{"id":80770,"date":"2026-03-06T00:51:23","date_gmt":"2026-03-05T16:51:23","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/80770.html"},"modified":"2026-03-06T00:51:23","modified_gmt":"2026-03-05T16:51:23","slug":"%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0%e5%88%86%e7%b1%bb%e7%ae%97%e6%b3%95%e4%b8%80-%e5%86%b3%e7%ad%96%e6%a0%91","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/80770.html","title":{"rendered":"\u673a\u5668\u5b66\u4e60\u5206\u7c7b\u7b97\u6cd5\u4e00\u2014\u2014\u51b3\u7b56\u6811"},"content":{"rendered":"

\u4e00\u3001\u7b97\u6cd5\u539f\u7406<\/h2>\n

\u51b3\u7b56\u6811\u7b97\u6cd5\u901a\u8fc7\u5c06\u6570\u636e\u96c6\u5212\u5206\u4e3a\u4e0d\u540c\u7684\u5b50\u96c6\u6765\u9884\u6d4b\u76ee\u6807\u53d8\u91cf\u3002\u5b83\u4ece\u6839\u8282\u70b9\u5f00\u59cb，\u6839\u636e\u67d0\u4e2a\u7279\u5f81\u5bf9\u6570\u636e\u96c6\u8fdb\u884c\u5212\u5206，\u7136\u540e\u9012\u5f52\u5730\u751f\u6210\u66f4\u591a\u7684\u5b50\u8282\u70b9，\u76f4\u5230\u6ee1\u8db3\u505c\u6b62\u6761\u4ef6\u4e3a\u6b62\u3002\u51b3\u7b56\u6811\u7684\u6bcf\u4e2a\u5185\u90e8\u8282\u70b9\u8868\u793a\u4e00\u4e2a\u7279\u5f81\u5c5e\u6027\u4e0a\u7684\u5224\u65ad\u6761\u4ef6，\u6bcf\u4e2a\u5206\u652f\u4ee3\u8868\u4e00\u4e2a\u53ef\u80fd\u7684\u5c5e\u6027\u503c，\u6bcf\u4e2a\u53f6\u8282\u70b9\u8868\u793a\u4e00\u4e2a\u5206\u7c7b\u7ed3\u679c\u3002<\/p>\n

\u4e8c\u3001\u53c2\u8003\u4ee3\u7801<\/h2>\n

import<\/span> numpy as<\/span> np
\nimport<\/span> matplotlib.<\/span>pyplot as<\/span> plt<\/p>\n

class<\/span> TreeNode<\/span>:<\/span>
\n def<\/span> __init__<\/span>(<\/span>self,<\/span> feature_idx=<\/span>None<\/span>,<\/span> threshold=<\/span>None<\/span>,<\/span> left=<\/span>None<\/span>,<\/span> right=<\/span>None<\/span>,<\/span> class_dist=<\/span>None<\/span>)<\/span>:<\/span>
\n self.<\/span>feature_idx =<\/span> feature_idx # \u5206\u5272\u7279\u5f81\u7d22\u5f15<\/span>
\n self.<\/span>threshold =<\/span> threshold # \u5206\u5272\u9608\u503c<\/span>
\n self.<\/span>left =<\/span> left # \u2264 threshold \u7684\u5b50\u6811<\/span>
\n self.<\/span>right =<\/span> right # > threshold \u7684\u5b50\u6811<\/span>
\n self.<\/span>class_dist =<\/span> class_dist # \u53f6\u5b50\u8282\u70b9\u7684\u7c7b\u522b\u5206\u5e03（\u7528\u4e8e\u9884\u6d4b）<\/span><\/p>\n

class<\/span> SimpleDecisionTree<\/span>:<\/span>
\n def<\/span> __init__<\/span>(<\/span>self,<\/span> max_depth=<\/span>3<\/span>)<\/span>:<\/span>
\n self.<\/span>max_depth =<\/span> max_depth
\n self.<\/span>tree =<\/span> None<\/span>
\n self.<\/span>n_features =<\/span> None<\/span><\/p>\n

def<\/span> fit<\/span>(<\/span>self,<\/span> X,<\/span> y)<\/span>:<\/span>
\n y =<\/span> np.<\/span>asarray(<\/span>y)<\/span>.<\/span>astype(<\/span>int<\/span>)<\/span> # \u786e\u4fdd y \u662f\u6574\u6570<\/span><\/p>\n

