arXiv subjects

Thomas J. Howard III

Publications and source records attributed to Thomas J. Howard III.

2 recordsLinked to original sources

arXiv2025

Let them have CAKES: A Cutting-Edge Algorithm for Scalable, Efficient, and Exact Search on Big Data

The ongoing Big Data explosion has created a demand for efficient and scalable algorithms for similarity search. Most recent work has focused on \textit{approximate} $k$-NN search, and while this may be sufficient for some applications, \textit{exact} $k$-NN search would be ideal for many applications. We present CAKES, a set of three novel, exact algorithms for $k$-NN search. CAKES's algorithms are generic over \textit{any} distance function, and they \textit{do not} scale with the cardinality or embedding dimension of the dataset, but rather with its metric entropy and fractal dimension. We test these claims on datasets from the ANN-Benchmarks suite under commonly-used distance functions, as well as on a genomic dataset with Levenshtein distance and a radio-frequency dataset with Dynamic Time Warping distance. We demonstrate that CAKES exhibits near-constant scaling with cardinality on data conforming to the manifold hypothesis, and has perfect recall on data in \textit{metric} spaces. We also demonstrate that CAKES exhibits significantly higher recall than state-of-the-art $k$-NN search algorithms when the distance function is not a metric. Additionally, we show that indexing and tuning time for CAKES is an order of magnitude, or more, faster than state-of-the-art approaches. We conclude that CAKES is a highly efficient and scalable algorithm for exact $k$-NN search on Big Data. We provide a Rust implementation of CAKES under an MIT license at https://github.com/URI-ABD/clam

cs.DS↗

arXiv2021

Clustered Hierarchical Anomaly and Outlier Detection Algorithms

Anomaly and outlier detection is a long-standing problem in machine learning. In some cases, anomaly detection is easy, such as when data are drawn from well-characterized distributions such as the Gaussian. However, when data occupy high-dimensional spaces, anomaly detection becomes more difficult. We present CLAM (Clustered Learning of Approximate Manifolds), a manifold mapping technique in any metric space. CLAM begins with a fast hierarchical clustering technique and then induces a graph from the cluster tree, based on overlapping clusters as selected using several geometric and topological features. Using these graphs, we implement CHAODA (Clustered Hierarchical Anomaly and Outlier Detection Algorithms), exploring various properties of the graphs and their constituent clusters to find outliers. CHAODA employs a form of transfer learning based on a training set of datasets, and applies this knowledge to a separate test set of datasets of different cardinalities, dimensionalities, and domains. On 24 publicly available datasets, we compare CHAODA (by measure of ROC AUC) to a variety of state-of-the-art unsupervised anomaly-detection algorithms. Six of the datasets are used for training. CHAODA outperforms other approaches on 16 of the remaining 18 datasets. CLAM and CHAODA scale to large, high-dimensional "big data" anomaly-detection problems, and generalize across datasets and distance functions. Source code to CLAM and CHAODA are freely available on GitHub at https://github.com/URI-ABD/clam.

cs.LG↗