Podcast
Questions and Answers
What is the purpose of Locality Sensitive Hashing in approximate nearest neighbours search?
What is the purpose of Locality Sensitive Hashing in approximate nearest neighbours search?
The K-Means algorithm is based on density-based clustering methods.
The K-Means algorithm is based on density-based clustering methods.
False
What is the main advantage of clustering before searching for k-NN?
What is the main advantage of clustering before searching for k-NN?
It reduces the number of comparisons needed to find the nearest neighbours.
The clustering approach that uses the smallest distance is known as __________.
The clustering approach that uses the smallest distance is known as __________.
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Match the clustering algorithms with their characteristics:
Match the clustering algorithms with their characteristics:
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What is the first step in constructing a Watts–Strogatz model?
What is the first step in constructing a Watts–Strogatz model?
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In the Kleinberg model, search procedures require embedding and hyperplanes.
In the Kleinberg model, search procedures require embedding and hyperplanes.
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What is the purpose of the reweighting process in the Watts–Strogatz model?
What is the purpose of the reweighting process in the Watts–Strogatz model?
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A proximity graph connects two vertices if they satisfy specific ______ requirements.
A proximity graph connects two vertices if they satisfy specific ______ requirements.
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Match the following concepts with their corresponding descriptions:
Match the following concepts with their corresponding descriptions:
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What is the method used to compress vectors with centroids?
What is the method used to compress vectors with centroids?
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Small world networks have a large degree of connections between most vertices.
Small world networks have a large degree of connections between most vertices.
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What are the two main types of graphs mentioned in the document?
What are the two main types of graphs mentioned in the document?
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A ______ graph has a degree of vertex 'K' for all vertices.
A ______ graph has a degree of vertex 'K' for all vertices.
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Match the following terms with their definitions:
Match the following terms with their definitions:
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What is a characteristic of small world networks?
What is a characteristic of small world networks?
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Proximity graphs can be weighted and directed.
Proximity graphs can be weighted and directed.
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In the Small World experiment by Stanley Milgram, what was discovered about social graphs?
In the Small World experiment by Stanley Milgram, what was discovered about social graphs?
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Study Notes
Approximate Nearest Neighbors Search
- Approximate nearest neighbor search (ANNS) is a method for finding approximate nearest neighbors in a dataset.
- ANNS prioritizes speed over absolute accuracy
- Various techniques are used to build ANNS, such as clustering (with IVF), and proximity graphs (NSW, HNSW).
Agenda
- ANNS overview (differentiating from ANNs)
- Clustering techniques (including IVF)
- Proximity graph methods (NSW, HNSW)
Before we start
- Inverted index data structures: evaluate their limitations related to data structure
- Understanding time complexity notation: O(f(N)), OA(f(N)), E(f(N))
Approximation for k-NN search (k-Nearest Neighbors)
- Pre-select elements from an approximate neighborhood (pre-ranking set); for example, Recall@1000 ≥ 0.875
- Re-rank the relevant elements from the approximate neighbourhood
- Methodologies include locality-sensitive hashing, search trees with supporting data structures, vector compression, clustering, inverted indexing, and proximity graphs.
Hierarchical clustering and Inverted index revised
- Revision of hierarchical clustering methods and inverted indexing techniques.
How clustering approaches differ?
- Various clustering algorithms (e.g., MiniBatchKMeans, AffinityPropagation, MeanShift, SpectralClustering, Ward, AgglomerativeClustering, DBSCAN, OPTICS, Birch, GaussianMixture) differ substantially in their performance characteristics on various data sets. Time complexity is significantly dependent on the algorithms used.
Linkage criteria
- Single linkage (smallest distance) is associated with DBSCAN
- Complete linkage (maximum distance)
- Minimum energy/variance (where merge operations produce slow variance growth)
- Average distance and centroid-based methods are often employed with k-Means
K-Means
- A clustering algorithm that partitions data points into k clusters based on minimizing the within-cluster sum of squares.
DBSCAN
- Density-based spatial clustering of applications with noise, identifying clusters of high density separated by regions of low density.
Why do we cluster?
- Clustering allows the rapid identification of k-nearest neighbors by efficiently reducing the number of comparisons required. For example, with clustered data, to efficiently identify similar clusters, calculations can be done in O(√N) time, instead of O(N) time (for unclustered data).
How do we cluster?
- Different hierarchical clustering approaches exist: Agglomerative vs. Divisive
Revised IVF. FAISS
- FAISS (Facebook AI Similarity Search) is a library implementing various efficient ANNS algorithms.
- It leverages these approaches:
- Voronoi diagram clustering (using k-Means) to approximate vectors using centroids (VQ)
- Scalar quantization (SQ): compressing cluster representations.
- Building inverted indexes for data points within clusters;
- Vector compression using Product Quantization (PQ), splitting 128-dimensional vectors into 8 groups of 16 floats. Then, perform 256-means clustering on these sub-vectors, and encode them with a single byte each.
Vector Quantization and Product Quantization
- Vector Quantization (VQ) and Product Quantization (PQ) techniques used in vector compression and similarity search.
Proximity graphs
- Proximity graphs are a type of graph where vertices are connected based on particular geometric requirements. For example, two vertices are linked if they are close to each other in Euclidean space.
Navigable small world networks
- Similar methodology to skip lists;
- Distance measurement methods: (e.g., dot product, Euclidean, L₁-norm, Hamming, Levenshtein)
- Useful for approximate search since the Delaunay graph may not be required for convergence.
Hierarchical navigable small world (github)
- Hierarchical structure of small world networks, useful for efficient searching:
- Start search from high-degree nodes in the network
- Layers, with increasing characteristics, that use progressively longer (skip list style) links.
To read
- Materials related to proximity graphs, efficient ANNS, and the use of hierarchical navigable graphs in search tasks.
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Description
This quiz covers the fundamentals of Approximate Nearest Neighbors Search (ANNS), focusing on its methods and techniques. Participants will explore clustering methods like IVF and proximity graph methodologies such as NSW and HNSW. The quiz will also touch on inverted index data structures and time complexity notation relevant to ANNS.
