V2EX affinity matrix

Affinity Matrix

释义 Definition

Affinity matrix(相似度矩阵/亲和矩阵):在数据分析与机器学习中,用一个矩阵来表示样本两两之间的“相似程度”或“连接强度”。矩阵元素 \(A_{ij}\) 通常表示第 \(i\) 个与第 \(j\) 个样本的相似度(值越大越相似),常用于谱聚类(spectral clustering)图学习(graph-based learning)网络分析等。
(在不同语境下也可指“亲和力/关联度”矩阵,具体取决于相似度定义方式。)

发音 Pronunciation (IPA)

/fnti metrks/

例句 Examples

We build an affinity matrix from the cosine similarity of the embeddings.
我们用向量嵌入的余弦相似度来构建相似度矩阵。

After normalizing the affinity matrix and computing its eigenvectors, the algorithm clusters the data into several groups.
在对相似度矩阵进行归一化并计算其特征向量之后,算法将数据聚成若干组。

词源 Etymology

affinity 源自拉丁语 affinitas,本义是“亲近、联系、姻亲关系”,后来引申为“吸引力、相似性、亲和性”;matrix 源自拉丁语 matrix(“母体/来源”),在数学中指“矩阵”。合起来 affinity matrix 就是“用矩阵形式表达对象之间亲和/相似关系”的工具。

相关词 Related Words

文学与经典著作 Literary Works

  • Pattern Recognition and Machine Learning(Christopher M. Bishop)在图模型/核方法与谱方法相关讨论中常涉及相似度(亲和)矩阵概念。
  • The Elements of Statistical Learning(Hastie, Tibshirani, Friedman)在聚类与基于相似度的方法背景下常出现相关表述。
  • Spectral Graph Theory(Fan Chung)图拉普拉斯矩阵与基于相似度/邻接关系的矩阵表示是核心内容。
  • Matrix Computations(Golub & Van Loan)从数值线性代数角度讨论矩阵分解,常用于实现与分析谱聚类所需的特征分解。
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