self.<\/span>n_features =<\/span> X.<\/span>shape[<\/span>1<\/span>]<\/span>
\n self.<\/span>tree =<\/span> self.<\/span>_grow_tree(<\/span>X,<\/span> y,<\/span> depth=<\/span>0<\/span>)<\/span><\/p>\n

def<\/span> _grow_tree<\/span>(<\/span>self,<\/span> X,<\/span> y,<\/span> depth)<\/span>:<\/span>
\n n_samples,<\/span> n_features =<\/span> X.<\/span>shape
\n n_classes =<\/span> len<\/span>(<\/span>np.<\/span>unique(<\/span>y)<\/span>)<\/span><\/p>\n

# \u505c\u6b62\u6761\u4ef6：\u8fbe\u5230\u6700\u5927\u6df1\u5ea6\u6216\u6240\u6709\u6837\u672c\u5c5e\u4e8e\u540c\u4e00\u7c7b\u522b<\/span>
\n if<\/span> depth >=<\/span> self.<\/span>max_depth or<\/span> n_classes ==<\/span> 1<\/span>:<\/span>
\n class_dist =<\/span> np.<\/span>bincount(<\/span>y,<\/span> minlength=<\/span>2<\/span>)<\/span>
\n return<\/span> TreeNode(<\/span>class_dist=<\/span>class_dist)<\/span><\/p>\n

# \u5bfb\u627e\u6700\u4f73\u5206\u5272<\/span>
\n best_feature,<\/span> best_threshold =<\/span> self.<\/span>_best_split(<\/span>X,<\/span> y)<\/span><\/p>\n

# \u9012\u5f52\u751f\u957f\u5de6\u53f3\u5b50\u6811<\/span>
\n left_idx =<\/span> X[<\/span>:<\/span>,<\/span> best_feature]<\/span> <=<\/span> best_threshold
\n right_idx =<\/span> ~<\/span>left_idx
\n left =<\/span> self.<\/span>_grow_tree(<\/span>X[<\/span>left_idx]<\/span>,<\/span> y[<\/span>left_idx]<\/span>,<\/span> depth +<\/span> 1<\/span>)<\/span>
\n right =<\/span> self.<\/span>_grow_tree(<\/span>X[<\/span>right_idx]<\/span>,<\/span> y[<\/span>right_idx]<\/span>,<\/span> depth +<\/span> 1<\/span>)<\/span><\/p>\n

return<\/span> TreeNode(<\/span>best_feature,<\/span> best_threshold,<\/span> left,<\/span> right)<\/span><\/p>\n

def<\/span> _best_split<\/span>(<\/span>self,<\/span> X,<\/span> y)<\/span>:<\/span>
\n best_gini =<\/span> float<\/span>(<\/span>'inf'<\/span>)<\/span>
\n best_feature,<\/span> best_threshold =<\/span> None<\/span>,<\/span> None<\/span><\/p>\n

for<\/span> feature_idx in<\/span> range<\/span>(<\/span>self.<\/span>n_features)<\/span>:<\/span>
\n thresholds =<\/span> np.<\/span>unique(<\/span>X[<\/span>:<\/span>,<\/span> feature_idx]<\/span>)<\/span>
\n for<\/span> threshold in<\/span> thresholds:<\/span>
\n gini =<\/span> self.<\/span>_gini_impurity(<\/span>X[<\/span>:<\/span>,<\/span> feature_idx]<\/span>,<\/span> y,<\/span> threshold)<\/span>
\n if<\/span> gini <<\/span> best_gini:<\/span>
\n best_gini =<\/span> gini
\n best_feature =<\/span> feature_idx
\n best_threshold =<\/span> threshold<\/p>\n

return<\/span> best_feature,<\/span> best_threshold<\/p>\n

def<\/span> _gini_impurity<\/span>(<\/span>self,<\/span> feature_col,<\/span> y,<\/span> threshold)<\/span>:<\/span>
\n left_idx =<\/span> feature_col <=<\/span> threshold
\n right_idx =<\/span> ~<\/span>left_idx<\/p>\n

