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数据科学·ML
12
engines
k-均值聚类(k-means)
k-means clustering
Lloyd 分配-更新 · 质心 · 簇内平方和 WCSS 单调下降
Lloyd's algorithm on 30 fixed points · WCSS decreases each iteration
混淆矩阵与评估指标
Confusion matrix & metrics
TP/FP/FN/TN · 准确率/精确率/召回率/F1
Set the four cells; precision, recall, specificity and F1 update exactly
基尼不纯度与分裂增益
Gini impurity & split gain
Gini=1−Σp² · 加权子节点 · 信息增益
How a decision tree scores a candidate split · Gini and entropy
k 近邻分类器
k-Nearest Neighbors classifier
欧氏距离 · k 个最近邻 · 多数表决
Classify a query point by the majority label of its k closest neighbors
偏差-方差权衡
Bias–variance tradeoff
偏差²+方差+不可约 · U 形总误差 · 最优复杂度
Total error = bias² + variance + irreducible noise, traded off by complexity
过拟合:多项式回归
Overfitting: polynomial regression
多项式次数扫描 · 训练/测试 RMSE · 高次震荡
Raise the degree and watch training error fall while test error turns back up
Naive Bayes · spam classifier
Naive Bayes · spam classifier
垃圾邮件过滤 · 对数后验 · 词似然
Accumulate word likelihoods in log space; decide spam / ham by Bayes
k-fold cross-validation
k-fold cross-validation
k 折划分 · 每折轮流验证 · 均值±标准差
Split data into k folds; each fold is held out for validation once. Aggregate the fold scores
Feature scaling · normalization & standardization
Feature scaling · normalization & standardization
Min-Max/Z-score/Robust · 统计量 · 分布重定位
Four methods reposition/rescale the same feature values onto comparable ranges
Softmax function · probability normalization
Softmax function · probability normalization
e^z/Σe^z · 概率和为 1 · 数值稳定(减最大值)
Turns raw scores (logits) into probabilities that sum to 1; the top score wins the most
Neural-net activation functions · curves & derivatives
Neural-net activation functions · curves & derivatives
sigmoid/tanh/ReLU/Leaky/ELU · 曲线+导数
Compare common activations and their derivatives over x ∈ [−6, 6]
L1 (Lasso) vs L2 (Ridge) regularization
L1 (Lasso) vs L2 (Ridge) regularization
Lasso 稀疏 vs Ridge 收缩 · 菱形 vs 圆形约束
Penalty geometry in weight space · why L1 gives sparsity and L2 shrinks smoothly