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1. Visual Search Engine for Handwritten and Typeset Math in Lecture Videos and LATEX Notes

   https://doi.org/10.1109/ICFHR-2018.2018.00018  

   Davila, Kenny ; Zanibbi, Richard ( August 2018 , Proc. International Conference on Frontiers in Handwriting Recognition)

   o fill a gap in online educational tools, we are working to support search in lecture videos using formulas from lecture notes and vice versa. We use an existing system to convert single-shot lecture videos to keyframe images that capture whiteboard contents along with the times they appear. We train classifiers for handwritten symbols using the CROHME dataset, and for LATEX symbols using generated images. Symbols detected in video keyframes and LATEX formula images are indexed using Line-of-Sight graphs. For search, we lookup pairs of symbols that can 'see' each other, and connected pairs are merged to identify the largestmore »match within each indexed image. We rank matches using symbol class probabilities and angles between symbol pairs. We demonstrate how our method effectively locates formulas between typeset and handwritten images using a set of linear algebra lectures. By combining our search engine Tangent-V) with temporal keyframe metadata, we are able to navigate to where a query formula in LATEX is first handwritten in a lecture video. Our system is available as open-source. For other domains, only the OCR modules require updating.« less
2. LPGA: Line-of-Sight Parsing with Graph-Based Attention for Math Formula Recognition

   Mahdavi, Mahshad ; Condon, Michael ; Davila, Kenny ; Zanibbi, Richard ( January 2019 , Proceedings of the International Conference on Document Analysis and Recognition)

   We present a model for recognizing typeset math formula images from connected components or symbols. In our approach, connected components are used to construct a line-of-sight (LOS) graph. The graph is used both to reduce the search space for formula structure interpretations, and to guide a classification attention model using separate channels for inputs and their local visual context. For classification, we used visual densities with Random Forests for initial development, and then converted this to a Convolutional Neural Network (CNN) with a second branch to capture context for each input image. Formula structure is extracted as a directed spanningmore »tree from a weighted LOS graph using Edmonds’ algorithm. We obtain strong results for formulas without grids or matrices in the InftyCDB-2 dataset (90.89% from components, 93.5% from symbols). Using tools from the CROHME handwritten formula recognition competitions, we were able to compile all symbol and structure recognition errors for analysis. Our data and source code are publicly available.« less
3. Tangent-CFT: An Embedding Model for Mathematical Formulas

   https://doi.org/10.1145/3341981.3344235  

   Mansouri, Behrooz ; Rohatgi, Shaurya ; Oard, Douglas W. ; Wu, Jian ; Giles, C. Lee ; Zanibbi, Richard ( January 2019 , ICTIR '19 Proceedings of the 2019 ACM SIGIR International Conference on Theory of Information Retrieval)

   When searching for mathematical content, accurate measures of formula similarity can help with tasks such as document ranking, query recommendation, and result set clustering. While there have been many attempts at embedding words and graphs, formula embedding is in its early stages. We introduce a new formula em- bedding model that we use with two hierarchical representations, (1) Symbol Layout Trees (SLTs) for appearance, and (2) Operator Trees (OPTs) for mathematical content. Following the approach of graph embeddings such as DeepWalk, we generate tuples represent- ing paths between pairs of symbols depth-first, embed tuples using the fastText n-gram embedding model,more »and then represent an SLT or OPT by its average tuple embedding vector. We then combine SLT and OPT embeddings, leading to state-of-the-art results for the NTCIR-12 formula retrieval task. Our fine-grained holistic vector representations allow us to retrieve many more partially similar for- mulas than methods using structural matching in trees. Combining our embedding model with structural matching in the Approach0 formula search engine produces state-of-the-art results for both fully and partially relevant results on the NTCIR-12 benchmark. Source code for our system is publicly available.« less
4. A Multi-match Approach to the Author Uncertainty Problem

   https://doi.org/10.2478/jdis-2019-0006  

   Carley, Stephen F. ; Porter, Alan L. ; Youtie, Jan L. ( June 2019 , Journal of Data and Information Science)