if<\/span> np.<\/span>sum<\/span>(<\/span>left_idx)<\/span> ==<\/span> 0<\/span> or<\/span> np.<\/span>sum<\/span>(<\/span>right_idx)<\/span> ==<\/span> 0<\/span>:<\/span>
\n return<\/span> float<\/span>(<\/span>'inf'<\/span>)<\/span><\/p>\n

left_dist =<\/span> np.<\/span>bincount(<\/span>y[<\/span>left_idx]<\/span>,<\/span> minlength=<\/span>2<\/span>)<\/span>
\n right_dist =<\/span> np.<\/span>bincount(<\/span>y[<\/span>right_idx]<\/span>,<\/span> minlength=<\/span>2<\/span>)<\/span><\/p>\n

left_prob =<\/span> left_dist \/<\/span> np.<\/span>sum<\/span>(<\/span>left_dist)<\/span>
\n right_prob =<\/span> right_dist \/<\/span> np.<\/span>sum<\/span>(<\/span>right_dist)<\/span><\/p>\n

gini_left =<\/span> 1<\/span> –<\/span> np.<\/span>sum<\/span>(<\/span>left_prob **<\/span> 2<\/span>)<\/span>
\n gini_right =<\/span> 1<\/span> –<\/span> np.<\/span>sum<\/span>(<\/span>right_prob **<\/span> 2<\/span>)<\/span><\/p>\n

total_gini =<\/span> (<\/span>np.<\/span>sum<\/span>(<\/span>left_idx)<\/span> *<\/span> gini_left +<\/span> np.<\/span>sum<\/span>(<\/span>right_idx)<\/span> *<\/span> gini_right)<\/span> \/<\/span> len<\/span>(<\/span>y)<\/span>
\n return<\/span> total_gini<\/p>\n

def<\/span> predict<\/span>(<\/span>self,<\/span> X)<\/span>:<\/span>
\n return<\/span> np.<\/span>array(<\/span>[<\/span>self.<\/span>_predict_single(<\/span>x,<\/span> self.<\/span>tree)<\/span> for<\/span> x in<\/span> X]<\/span>)<\/span><\/p>\n

def<\/span> _predict_single<\/span>(<\/span>self,<\/span> x,<\/span> node)<\/span>:<\/span>
\n if<\/span> node.<\/span>feature_idx is<\/span> None<\/span>:<\/span> # \u53f6\u5b50\u8282\u70b9<\/span>
\n return<\/span> np.<\/span>argmax(<\/span>node.<\/span>class_dist)<\/span>
\n if<\/span> x[<\/span>node.<\/span>feature_idx]<\/span> <=<\/span> node.<\/span>threshold:<\/span>
\n return<\/span> self.<\/span>_predict_single(<\/span>x,<\/span> node.<\/span>left)<\/span>
\n else<\/span>:<\/span>
\n return<\/span> self.<\/span>_predict_single(<\/span>x,<\/span> node.<\/span>right)<\/span><\/p>\n

def<\/span> visualize_tree<\/span>(<\/span>self,<\/span> feature_names=<\/span>None<\/span>,<\/span> class_names=<\/span>None<\/span>)<\/span>:<\/span>
\n if<\/span> feature_names is<\/span> None<\/span>:<\/span>
\n feature_names =<\/span> [<\/span>f"Feature <\/span>{<\/span>i}<\/span><\/span>"<\/span><\/span> for<\/span> i in<\/span> range<\/span>(<\/span>self.<\/span>n_features)<\/span>]<\/span>
\n if<\/span> class_names is<\/span> None<\/span>:<\/span>
\n class_names =<\/span> [<\/span>"no"<\/span>,<\/span> "yes"<\/span>]<\/span><\/p>\n

fig,<\/span> ax =<\/span> plt.<\/span>subplots(<\/span>figsize=<\/span>(<\/span>10<\/span>,<\/span> 6<\/span>)<\/span>)<\/span>
\n ax.<\/span>axis(<\/span>"off"<\/span>)<\/span><\/p>\n

