The Big Data explosion has necessitated the development of search algorithms that scale sub-linearly in time and memory. While compression algorithms and search algorithms do exist independently, few algorithms offer both, and those which do are domain-specific. We present panCAKES, a novel approach to compressive search, i.e., a way to perform k-NN and ρ-NN search on compressed data while only decompressing a small, relevant, portion of the data. panCAKES assumes the manifold hypothesis and leverages the low-dimensional structure of the data to compress and search it efficiently. panCAKES is generic over any distance function for which the distance between two points is proportional to the memory cost of storing an encoding of one in terms of the other. This property holds for many widely-used distance functions, e.g. string edit distances (Levenshtein, Needleman-Wunsch, etc.) and set dissimilarity measures (Jaccard, Dice, etc.). We benchmark panCAKES on a variety of datasets, including genomic, proteomic, and set data. We compare compression ratios to gzip, and search performance between the compressed and uncompressed versions of the same dataset. panCAKES achieves compression ratios close to those of gzip, while offering sub-linear time performance for k-NN and ρ-NN search. We conclude that panCAKES is an efficient, general-purpose algorithm for exact compressive search on large datasets that obey the manifold hypothesis. We provide an open-source implementation of panCAKES in the Rust programming language.

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 GitHub1.