How Do I Compute the Cosin Similarity of Every Entry Embedding?

Primary clustering tools for practical applications include K-means using scikit-learn or Faiss, agglomerative clustering leveraging cosine similarity with scikit-learn, and density-based methods like DBSCAN or HDBSCAN. For determining the optimal number of clusters, silhouette score is generally preferred over inertia-based visual heuristics, and it natively supports pre-computed distance matrices.

Links

• Notes and resources at ocdevel.com/mlg/mla-11
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K-means Clustering

• K-means is the most widely used clustering algorithm and is typically the first method to try for general clustering tasks.
• The scikit-learn KMeans implementation is suitable for small to medium-sized datasets, while Faiss's kmeans is more efficient and accurate for very large datasets.
• K-means requires the number of clusters to be specified in advance and relies on the Euclidean distance metric, which performs poorly in high-dimensional spaces.
• When document embeddings have high dimensionality (e.g., 768 dimensions from sentence transformers), K-means becomes less effective due to the limitations of Euclidean distance in such spaces.

Alternatives to K-means for High Dimensions

• For text embeddings with high dimensionality, agglomerative (hierarchical) clustering methods are preferable, particularly because they allow the use of different similarity metrics.
• Agglomerative clustering in scikit-learn accepts a pre-computed cosine similarity matrix, which is more appropriate for natural language processing.
• Constructing the pre-computed distance (or similarity) matrix involves normalizing vectors and computing dot products, which can be efficiently achieved with linear algebra libraries like PyTorch.
• Hierarchical algorithms do not use inertia in the same way as K-means and instead rely on external metrics, such as silhouette score.
• Other clustering algorithms exist, including spectral, mean shift, and affinity propagation, which are not covered in this episode.

Semantic Search and Vector Indexing

• Libraries such as Faiss, Annoy, and HNSWlib provide approximate nearest neighbor search for efficient semantic search on large-scale vector data.
• These systems create an index of your embeddings to enable rapid similarity search, often with the ability to specify cosine similarity as the metric.
• Sample code using these libraries with sentence transformers can be found in the UKP Lab sentence-transformers examples directory.

Determining the Optimal Number of Clusters

• Both K-means and agglomerative clustering require a predefined number of clusters, but this is often unknown beforehand.
• The "elbow" method involves running the clustering algorithm with varying cluster counts and plotting the inertia (sum of squared distances within clusters) to visually identify the point of diminishing returns; see kmeans.inertia_.
• The kneed package can automatically detect the "elbow" or "knee" in the inertia plot, eliminating subjective human judgment; sample code available here.
• The silhouette score, calculated via silhouette_score, considers both inter- and intra-cluster distances and allows for direct selection of the number of clusters with the maximum score.
• The silhouette score can be computed using a pre-computed distance matrix (such as from cosine similarities), making it well-suited for applications involving non-Euclidean metrics and hierarchical clustering.

Density-Based Clustering: DBSCAN and HDBSCAN

• DBSCAN is a hierarchical clustering method that does not require specifying the number of clusters, instead discovering clusters based on data density.
• HDBSCAN is a more popular and versatile implementation of density-based clustering, capable of handling various types of data without significant parameter tuning.
• DBSCAN and HDBSCAN can be preferable to K-means or agglomerative clustering when automatic determination of cluster count or robustness to noise is important.
• However, these algorithms may not perform well with all types of high-dimensional embedding data, as illustrated by the challenges faced when clustering 768-dimensional text embeddings.

Summary Recommendations and Links

• For low- to medium-sized, low-dimensional data, use K-means with silhouette score to choose the optimal number of clusters: scikit-learn KMeans, silhouette_score.
• For very large data or vector search, use Faiss.kmeans.
• For high-dimensional data using cosine similarity, use Agglomerative Clustering with a pre-computed square matrix of cosine similarities; sample code.
• For density-based clustering, consider DBSCAN or HDBSCAN.
• Exploratory code and further examples can be found in the UKP Lab sentence-transformers examples.