# \u52a8\u6001\u8ba1\u7b97\u6811\u7684\u9ad8\u5ea6（\u9012\u5f52\u6df1\u5ea6）<\/span>
\n def<\/span> calc_depth<\/span>(<\/span>node)<\/span>:<\/span>
\n if<\/span> node is<\/span> None<\/span>:<\/span>
\n return<\/span> 0<\/span>
\n left_depth =<\/span> calc_depth(<\/span>node.<\/span>left)<\/span>
\n right_depth =<\/span> calc_depth(<\/span>node.<\/span>right)<\/span>
\n return<\/span> max<\/span>(<\/span>left_depth,<\/span> right_depth)<\/span> +<\/span> 1<\/span><\/p>\n

tree_depth =<\/span> calc_depth(<\/span>self.<\/span>tree)<\/span><\/p>\n

# \u9012\u5f52\u7ed8\u5236\u8282\u70b9（\u52a8\u6001\u8c03\u6574\u4f4d\u7f6e）<\/span>
\n def<\/span> _draw_node<\/span>(<\/span>node,<\/span> x,<\/span> y,<\/span> x_offset,<\/span> y_step,<\/span> depth)<\/span>:<\/span>
\n if<\/span> node is<\/span> None<\/span>:<\/span>
\n return<\/span><\/p>\n

# \u7ed8\u5236\u5f53\u524d\u8282\u70b9<\/span>
\n if<\/span> node.<\/span>feature_idx is<\/span> not<\/span> None<\/span>:<\/span> # \u5206\u5272\u8282\u70b9<\/span>
\n ax.<\/span>text(<\/span>
\n x,<\/span>
\n y,<\/span>
\n f"<\/span>{<\/span>feature_names[<\/span>node.<\/span>feature_idx]<\/span>}<\/span><\/span> \u2264 <\/span>{<\/span>node.<\/span>threshold:<\/span>.1f<\/span>}<\/span><\/span>"<\/span><\/span>,<\/span>
\n ha=<\/span>"center"<\/span>,<\/span>
\n va=<\/span>"center"<\/span>,<\/span>
\n bbox=<\/span>dict<\/span>(<\/span>facecolor=<\/span>"white"<\/span>,<\/span> edgecolor=<\/span>"black"<\/span>,<\/span> boxstyle=<\/span>"round"<\/span>)<\/span>,<\/span>
\n )<\/span>
\n else<\/span>:<\/span> # \u53f6\u5b50\u8282\u70b9<\/span>
\n class_idx =<\/span> np.<\/span>argmax(<\/span>node.<\/span>class_dist)<\/span>
\n class_label =<\/span> class_names[<\/span>class_idx]<\/span>
\n n_samples =<\/span> np.<\/span>sum<\/span>(<\/span>node.<\/span>class_dist)<\/span>
\n prob =<\/span> node.<\/span>class_dist[<\/span>class_idx]<\/span> \/<\/span> n_samples
\n ax.<\/span>text(<\/span>
\n x,<\/span>
\n y,<\/span>
\n f"Predict: <\/span>{<\/span>class_label}<\/span><\/span>\\\\n(n=<\/span>{<\/span>n_samples}<\/span><\/span>, p=<\/span>{<\/span>prob:<\/span>.2f<\/span>}<\/span><\/span>)"<\/span><\/span>,<\/span>
\n ha=<\/span>"center"<\/span>,<\/span>
\n va=<\/span>"center"<\/span>,<\/span>
\n bbox=<\/span>dict<\/span>(<\/span>
\n facecolor=<\/span>"lightgreen"<\/span> if<\/span> class_idx ==<\/span> 1<\/span> else<\/span> "lightcoral"<\/span>,<\/span>
\n edgecolor=<\/span>"black"<\/span>,<\/span>
\n boxstyle=<\/span>"round"<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span><\/p>\n

# \u9012\u5f52\u7ed8\u5236\u5b50\u8282\u70b9（\u52a8\u6001\u8c03\u6574\u4f4d\u7f6e）<\/span>
\n if<\/span> node.<\/span>left or<\/span> node.<\/span>right:<\/span>
\n _draw_node(<\/span>node.<\/span>left,<\/span> x –<\/span> x_offset,<\/span> y –<\/span> y_step,<\/span> x_offset \/<\/span> 2<\/span>,<\/span> y_step,<\/span> depth +<\/span> 1<\/span>)<\/span>
\n _draw_node(<\/span>node.<\/span>right,<\/span> x +<\/span> x_offset,<\/span> y –<\/span> y_step,<\/span> x_offset \/<\/span> 2<\/span>,<\/span> y_step,<\/span> depth +<\/span> 1<\/span>)<\/span><\/p>\n

