Symbolic and Visual Retrieval of Mathematical Notation using Formula Graph Symbol Pair Matching and Structural Alignment

Large data collections containing millions of math formulae in different formats are available on-line. Retrieving math expressions from these collections is challenging. We propose a framework for retrieval of mathematical notation using symbol pairs extracted from visual and semantic representations of mathematical expressions on the symbolic domain for retrieval of text documents. We further adapt our model for retrieval of mathematical notation on images and lecture videos. Graph-based representations are used on each modality to describe math formulas. For symbolic formula retrieval, where the structure is known, we use symbol layout trees and operator trees. For image-based formula retrieval, since the structure is unknown we use a more general Line of Sight graph representation. Paths of these graphs define symbol pairs tuples that are used as the entries for our inverted index of mathematical notation. Our retrieval framework uses a three-stage approach with a fast selection of candidates as the first layer, a more detailed matching algorithm with similarity metric computation in the second stage, and finally when relevance assessments are available, we use an optional third layer with linear regression for estimation of relevance using multiple similarity scores for final re-ranking. Our model has been evaluated using large collections of documents, and preliminary results are presented for videos and cross-modal search. The proposed framework can be adapted for other domains like chemistry or technical diagrams where two visually similar elements from a collection are usually related to each other

Evaluating Information Retrieval and Access Tasks

This open access book summarizes the first two decades of the NII Testbeds and Community for Information access Research (NTCIR). NTCIR is a series of evaluation forums run by a global team of researchers and hosted by the National Institute of Informatics (NII), Japan. The book is unique in that it discusses not just what was done at NTCIR, but also how it was done and the impact it has achieved. For example, in some chapters the reader sees the early seeds of what eventually grew to be the search engines that provide access to content on the World Wide Web, today’s smartphones that can tailor what they show to the needs of their owners, and the smart speakers that enrich our lives at home and on the move. We also get glimpses into how new search engines can be built for mathematical formulae, or for the digital record of a lived human life. Key to the success of the NTCIR endeavor was early recognition that information access research is an empirical discipline and that evaluation therefore lay at the core of the enterprise. Evaluation is thus at the heart of each chapter in this book. They show, for example, how the recognition that some documents are more important than others has shaped thinking about evaluation design. The thirty-three contributors to this volume speak for the many hundreds of researchers from dozens of countries around the world who together shaped NTCIR as organizers and participants. This book is suitable for researchers, practitioners, and students—anyone who wants to learn about past and present evaluation efforts in information retrieval, information access, and natural language processing, as well as those who want to participate in an evaluation task or even to design and organize one

Leveraging Formulae and Text for Improved Math Retrieval

Large collections containing millions of math formulas are available online. Retrieving math expressions from these collections is challenging. Users can use formula, formula+text, or math questions to express their math information needs. The structural complexity of formulas requires specialized processing. Despite the existence of math search systems and online community question-answering websites for math, little is known about mathematical information needs. This research first explores the characteristics of math searches using a general search engine. The findings show how math searches are different from general searches. Then, test collections for math-aware search are introduced. The ARQMath test collections have two main tasks: 1) finding answers for math questions and 2) contextual formula search. In each test collection (ARQMath-1 to -3) the same collection is used, Math Stack Exchange posts from 2010 to 2018, introducing different topics for each task. Compared to the previous test collections, ARQMath has a much larger number of diverse topics, and improved evaluation protocol. Another key role of this research is to leverage text and math information for improved math information retrieval. Three formula search models that only use the formula, with no context are introduced. The first model is an n-gram embedding model using both symbol layout tree and operator tree representations. The second model uses tree-edit distance to re-rank the results from the first model. Finally, a learning-to-rank model that leverages full-tree, sub-tree, and vector similarity scores is introduced. To use context, Math Abstract Meaning Representation (MathAMR) is introduced, which generalizes AMR trees to include math formula operations and arguments. This MathAMR is then used for contextualized formula search using a fine-tuned Sentence-BERT model. The experiments show tree-edit distance ranking achieves the current state-of-the-art results on contextual formula search task, and the MathAMR model can be beneficial for re-ranking. This research also addresses the answer retrieval task, introducing a two-step retrieval model in which similar questions are first found and then answers previously given to those similar questions are ranked. The proposed model, fine-tunes two Sentence-BERT models, one for finding similar questions and another one for ranking the answers. For Sentence-BERT model, raw text as well as MathAMR are used

