Norm Adjusted Proximity Graph for MIPS Edge Selection
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Solution Overview
Problem
Existing methods for efficient inner product search, such as HNSW, face challenges due to their edge selection algorithms being based on triangle inequality, which are not suitable for inner product metrics, leading to inefficient proximity graphs and poor performance in retrieving relevant data, especially for top-k results.
Innovation Solution
The Norm Adjusted Proximity Graph (NAPG) methodology adjusts the 2-norms of data points using a carefully selected factor α, allowing for effective edge selection and construction of more connected index graphs, bridging the gap between metric measures and inner product, thereby improving the performance of graph-based MIPS methods.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If HNSW edge selection algorithm is used for inner product search, then the method can be extended to MIPS, but the performance is poor due to triangle inequality basis not being suitable for inner product metrics
Solution Approach 1:
The patent modifies the edge selection criterion by changing the metric parameter from triangle-inequality-based distance to inner product-based similarity. Specifically, it uses the condition inner_product(u, v) > inner_product(u, w) + inner_product(v, w) to select edges, which is adapted from the triangle inequality but optimized for inner product space, thereby resolving the incompatibility between HNSW and MIPS
2Productivity
If classical ANN search methods are used for inner product search, then the search can be performed, but the performance is limited due to metric space assumptions not holding
Solution Approach 1:
The patent transforms the search metric from Euclidean distance to inner product by modifying the distance function parameter. It uses the relationship distance(u, v) = ||u|| * ||v|| - inner_product(u, v), and optimizes the search to maximize inner_product(u, v) directly, thereby adapting ANN search to the inner product metric space and improving both speed and effectiveness
3Stability of the object's composition
If norm-adjusted edge selection is applied, then the connectivity of index graphs is improved, but the complexity of edge selection increases
Solution Approach 1:
The patent introduces a norm adjustment parameter α to balance the edge selection criterion. By setting α = min(||u||, ||v||) / max(||u||, ||v||), it normalizes the inner product values to account for varying vector norms, which improves graph connectivity without significantly increasing computational complexity since the norm values are already computed during inner product calculation
Data Source
AI summary
Efficient inner product search is important for many data ranking services, such as recommendation and Information Retrieval. Efficient retrieval via inner product dramatically influences the performance of such data searching and retrieval systems. To resolve deficiencies of prior approaches, embodiments of a new index graph construction approach, referred to generally as Norm Adjusted Proximity Graph (NAPG), for approximate Maximum Inner Product Search (MIPS) are presented. With adjusting factors estimated on sampled data, NAPG embodiments select more meaningful data points to connect with when constructing a graph-based index for inner product search. Extensive experiments verify that the improved graph-based index pushes the state-of-the-art of inner product search forward greatly, in the trade-off between search efficiency and effectiveness.