# \u7ed8\u5236\u5e26\u7bad\u5934\u7684\u8fde\u7ebf<\/span>
\n ax.<\/span>annotate(<\/span>
\n ""<\/span>,<\/span>
\n xy=<\/span>(<\/span>x –<\/span> x_offset,<\/span> y –<\/span> y_step +<\/span> 0.1<\/span>)<\/span>,<\/span>
\n xytext=<\/span>(<\/span>x,<\/span> y –<\/span> 0.1<\/span>)<\/span>,<\/span>
\n arrowprops=<\/span>dict<\/span>(<\/span>arrowstyle=<\/span>"->"<\/span>,<\/span> color=<\/span>"blue"<\/span>)<\/span>,<\/span>
\n )<\/span>
\n ax.<\/span>annotate(<\/span>
\n ""<\/span>,<\/span>
\n xy=<\/span>(<\/span>x +<\/span> x_offset,<\/span> y –<\/span> y_step +<\/span> 0.1<\/span>)<\/span>,<\/span>
\n xytext=<\/span>(<\/span>x,<\/span> y –<\/span> 0.1<\/span>)<\/span>,<\/span>
\n arrowprops=<\/span>dict<\/span>(<\/span>arrowstyle=<\/span>"->"<\/span>,<\/span> color=<\/span>"red"<\/span>)<\/span>,<\/span>
\n )<\/span><\/p>\n

# \u521d\u59cb\u4f4d\u7f6e\u548c\u6b65\u957f（\u7f29\u5c0f\u95f4\u8ddd）<\/span>
\n initial_x_offset =<\/span> 0.5<\/span> \/<\/span> tree_depth # \u6839\u636e\u6811\u6df1\u5ea6\u52a8\u6001\u8c03\u6574<\/span>
\n y_step =<\/span> 1<\/span> \/<\/span> tree_depth # \u5782\u76f4\u95f4\u8ddd<\/span>
\n _draw_node(<\/span>self.<\/span>tree,<\/span> x=<\/span>0.5<\/span>,<\/span> y=<\/span>0.9<\/span>,<\/span> x_offset=<\/span>initial_x_offset,<\/span> y_step=<\/span>y_step,<\/span> depth=<\/span>0<\/span>)<\/span><\/p>\n

plt.<\/span>tight_layout(<\/span>)<\/span>
\n plt.<\/span>show(<\/span>)<\/span><\/p>\n

\u4e09\u3001\u4ee3\u7801\u5206\u6790<\/h2>\n

1\u3001\u51b3\u7b56\u6811\u751f\u6210\u903b\u8f91<\/h3>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

2\u3001\u51b3\u7b56\u6811\u9884\u6d4b\u903b\u8f91<\/h3>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

3\u3001\u6700\u4f73\u5206\u5272\u7ebf<\/h3>\n

def<\/span> _best_split<\/span>(<\/span>self,<\/span> X,<\/span> y)<\/span>:<\/span>
\n best_gini =<\/span> float<\/span>(<\/span>'inf'<\/span>)<\/span>
\n best_feature,<\/span> best_threshold =<\/span> None<\/span>,<\/span> None<\/span><\/p>\n

for<\/span> feature_idx in<\/span> range<\/span>(<\/span>self.<\/span>n_features)<\/span>:<\/span>
\n thresholds =<\/span> np.<\/span>unique(<\/span>X[<\/span>:<\/span>,<\/span> feature_idx]<\/span>)<\/span>
\n for<\/span> threshold in<\/span> thresholds:<\/span>
\n gini =<\/span> self.<\/span>_gini_impurity(<\/span>X[<\/span>:<\/span>,<\/span> feature_idx]<\/span>,<\/span> y,<\/span> threshold)<\/span>
\n if<\/span> gini <<\/span> best_gini:<\/span>
\n best_gini =<\/span> gini
\n best_feature =<\/span> feature_idx
\n best_threshold =<\/span> threshold<\/p>\n

return<\/span> best_feature,<\/span> best_threshold<\/p>\n

def<\/span> _gini_impurity<\/span>(<\/span>self,<\/span> feature_col,<\/span> y,<\/span> threshold)<\/span>:<\/span>
\n left_idx =<\/span> feature_col <=<\/span> threshold
\n right_idx =<\/span> ~<\/span>left_idx<\/p>\n