بناء أداة تفاعلية متعددة اللغات لاسترجاع المعلومات

The growing requirement on the Internet have made users access to the information expressed in a language other than their own , which led to Cross lingual information retrieval (CLIR) .CLIR is established as a major topic in Information Retrieval (IR). One approach to CLIR uses different methods of translation to translate queries to documents and indexes in other languages. As queries submitted to search engines suffer lack of untranslatable query keys (i.e., words that the dictionary is missing) and translation ambiguity, which means difficulty in choosing between alternatives of translation. Our approach in this thesis is to build and develop the software tool (MORTAJA-IR-TOOL) , a new tool for retrieving information using programming JAVA language with JDK 1.6. This tool has many features, which is develop multiple systematic languages system to be use as a basis for translation when using CLIR, as well as the process of stemming the words entered in the query process as a stage preceding the translation process. The evaluation of the proposed methodology translator of the query comparing it with the basic translation that uses readable dictionary automatically the percentage of improvement is 8.96%. The evaluation of the impact of the process of stemming the words entered in the query on the quality of the output process in the retrieval of matched data in other process the rate of improvement is 4.14%. Finally the rated output of the merger between the use of stemming methodology proposed and translation process (MORTAJA-IR-TOOL) which concluded that the proportion of advanced in the process of improvement in data rate of retrieval is 15.86%. Keywords: Cross lingual information retrieval, CLIR, Information Retrieval, IR, Translation, stemming.الاحتياجات المتنامية على شبكة الإنترنت جعلت المستخدمين لهم حق الوصول إلى المعلومات بلغة غير لغتهم الاصلية، مما يقودنا الى مصطلح عبور اللغات لاسترجاع المعلومات (CLIR). CLIR أنشئت كموضوع رئيسي في "استرجاع المعلومات" (IR). نهج واحد ل CLIR يستخدم أساليب مختلفة للترجمة ومنها لترجمة الاستعلامات وترجمة الوثائق والفهارس في لغات أخرى. الاستفسارات والاستعلامات المقدمة لمحركات البحث تعاني من عدم وجود ترجمه لمفاتيح الاستعلام (أي أن العبارة مفقودة من القاموس) وايضا تعاني من غموض الترجمة، مما يعني صعوبة في الاختيار بين بدائل الترجمة. في نهجنا في هذه الاطروحة تم بناء وتطوير الأداة البرمجية (MORTAJA-IR-TOOL) أداة جديدة لاسترجاع المعلومات باستخدام لغة البرمجة JAVA مع JDK 1.6، وتمتلك هذه الأداة العديد من الميزات، حيث تم تطوير منظومة منهجية متعددة اللغات لاستخدامها كأساس للترجمة عند استخدام CLIR، وكذلك عملية تجذير للكلمات المدخلة في عملية الاستعلام كمرحلة تسبق عملية الترجمة. وتم تقييم الترجمة المنهجية المقترحة للاستعلام ومقارنتها مع الترجمة الأساسية التي تستخدم قاموس مقروء اليا كأساس للترجمة في تجربة تركز على المستخدم وكانت نسبة التحسين 8.96% , وكذلك يتم تقييم مدى تأثير عملية تجذير الكلمات المدخلة في عملية الاستعلام على جودة المخرجات في عملية استرجاع البيانات المتطابقة باللغة الاخرى وكانت نسبة التحسين 4.14% , وفي النهاية تم تقييم ناتج عملية الدمج بين استخدام التجذير والترجمة المنهجية المقترحة (MORTAJA-IR-TOOL) والتي خلصت الى نسبة متقدمة في عملية التحسين في نسبة البيانات المرجعة وكانت 15.86%

Improved cross-language information retrieval via disambiguation and vocabulary discovery