   Abstract Purpose The ability to identify the scholarship of individual authors is essential for performance evaluation. A number of factors hinder this endeavor. Common and similarly spelled surnames make it difficult to isolate the scholarship of individual authors indexed on large databases. Variations in name spelling of individual scholars further complicates matters. Common family names in scientific powerhouses like China make it problematic to distinguish between authors possessing ubiquitous and/or anglicized surnames (as well as the same or similar first names). The assignment of unique author identifiers provides a major step toward resolving these difficulties. We maintain, however, that inmore »and of themselves, author identifiers are not sufficient to fully address the author uncertainty problem. In this study we build on the author identifier approach by considering commonalities in fielded data between authors containing the same surname and first initial of their first name. We illustrate our approach using three case studies. Design/methodology/approach The approach we advance in this study is based on commonalities among fielded data in search results. We cast a broad initial net—i.e., a Web of Science (WOS) search for a given author’s last name, followed by a comma, followed by the first initial of his or her first name (e.g., a search for ‘John Doe’ would assume the form: ‘Doe, J’). Results for this search typically contain all of the scholarship legitimately belonging to this author in the given database (i.e., all of his or her true positives), along with a large amount of noise, or scholarship not belonging to this author (i.e., a large number of false positives). From this corpus we proceed to iteratively weed out false positives and retain true positives. Author identifiers provide a good starting point—e.g., if ‘Doe, J’ and ‘Doe, John’ share the same author identifier, this would be sufficient for us to conclude these are one and the same individual. We find email addresses similarly adequate—e.g., if two author names which share the same surname and same first initial have an email address in common, we conclude these authors are the same person. Author identifier and email address data is not always available, however. When this occurs, other fields are used to address the author uncertainty problem. Commonalities among author data other than unique identifiers and email addresses is less conclusive for name consolidation purposes. For example, if ‘Doe, John’ and ‘Doe, J’ have an affiliation in common, do we conclude that these names belong the same person? They may or may not; affiliations have employed two or more faculty members sharing the same last and first initial. Similarly, it’s conceivable that two individuals with the same last name and first initial publish in the same journal, publish with the same co-authors, and/or cite the same references. Should we then ignore commonalities among these fields and conclude they’re too imprecise for name consolidation purposes? It is our position that such commonalities are indeed valuable for addressing the author uncertainty problem, but more so when used in combination. Our approach makes use of automation as well as manual inspection, relying initially on author identifiers, then commonalities among fielded data other than author identifiers, and finally manual verification. To achieve name consolidation independent of author identifier matches, we have developed a procedure that is used with bibliometric software called VantagePoint (see www.thevantagepoint.com) While the application of our technique does not exclusively depend on VantagePoint, it is the software we find most efficient in this study. The script we developed to implement this procedure is designed to implement our name disambiguation procedure in a way that significantly reduces manual effort on the user’s part. Those who seek to replicate our procedure independent of VantagePoint can do so by manually following the method we outline, but we note that the manual application of our procedure takes a significant amount of time and effort, especially when working with larger datasets. Our script begins by prompting the user for a surname and a first initial (for any author of interest). It then prompts the user to select a WOS field on which to consolidate author names. After this the user is prompted to point to the name of the authors field, and finally asked to identify a specific author name (referred to by the script as the primary author) within this field whom the user knows to be a true positive (a suggested approach is to point to an author name associated with one of the records that has the author’s ORCID iD or email address attached to it). The script proceeds to identify and combine all author names sharing the primary author’s surname and first initial of his or her first name who share commonalities in the WOS field on which the user was prompted to consolidate author names. This typically results in significant reduction in the initial dataset size. After the procedure completes the user is usually left with a much smaller (and more manageable) dataset to manually inspect (and/or apply additional name disambiguation techniques to). Research limitations Match field coverage can be an issue. When field coverage is paltry dataset reduction is not as significant, which results in more manual inspection on the user’s part. Our procedure doesn’t lend itself to scholars who have had a legal family name change (after marriage, for example). Moreover, the technique we advance is (sometimes, but not always) likely to have a difficult time dealing with scholars who have changed careers or fields dramatically, as well as scholars whose work is highly interdisciplinary. Practical implications The procedure we advance has the ability to save a significant amount of time and effort for individuals engaged in name disambiguation research, especially when the name under consideration is a more common family name. It is more effective when match field coverage is high and a number of match fields exist. Originality/value Once again, the procedure we advance has the ability to save a significant amount of time and effort for individuals engaged in name disambiguation research. It combines preexisting with more recent approaches, harnessing the benefits of both. Findings Our study applies the name disambiguation procedure we advance to three case studies. Ideal match fields are not the same for each of our case studies. We find that match field effectiveness is in large part a function of field coverage. Comparing original dataset size, the timeframe analyzed for each case study is not the same, nor are the subject areas in which they publish. Our procedure is more effective when applied to our third case study, both in terms of list reduction and 100% retention of true positives. We attribute this to excellent match field coverage, and especially in more specific match fields, as well as having a more modest/manageable number of publications. While machine learning is considered authoritative by many, we do not see it as practical or replicable. The procedure advanced herein is both practical, replicable and relatively user friendly. It might be categorized into a space between ORCID and machine learning. Machine learning approaches typically look for commonalities among citation data, which is not always available, structured or easy to work with. The procedure we advance is intended to be applied across numerous fields in a dataset of interest (e.g. emails, coauthors, affiliations, etc.), resulting in multiple rounds of reduction. Results indicate that effective match fields include author identifiers, emails, source titles, co-authors and ISSNs. While the script we present is not likely to result in a dataset consisting solely of true positives (at least for more common surnames), it does significantly reduce manual effort on the user’s part. Dataset reduction (after our procedure is applied) is in large part a function of (a) field availability and (b) field coverage.« less
5. Robustly Self-Ordered Graphs: Constructions and Applications to Property Testing