if<\/span> np.<\/span>sum<\/span>(<\/span>left_idx)<\/span> ==<\/span> 0<\/span> or<\/span> np.<\/span>sum<\/span>(<\/span>right_idx)<\/span> ==<\/span> 0<\/span>:<\/span>
\n return<\/span> float<\/span>(<\/span>'inf'<\/span>)<\/span><\/p>\n

left_dist =<\/span> np.<\/span>bincount(<\/span>y[<\/span>left_idx]<\/span>,<\/span> minlength=<\/span>2<\/span>)<\/span>
\n right_dist =<\/span> np.<\/span>bincount(<\/span>y[<\/span>right_idx]<\/span>,<\/span> minlength=<\/span>2<\/span>)<\/span><\/p>\n

left_prob =<\/span> left_dist \/<\/span> np.<\/span>sum<\/span>(<\/span>left_dist)<\/span>
\n right_prob =<\/span> right_dist \/<\/span> np.<\/span>sum<\/span>(<\/span>right_dist)<\/span><\/p>\n

gini_left =<\/span> 1<\/span> –<\/span> np.<\/span>sum<\/span>(<\/span>left_prob **<\/span> 2<\/span>)<\/span>
\n gini_right =<\/span> 1<\/span> –<\/span> np.<\/span>sum<\/span>(<\/span>right_prob **<\/span> 2<\/span>)<\/span><\/p>\n

total_gini =<\/span> (<\/span>np.<\/span>sum<\/span>(<\/span>left_idx)<\/span> *<\/span> gini_left +<\/span> np.<\/span>sum<\/span>(<\/span>right_idx)<\/span> *<\/span> gini_right)<\/span> \/<\/span> len<\/span>(<\/span>y)<\/span>
\n return<\/span> total_gini<\/p>\n

（1）Gini\u4e0d\u7eaf\u5ea6<\/h4>\n

\u5b9a\u4e49：Gini \u4e0d\u7eaf\u5ea6\u8861\u91cf\u7684\u662f\u4e00\u4e2a\u6570\u636e\u96c6\u4e2d \u968f\u673a\u9009\u53d6\u4e24\u4e2a\u6837\u672c，\u5176\u7c7b\u522b\u4e0d\u4e00\u81f4\u7684\u6982\u7387\u3002 \u516c\u5f0f：<\/p>\n

<\/p>\n

G<\/p>\n

i<\/p>\n

n<\/p>\n

i<\/p>\n

=<\/p>\n

1<\/p>\n

\u2212<\/p>\n

\u2211<\/p>\n

k<\/p>\n

=<\/p>\n

1<\/p>\n

K<\/p>\n

p<\/p>\n

k<\/p>\n

2<\/p>\n

Gini =1-\\\\sum_{k=1}^{K}p_k^2<\/p>\n

<\/span><\/span>G<\/span>ini<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>\u2211<\/span><\/span>k<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>K<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>p<\/span><\/span>k<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5176\u4e2d，\u5176\u4e2d：K\u662f\u7c7b\u522b\u603b\u6570（\u5982\u4e8c\u5206\u7c7b\u95ee\u9898\u4e2d K=2）\u3002<\/p>\n

p<\/p>\n

k<\/p>\n

p_k<\/p>\n

<\/span><\/span>p<\/span><\/span>k<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u7b2c k\u7c7b\u6837\u672c\u5728\u6570\u636e\u96c6\u4e2d\u7684\u6bd4\u4f8b\u3002 \u8ba1\u7b97\u6b65\u9aa4：<\/p>\n

1）\u9009\u62e9\u4e00\u4e2a\u5206\u5272\u7279\u5f81\u548c\u9608\u503c<\/h5>\n

\u5982age \u2264 40<\/p>\n

2）\u5212\u5206\u6570\u636e：<\/h5>\n

\u5de6\u5b50\u96c6：\u6ee1\u8db3\u6761\u4ef6\u7684\u6570\u636e（age \u2264 40）\u3002 \u53f3\u5b50\u96c6：\u4e0d\u6ee1\u8db3\u6761\u4ef6\u7684\u6570\u636e（age > 40）\u3002<\/p>\n

