Faster and smaller inverted indices with treaps.

SIGIR 2013: 193-202
Faster and smaller inverted indices with treaps.
Roberto Konow, Gonzalo Navarro, Charles L. A. Clarke, Alejandro López-Ortiz
eBay Authors

We introduce a new representation of the inverted index that performs faster ranked unions and intersections while using less space. Our index is based on the treap data structure, which allows us to intersect/merge the document identifiers while simultaneously thresholding by frequency, instead of the costlier two-step classical processing methods. To achieve compression we represent the treap topology using compact data structures. Further, the treap invariants allow us to elegantly encode differentially both document identifiers and frequencies. Results show that our index uses about 20% less space, and performs queries up to three times faster, than state-of-the-art compact representations.

Another publication from the same author:

Information Systems 60: 34-49 (2016)

Aggregated 2D range queries on clustered points.

Nieves R. Brisaboa, Guillermo de Bernardo, Roberto Konow, Gonzalo Navarro, Diego Seco

Efficient processing of aggregated range queries on two-dimensional grids is a common requirement in information retrieval and data mining systems, for example in Geographic Information Systems and OLAP cubes. We introduce a technique to represent grids supporting aggregated range queries that requires little space when the data points in the grid are clustered, which is common in practice. We show how this general technique can be used to support two important types of aggregated queries, which are ranked range queries and counting range queries. Our experimental evaluation shows that this technique can speed up aggregated queries up to more than an order of magnitude, with a small space overhead.


Another publication from the same category: Machine Learning and Data Science

IEEE Computing Conference 2018, London, UK

Regularization of the Kernel Matrix via Covariance Matrix Shrinkage Estimation

The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix of the data requires outer products. Therefore, their spectral properties are tightly connected. This allows us to examine the kernel matrix through the sample covariance matrix in the feature space and vice versa. The use of kernels often involves a large number of features, compared to the number of observations. In this scenario, the sample covariance matrix is not well-conditioned nor is it necessarily invertible, mandating a solution to the problem of estimating high-dimensional covariance matrices under small sample size conditions. We tackle this problem through the use of a shrinkage estimator that offers a compromise between the sample covariance matrix and a well-conditioned matrix (also known as the "target") with the aim of minimizing the mean-squared error (MSE). We propose a distribution-free kernel matrix regularization approach that is tuned directly from the kernel matrix, avoiding the need to address the feature space explicitly. Numerical simulations demonstrate that the proposed regularization is effective in classification tasks.