Cross-lingual information retrieval (CLIR) allows people to find documents irrespective of the language used in the query or document. This thesis is concerned with the development of techniques to improve the effectiveness of Chinese-English CLIR. In Chinese-English CLIR, the accuracy of dictionary-based query translation is limited by two major factors: translation ambiguity and the presence of out-of-vocabulary (OOV) terms. We explore alternative methods for translation disambiguation, and demonstrate new techniques based on a Markov model and the use of web documents as a corpus to provide context for disambiguation. This simple disambiguation technique has proved to be extremely robust and successful. Queries that seek topical information typically contain OOV terms that may not be found in a translation dictionary, leading to inappropriate translations and consequent poor retrieval performance. Our novel OOV term translation method is based on the Chinese authorial practice of including unfamiliar English terms in both languages. It automatically extracts correct translations from the web and can be applied to both Chinese-English and English-Chinese CLIR. Our OOV translation technique does not rely on prior segmentation and is thus free from seg mentation error. It leads to a significant improvement in CLIR effectiveness and can also be used to improve Chinese segmentation accuracy. Good quality translation resources, especially bilingual dictionaries, are valuable resources for effective CLIR. We developed a system to facilitate construction of a large-scale translation lexicon of Chinese-English OOV terms using the web. Experimental results show that this method is reliable and of practical use in query translation. In addition, parallel corpora provide a rich source of translation information. We have also developed a system that uses multiple features to identify parallel texts via a k-nearest-neighbour classifier, to automatically collect high quality parallel Chinese-English corpora from the web. These two automatic web mining systems are highly reliable and easy to deploy. In this research, we provided new ways to acquire linguistic resources using multilingual content on the web. These linguistic resources not only improve the efficiency and effectiveness of Chinese-English cross-language web retrieval; but also have wider applications than CLIR

Making Presentation Math Computable

This Open-Access-book addresses the issue of translating mathematical expressions from LaTeX to the syntax of Computer Algebra Systems (CAS). Over the past decades, especially in the domain of Sciences, Technology, Engineering, and Mathematics (STEM), LaTeX has become the de-facto standard to typeset mathematical formulae in publications. Since scientists are generally required to publish their work, LaTeX has become an integral part of today's publishing workflow. On the other hand, modern research increasingly relies on CAS to simplify, manipulate, compute, and visualize mathematics. However, existing LaTeX import functions in CAS are limited to simple arithmetic expressions and are, therefore, insufficient for most use cases. Consequently, the workflow of experimenting and publishing in the Sciences often includes time-consuming and error-prone manual conversions between presentational LaTeX and computational CAS formats. To address the lack of a reliable and comprehensive translation tool between LaTeX and CAS, this thesis makes the following three contributions. First, it provides an approach to semantically enhance LaTeX expressions with sufficient semantic information for translations into CAS syntaxes. Second, it demonstrates the first context-aware LaTeX to CAS translation framework LaCASt. Third, the thesis provides a novel approach to evaluate the performance for LaTeX to CAS translations on large-scaled datasets with an automatic verification of equations in digital mathematical libraries. This is an open access book

Making Presentation Math Computable

This Open-Access-book addresses the issue of translating mathematical expressions from LaTeX to the syntax of Computer Algebra Systems (CAS). Over the past decades, especially in the domain of Sciences, Technology, Engineering, and Mathematics (STEM), LaTeX has become the de-facto standard to typeset mathematical formulae in publications. Since scientists are generally required to publish their work, LaTeX has become an integral part of today's publishing workflow. On the other hand, modern research increasingly relies on CAS to simplify, manipulate, compute, and visualize mathematics. However, existing LaTeX import functions in CAS are limited to simple arithmetic expressions and are, therefore, insufficient for most use cases. Consequently, the workflow of experimenting and publishing in the Sciences often includes time-consuming and error-prone manual conversions between presentational LaTeX and computational CAS formats. To address the lack of a reliable and comprehensive translation tool between LaTeX and CAS, this thesis makes the following three contributions. First, it provides an approach to semantically enhance LaTeX expressions with sufficient semantic information for translations into CAS syntaxes. Second, it demonstrates the first context-aware LaTeX to CAS translation framework LaCASt. Third, the thesis provides a novel approach to evaluate the performance for LaTeX to CAS translations on large-scaled datasets with an automatic verification of equations in digital mathematical libraries. This is an open access book