3）\u8ba1\u7b97\u5de6\u53f3\u5b50\u96c6\u7684 Gini \u4e0d\u7eaf\u5ea6：<\/h5>\n

\u5bf9\u5de6\u5b50\u96c6\u548c\u53f3\u5b50\u96c6\u5206\u522b\u8ba1\u7b97 Gini \u4e0d\u7eaf\u5ea6\u3002<\/p>\n

4）\u8ba1\u7b97\u52a0\u6743\u5e73\u5747 Gini \u4e0d\u7eaf\u5ea6：<\/h5>\n

<\/p>\n

T<\/p>\n

o<\/p>\n

t<\/p>\n

e<\/p>\n

l<\/p>\n

_<\/p>\n

G<\/p>\n

i<\/p>\n

n<\/p>\n

i<\/p>\n

=<\/p>\n

n<\/p>\n

l<\/p>\n

e<\/p>\n

f<\/p>\n

t<\/p>\n

n<\/p>\n

t<\/p>\n

o<\/p>\n

t<\/p>\n

e<\/p>\n

l<\/p>\n

\u2217<\/p>\n

G<\/p>\n

i<\/p>\n

n<\/p>\n

i<\/p>\n

l<\/p>\n

e<\/p>\n

f<\/p>\n

t<\/p>\n

+<\/p>\n

n<\/p>\n

r<\/p>\n

i<\/p>\n

g<\/p>\n

h<\/p>\n

t<\/p>\n

n<\/p>\n

t<\/p>\n

o<\/p>\n

t<\/p>\n

e<\/p>\n

l<\/p>\n

\u2217<\/p>\n

G<\/p>\n

i<\/p>\n

n<\/p>\n

i<\/p>\n

r<\/p>\n

i<\/p>\n

g<\/p>\n

h<\/p>\n

t<\/p>\n

Totel \\\\_ Gini=\\\\frac{n_{left}}{n_{totel}}*Gini_{left}+\\\\frac{n_{right}}{n_{totel}}*Gini_{right}<\/p>\n

<\/span><\/span>T<\/span>o<\/span>t<\/span>e<\/span>l<\/span>_<\/span>G<\/span>ini<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>n<\/span><\/span>t<\/span>o<\/span>t<\/span>e<\/span>l<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>n<\/span><\/span>l<\/span>e<\/span>f<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2217<\/span><\/span><\/span><\/span>G<\/span>in<\/span>i<\/span><\/span>l<\/span>e<\/span>f<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>n<\/span><\/span>t<\/span>o<\/span>t<\/span>e<\/span>l<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>n<\/span><\/span>r<\/span>i<\/span>g<\/span>h<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2217<\/span><\/span><\/span><\/span>G<\/span>in<\/span>i<\/span><\/span>r<\/span>i<\/span>g<\/span>h<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5176\u4e2d,<\/p>\n

n<\/p>\n

r<\/p>\n

i<\/p>\n

g<\/p>\n

h<\/p>\n

t<\/p>\n

\u3001<\/p>\n

n<\/p>\n

l<\/p>\n

e<\/p>\n

f<\/p>\n

t<\/p>\n

\u3001<\/p>\n

n<\/p>\n

t<\/p>\n

o<\/p>\n

t<\/p>\n

e<\/p>\n

l<\/p>\n

n_{right}\u3001n_{left}\u3001n_{totel}<\/p>\n

<\/span><\/span>n<\/span><\/span>r<\/span>i<\/span>g<\/span>h<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001<\/span>n<\/span><\/span>l<\/span>e<\/span>f<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001<\/span>n<\/span><\/span>t<\/span>o<\/span>t<\/span>e<\/span>l<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5206\u522b\u4e3a\u5de6\u5b50\u96c6\u3001\u53f3\u5b50\u96c6\u548c\u603b\u96c6\u7684\u6837\u672c\u4e2a\u6570\u3002<\/p>\n

\u53c2\u8003\u6587\u732e<\/h2>\n

1\u3001\u3010\u603b\u7ed3\u3011\u673a\u5668\u5b66\u4e60\u4e2d\u768415\u79cd\u5206\u7c7b\u7b97\u6cd5 <\/p>\n","protected":false},"excerpt":{"rendered":"