   Goldreich, Oded ; Wigderson, Avi ( November 2020 , Electronic colloquium on computational complexity)

   A graph G is called {\em self-ordered} (a.k.a asymmetric) if the identity permutation is its only automorphism. Equivalently, there is a unique isomorphism from G to any graph that is isomorphic to G. We say that G=(VE) is {\em robustly self-ordered}if the size of the symmetric difference between E and the edge-set of the graph obtained by permuting V using any permutation :VV is proportional to the number of non-fixed-points of . In this work, we initiate the study of the structure, construction and utility of robustly self-ordered graphs. We show that robustly self-ordered bounded-degree graphs exist (in abundance), andmore »that they can be constructed efficiently, in a strong sense. Specifically, given the index of a vertex in such a graph, it is possible to find all its neighbors in polynomial-time (i.e., in time that is poly-logarithmic in the size of the graph). We provide two very different constructions, in tools and structure. The first, a direct construction, is based on proving a sufficient condition for robust self-ordering, which requires that an auxiliary graph, on {\em pairs} of vertices of the original graph, is expanding. In this case the original graph is (not only robustly self-ordered but) also expanding. The second construction proceeds in three steps: It boosts the mere existence of robustly self-ordered graphs, which provides explicit graphs of sublogarithmic size, to an efficient construction of polynomial-size graphs, and then, repeating it again, to exponential-size(robustly self-ordered) graphs that are locally constructible. This construction can yield robustly self-ordered graphs that are either expanders or highly disconnected, having logarithmic size connected components. We also consider graphs of unbounded degree, seeking correspondingly unbounded robustness parameters. We again demonstrate that such graphs (of linear degree)exist (in abundance), and that they can be constructed efficiently, in a strong sense. This turns out to require very different tools. Specifically, we show that the construction of such graphs reduces to the construction of non-malleable two-source extractors with very weak parameters but with some additional natural features. We actually show two reductions, one simpler than the other but yielding a less efficient construction when combined with the known constructions of extractors. We demonstrate that robustly self-ordered bounded-degree graphs are useful towards obtaining lower bounds on the query complexity of testing graph properties both in the bounded-degree and the dense graph models. Indeed, their robustness offers efficient, local and distance preserving reductions from testing problems on ordered structures (like sequences) to the unordered (effectively unlabeled) graphs. One of the results that we obtain, via such a reduction, is a subexponential separation between the query complexities of testing and tolerant testing of graph properties in the bounded-degree graph model. Changes to previous version: We retract the claims made in our initial posting regarding the construction of non-malleable two-source extractors (which are quasi-orthogonal) as well as the claims about the construction of relocation-detecting codes (see Theorems 1.5 and 1.6 in the original version). The source of trouble is a fundamental flaw in the proof of Lemma 9.7 (in the original version), which may as well be wrong. Hence, the original Section 9 was omitted, except that the original Section 9.3 was retained as a new Section 8.3. The original Section 8 appears as Section 8.0 and 8.1, and Section 8.2 is new.« less