To Index or Not to Index: Optimizing Exact Maximum Inner Product Search

Exact Maximum Inner Product Search (MIPS) is an important task that is widely pertinent to recommender systems and high-dimensional similarity search. The brute-force approach to solving exact MIPS is computationally expensive, thus spurring recent development of novel indexes and pruning techniques for this task. In this paper, we show that a hardware-efficient brute-force approach, blocked matrix multiply (BMM), can outperform the state-of-the-art MIPS solvers by over an order of magnitude, for some -- but not all -- inputs. In this paper, we also present a novel MIPS solution, MAXIMUS, that takes advantage of hardware efficiency and pruning of the search space. Like BMM, MAXIMUS is faster than other solvers by up to an order of magnitude, but again only for some inputs. Since no single solution offers the best runtime performance for all inputs, we introduce a new data-dependent optimizer, OPTIMUS, that selects online with minimal overhead the best MIPS solver for a given input. Together, OPTIMUS and MAXIMUS outperform state-of-the-art MIPS solvers by 3.2$\times$ on average, and up to 10.9$\times$, on widely studied MIPS datasets.Comment: 12 pages, 8 figures, 2 table

A new perspective on the competitiveness of nations

The capability of firms to survive and to have a competitive advantage in global markets depends on, amongst other things, the efficiency of public institutions, the excellence of educational, health and communications infrastructures, as well as on the political and economic stability of their home country. The measurement of competitiveness and strategy development is thus an important issue for policy-makers. Despite many attempts to provide objectivity in the development of measures of national competitiveness, there are inherently subjective judgments that involve, for example, how data sets are aggregated and importance weights are applied. Generally, either equal weighting is assumed in calculating a final index, or subjective weights are specified. The same problem also occurs in the subjective assignment of countries to different clusters. Developed as such, the value of these type indices may be questioned by users. The aim of this paper is to explore methodological transparency as a viable solution to problems created by existing aggregated indices. For this purpose, a methodology composed of three steps is proposed. To start, a hierarchical clustering analysis is used to assign countries to appropriate clusters. In current methods, country clustering is generally based on GDP. However, we suggest that GDP alone is insufficient for purposes of country clustering. In the proposed methodology, 178 criteria are used for this purpose. Next, relationships between the criteria and classification of the countries are determined using artificial neural networks (ANNs). ANN provides an objective method for determining the attribute/criteria weights, which are, for the most part, subjectively specified in existing methods. Finally, in our third step, the countries of interest are ranked based on weights generated in the previous step. Beyond the ranking of countries, the proposed methodology can also be used to identify those attributes that a given country should focus on in order to improve its position relative to other countries, i.e., to transition from its current cluster to the next higher one