\u4e00\u3001\u7b97\u6cd5\u539f\u7406
\n\u51b3\u7b56\u6811\u7b97\u6cd5\u901a\u8fc7\u5c06\u6570\u636e\u96c6\u5212\u5206\u4e3a\u4e0d\u540c\u7684\u5b50\u96c6\u6765\u9884\u6d4b\u76ee\u6807\u53d8\u91cf\u3002\u5b83\u4ece\u6839\u8282\u70b9\u5f00\u59cb，\u6839\u636e\u67d0\u4e2a\u7279\u5f81\u5bf9\u6570\u636e\u96c6\u8fdb\u884c\u5212\u5206，\u7136\u540e\u9012\u5f52\u5730\u751f\u6210\u66f4\u591a\u7684\u5b50\u8282\u70b9，\u76f4\u5230\u6ee1\u8db3\u505c\u6b62\u6761\u4ef6\u4e3a\u6b62\u3002\u51b3\u7b56\u6811\u7684\u6bcf\u4e2a\u5185\u90e8\u8282\u70b9\u8868\u793a\u4e00\u4e2a\u7279\u5f81\u5c5e\u6027\u4e0a\u7684\u5224\u65ad\u6761\u4ef6，\u6bcf\u4e2a\u5206\u652f\u4ee3\u8868\u4e00\u4e2a\u53ef\u80fd\u7684\u5c5e\u6027\u503c，\u6bcf\u4e2a\u53f6\u8282\u70b9\u8868\u793a\u4e00\u4e2a\u5206\u7c7b\u7ed3\u679c\u3002
\n\u4e8c\u3001\u53c2\u8003\u4ee3\u7801
\nimport numpy as np
\nimport matplotlib.pyplot as pltclass Tr<\/p>\n","protected":false},"author":2,"featured_media":80768,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[3408,2395,207],"topic":[],"class_list":["post-80770","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-3408","tag-2395","tag-207"],"yoast_head":"\n\u673a\u5668\u5b66\u4e60\u5206\u7c7b\u7b97\u6cd5\u4e00\u2014\u2014\u51b3\u7b56\u6811 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/80770.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u673a\u5668\u5b66\u4e60\u5206\u7c7b\u7b97\u6cd5\u4e00\u2014\u2014\u51b3\u7b56\u6811 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u4e00\u3001\u7b97\u6cd5\u539f\u7406 \u51b3\u7b56\u6811\u7b97\u6cd5\u901a\u8fc7\u5c06\u6570\u636e\u96c6\u5212\u5206\u4e3a\u4e0d\u540c\u7684\u5b50\u96c6\u6765\u9884\u6d4b\u76ee\u6807\u53d8\u91cf\u3002\u5b83\u4ece\u6839\u8282\u70b9\u5f00\u59cb，\u6839\u636e\u67d0\u4e2a\u7279\u5f81\u5bf9\u6570\u636e\u96c6\u8fdb\u884c\u5212\u5206，\u7136\u540e\u9012\u5f52\u5730\u751f\u6210\u66f4\u591a\u7684\u5b50\u8282\u70b9，\u76f4\u5230\u6ee1\u8db3\u505c\u6b62\u6761\u4ef6\u4e3a\u6b62\u3002\u51b3\u7b56\u6811\u7684\u6bcf\u4e2a\u5185\u90e8\u8282\u70b9\u8868\u793a\u4e00\u4e2a\u7279\u5f81\u5c5e\u6027\u4e0a\u7684\u5224\u65ad\u6761\u4ef6，\u6bcf\u4e2a\u5206\u652f\u4ee3\u8868\u4e00\u4e2a\u53ef\u80fd\u7684\u5c5e\u6027\u503c，\u6bcf\u4e2a\u53f6\u8282\u70b9\u8868\u793a\u4e00\u4e2a\u5206\u7c7b\u7ed3\u679c\u3002 \u4e8c\u3001\u53c2\u8003\u4ee3\u7801 import numpy as np import matplotlib.pyplot as pltclass Tr\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/80770.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-03-05T16:51:23+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/03\/20260305165121-69a9b489e3a63.jpg\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/80770.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/80770.html\",\"name\":\"\u673a\u5668\u5b66\u4e60\u5206\u7c7b\u7b97\u6cd5\u4e00\u2014\u2014\u51b3\u7b56\u6811 - 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