Which one is better: presentation-based or content-based math search?

Mathematical content is a valuable information source and retrieving this content has become an important issue. This paper compares two searching strategies for math expressions: presentation-based and content-based approaches. Presentation-based search uses state-of-the-art math search system while content-based search uses semantic enrichment of math expressions to convert math expressions into their content forms and searching is done using these content-based expressions. By considering the meaning of math expressions, the quality of search system is improved over presentation-based systems

A Survey on Retrieval of Mathematical Knowledge

We present a short survey of the literature on indexing and retrieval of mathematical knowledge, with pointers to 72 papers and tentative taxonomies of both retrieval problems and recurring techniques.Comment: CICM 2015, 20 page

Retrieval of similar chess positions

We address the problem of retrieving chess game positions similar to a given query position from a collection of archived chess games. We investigate this problem from an information retrieval (IR) perspective. The advantage of our proposed IR-based approach is that it allows using the standard inverted organization of stored chess positions, leading to an ecient retrieval. Moreover, in contrast to retrieving exactly identical board positions, the IR-based approach is able to provide approximate search functionality. In order to define the similarity between two chess board positions, we encode each game state with a textual representation. This textual encoding is designed to represent the position, reachability and the connectivity between chess pieces. Due to the absence of a standard IR dataset that can be used for this search task, a new evaluation benchmark dataset was constructed comprising of documents (chess positions) from a freely available chess game archive. Experiments conducted on this dataset demonstrate that our proposed method of similarity computation, which takes into account a combination of the mobility and the connectivities between the chess pieces, performs well on the search task, achieving MAP and nDCG values of 0:4233 and 0:6922 respectively

Discovering real-world usage scenarios for a multimodal math search interface

To use math expressions in search, current search engines require knowing expression names or using a structure editor or string encoding (e.g., LaTeX) to enter expressions. This is unfortunate for people who are not math experts, as this can lead to an intention gap between the math query they wish to express, and what the interface will allow. min is a search interface that supports drawing expressions on a canvas using a mouse/touch, keyboard and images. We designed a user study to examine how the multimodal interface of min changes search behavior for mathematical non-experts, and discover real-world usage scenarios. Participants demonstrated increased use of math expressions in queries when using min. There was little difference in task success reported by participants using min vs. text-based search, but the majority of participants appreciated the multimodal input, and identified real-world scenarios in which they would like to use systems like min

Semantic Tagging of Mathematical Expressions

Semantic tagging of mathematical expressions (STME) gives semantic meanings to tokens in mathematical expressions. In this work, we propose a novel STME approach that relies on neither text along with expressions, nor labelled train-ing data. Instead, our method only requires a mathemati-cal grammar set. We point out that, besides the grammar of mathematics, the special property of variables and user habits of writing expressions help us understand the im-plicit intents of the user. We build a system that considers both restrictions from the grammar and variable properties, and then apply an unsupervised method to our probabilis-tic model to learn the user habits. To evaluate our system, we build large-scale training and test datasets automatically from a public math forum. The results demonstrate the significant improvement of our method, compared to the maximum-frequency baseline. We also create statistics to reveal the properties of mathematics language

A math-aware search engine for math question answering system

We propose a math-aware search engine that is capable of handling both textual keywords as well as mathematical expressions. Our math feature extraction and representation framework captures the semantics of math expressions via a Finite State Machine model. We adapt the passive aggressive online learning binary classifier as the ranking model. We benchmarked our approach against three classical information retrieval (IR) strategies on math documents crawled from Math Over ow, a well-known online math question answering system. Experimental results show that our proposed approach can perform better than other methods by more than 9%

数学情報アクセスのための数式表現の検索と曖昧性解消

学位の種別: 課程博士審査委員会委員 : （主査）東京大学准教授 渋谷 哲朗, 東京大学教授 萩谷 昌己, 東京大学准教授 蓮尾 一郎, 東京大学准教授 鶴岡 慶雅, 東京工業大学准教授 藤井 敦University of Tokyo(東京大学

MECA: Mathematical Expression Based Post Publication Content Analysis

Mathematical expressions (ME) are critical abstractions for technical publications. While the sheer volume of technical publications grows in time, few ME centric applications have been developed due to the steep gap between the typesetting data in post-publication digital documents and the high-level technical semantics. With the acceleration of the technical publications every year, word-based information analysis technologies are inadequate to enable users in discovery, organizing, and interrelating technical work efficiently and effectively. This dissertation presents a modeling framework and the associated algorithms, called the mathematical-centered post-publication content analysis (MECA) system to address several critical issues to build a layered solution architecture for recovery of high-level technical information. Overall, MECA is consisted of four layers of modeling work, starting from the extraction of MEs from Portable Document Format (PDF) files. Specifically, a weakly-supervised sequential typesetting Bayesian model is developed by using a concise font-value based feature space for Bayesian inference of ME vs. words for the rendering units separated by space. A Markov Random Field (MRF) model is designed to merge and correct the MEs identified from the rendering units, which are otherwise prone to fragmentation of large MEs. At the next layer, MECA aims at the recovery of ME semantics. The first step is the ME layout analysis to disambiguate layout structures based on a Content-Constrained Spatial (CCS) global inference model to overcome local errors. It achieves high accuracy at low computing cost by a parametric lognormal model for the feature distribution of typographic systems. The ME layout is parsed into ME semantics with a three-phase processing workflow to overcome a variety of semantic ambiguities. In the first phase, the ME layout is linearized into a token sequence, upon which the abstract syntax tree (AST) is constructed in the second phase using probabilistic context-free grammar. Tree rewriting will transform the AST into ME objects in the third phase. Built upon the two layers of ME extraction and semantics modeling work, next we explore one of the bonding relationships between words and MEs: ME declarations, where the words and MEs are respectively the qualitative and quantitative (QuQn) descriptors of technical concepts. Conventional low-level PoS tagging and parsing tools have poor performance in the processing of this type of mixed word-ME (MWM) sentences. As such, we develop an MWM processing toolkit. A semi-automated weakly-supervised framework is employed for mining of declaration templates from a large amount of unlabeled data so that the templates can be used for the detection of ME declarations. On the basis of the three low-level content extraction and prediction solutions, the MECA system can extract MEs, interpret their mathematical semantics, and identify their bonding declaration words. By analyzing the dependency among these elements in a paper, we can construct a QuQn map, which essentially represents the reasoning flow of a paper. Three case studies are conducted for QuQn map applications: differential content comparison of papers, publication trend generation, and interactive mathematical learning. Outcomes from these studies suggest that MECA is a highly practical content analysis technology based on a theoretically sound framework. Much more can be expanded and improved upon for the next generation of deep content analysis solutions