
把K线形态编码成模型能吃的数字
这段逻辑干的事很直接：把每根K线的涨跌方向和实体占比，转成离散特征喂给后续模型。先判涨跌——若当前收盘不低于开盘，predictors[i][0]记0，否则记1，相当于给每根K线贴个多空标签。
| 实体占比用 | 收盘-开盘 | 除以 | 最高-最低 | 算，阈值切四档：≥0.75记0（实体饱满），0.5~0.75记1，0.25~0.5记2，低于0.25记3（针线）。外汇和贵金属这种高杠杆品种，影线占比突变往往伴随假突破，这档位划分能给模型留出识别毛刺的空间，但本身不预示方向，只是特征工程。 |
|---|
第三列存相邻K线关系：两根都涨且高、低都抬，记2；两根都跌但低点下移、高点抬（下跌收敛），记1；其余记0。i<1时没前一根，直接填0并跳过。 最后把 prices 和 predictors 对齐行数、拼成 fullFeatureMatrix，对第4/5/6列做 OneHot 编码。若行数对不上 targets 或矩阵合并失败，直接 Print 报错 return。开 MT5 把这段塞进你的特征函数，先 Print 出 original predictors 看分布，再决定阈值要不要按品种波动率重调。
MQL5 / C++
predictors[i][class="num">0] = class="num">0.0; else predictors[i][class="num">0] = class="num">1.0; bodyratio = MathAbs(prices[i][class="num">3]-prices[i][class="num">0])/MathAbs(prices[i][class="num">1]-prices[i][class="num">2]); if(bodyratio >=class="num">0.75) predictors[i][class="num">1] = class="num">0.0; else if(bodyratio<class="num">0.75 && bodyratio>=class="num">0.5) predictors[i][class="num">1] = class="num">1.0; else if(bodyratio<class="num">0.5 && bodyratio>=class="num">0.25) predictors[i][class="num">1] = class="num">2.0; else predictors[i][class="num">1] = class="num">3.0; if(i<class="num">1) { predictors[i][class="num">2] = class="num">0.0; class="kw">continue; } if(predictors[i][class="num">0]==class="num">1.0 && predictors[i-class="num">1][class="num">0]==class="num">1.0 && prices[i][class="num">1]>prices[i-class="num">1][class="num">1] && prices[i][class="num">2]>prices[i-class="num">1][class="num">2]) predictors[i][class="num">2] = class="num">2.0; else if(predictors[i][class="num">0]==class="num">0.0 && predictors[i-class="num">1][class="num">0]==class="num">0.0 && prices[i][class="num">2]<prices[i-class="num">1][class="num">2] && prices[i][class="num">1]>prices[i-class="num">1][class="num">1]) predictors[i][class="num">2] = class="num">1.0; else predictors[i][class="num">2] = class="num">0.0; } targets = np::sliceVector(targets,class="num">1); prices = np::sliceMatrixRows(prices,class="num">1,predictors.Rows()-class="num">1); predictors = np::sliceMatrixRows(predictors,class="num">1,predictors.Rows()-class="num">1); matrix fullFeatureMatrix(predictors.Rows(),predictors.Cols()+prices.Cols()); if(!np::matrixCopyCols(fullFeatureMatrix,prices,class="num">0,prices.Cols()) || !np::matrixCopyCols(fullFeatureMatrix,predictors,prices.Cols())) { Print("Failed to merge matrices"); class="kw">return; } if(predictors.Rows()!=targets.Size()) { Print(" Error in aligning data structures "); class="kw">return; } COneHotEncoder enc; class="type">ulong selectedcols[] = {class="num">4,class="num">5,class="num">6}; if(!enc.fit(fullFeatureMatrix,selectedcols)) class="kw">return; matrix transformed = enc.transform(fullFeatureMatrix); Print(" Original predictors \n", fullFeatureMatrix);
让小布替你跑这套编码检查
这些诊断小布盯盘的 AIGC 已内置，打开对应品种页即可看到哪些名义字段被误当序数送入模型，你只管调特征。
常见问题
名义变量类别间无内在顺序，如K线形态；序数变量有等级，如趋势强度。误把名义当序数会让算法虚构层级关系。
它们需要数值输入且对数值大小敏感，名义类别无数学意义，必须转成可解释的数字形式才能训练。
可以，小布在品种页内置了特征诊断，会标记被误赋序数的名义字段，帮你避开人工编码带来的模型偏差。
MQL5 原生无类别容器，多用整数区分，写映射逻辑更繁琐，但能直接在 EA 内闭环，不必跨语言搬运数据。
文中按形态模式分三类，彼此无等级，属名义变量；若按高低排列赋予顺序才转成序数，原始定义不可乱序。