『度量学习』知识梳理

graph RL subgraph 0 a1[度量学习] --> |也称为马氏度量学习问题|b1[线性变换] a1[度量学习] --> b2[非线性变换] end subgraph 1 b1 --> c1[监督学习] c1 --> |该类型的算法充分利用数据的标签信息|d1[全局] c1 --> |该类型的算法同时考虑数据的标签信息和数据点之间的几何关系|d2[局部] end subgraph 2 b1 --> c2[非监督学习] end subgraph 3 d1 --> f1[ITML] d1 --> f2[MMC] d1 --> f3[MCML] end subgraph 4 d2 --> g1[NCA] d2 --> g2[LMNN] d2 --> g3[RCA] d2 --> g4[Local LDA] end subgraph 5 c2 --> e1[PCA] c2 --> e2[MDS] c2 --> e3[NMF] c2 --> e4[ICA] c2 --> e5[NPE] c2 --> e6[LPP] end subgraph 6 b2 --> b3[非线性降维] b2 --> b4[核方法] end subgraph 7 b3 --> h1[ISOMAP] b3 --> h2[LLE] b3 --> h3[LE] end subgraph 8 b4 --> t1[Non-Mahalanobis Local Distance Functions] b4 --> t2[Mahalanobis Local Distance Functions] b4 --> t3[Metric Learning with Neural Networks] end

• ITML: Information-theoretic metric learning
• MMC: Mahalanobis Metric Learning for Clustering
• MCML: Maximally Collapsing Metric Learning
• NCA: Neighbourhood Components Analysis
• LMNN: Large-Margin Nearest Neighbors
• RCA: Relevant Component Analysis
• Local LDA: Local Linear Discriminative Analysis
• PCA: Pricipal Components Analysis（主成分分析）
• MDS: Multi-dimensional Scaling（多维尺度变换）
• NMF: Non-negative Matrix Factorization（非负矩阵分解）
• ICA: Independent components analysis（独立成分分析）
• NPE: Neighborhood Preserving Embedding（邻域保持嵌入）
• LPP: Locality Preserving Projections（局部保留投影）
• ISOMAP: Isometric Mapping（等距映射）
• LLE: Locally Linear Embedding（局部线性嵌入）
• LE: Laplacian Eigenmap（拉普拉斯特征映射）

几篇经典论文

• Distance metric learning with application to clustering with side-information
• Information-theoretic metric learning(关于ITML)
• Distance metric learning for large margin nearest neighbor classification(关于LMNN)
• Learning the parts of objects by non-negative matrix factorization（Nature关于RCA的文章）
• Neighbourhood components analysis(关于NCA)
• Metric Learning by Collapsing Classes(关于MCML)
• Distance metric learning a comprehensive survey(一篇经典的综述)

Python 封装了一些度量方法：metric-learn