In this paper, we present an ontology of mathematical knowledge concepts that covers a wide range of the fields of mathematics and introduces a balanced representation between comprehensive and sensible models. We demonstrate the applications of this representation in information extraction, semantic search, and education. We argue that the ontology can be a core of future integration of math-aware data sets in the Web of Data and, therefore, provide mappings onto relevant datasets, such as DBpedia and ScienceWISE.
A SKOS-based adaptation of Mathematics Subject Classification http: www.ams.org msc ‎ is exposed as a linked dataset @cite_18 . ontology overlaps with this dataset in case of modeling hierarchy of fields, but it is significantly richer for representing terms and their interactions.
@cite_18
87802918 1594098193 1589824882 1994348648
The Mathematics Subject Classification (MSC), maintained by the American Mathematical Society's Mathematical Reviews (MR) and FIZ Karlsruhe's Zentralblatt fur Mathematik (Zbl), is a scheme for classifying publications in mathematics. While it is widely used, its traditional, idiosyncratic conceptualization and representation did not encourage wide reuse on the Web, and it made the scheme hard to maintain. We have reimplemented its current version MSC2010 as a Linked Open Dataset using SKOS, and our focus is concentrated on turning it into the new MSC authority. This paper explains the motivation and details of our design considerations and how we realized them in the implementation, presents use cases, and future applications. Current high-quality object detection approaches use the scheme of salience-based object proposal methods followed by post-classification using deep convolutional features. This spurred recent research in improving object proposal methods. However, domain agnostic proposal generation has the principal drawback that the proposals come unranked or with very weak ranking, making it hard to trade-off quality for running time. This raises the more fundamental question of whether high-quality proposal generation requires careful engineering or can be derived just from data alone. We demonstrate that learning-based proposal methods can effectively match the performance of hand-engineered methods while allowing for very efficient runtime-quality trade-offs. Using the multi-scale convolutional MultiBox (MSC-MultiBox) approach, we substantially advance the state-of-the-art on the ILSVRC 2014 detection challenge data set, with @math mAP for a single model and @math mAP for an ensemble of two models. MSC-Multibox significantly improves the proposal quality over its predecessor MultiBox method: AP increases from @math to @math for the ILSVRC detection challenge. Finally, we demonstrate improved bounding-box recall compared to Multiscale Combinatorial Grouping with less proposals on the Microsoft-COCO data set. Computing least common subsumers (lcs) and most specific concepts (msc) are inference tasks that can be used to support the bottom up'''' construction of knowledge bases for KR systems based on description logic. For the description logic ALN, the msc need not always exist if one restricts the attention to acyclic concept descriptions. In this paper, we extend the notions lcs and msc to cyclic descriptions, and show how they can be computed. Our approach is based on the automata-theoretic characterizations of fixed-point semantics for cyclic terminologies developed in previous papers. We present a novel domain adaptation approach for solving cross-domain pattern recognition problems, i.e., the data or features to be processed and recognized are collected from different domains of interest. Inspired by canonical correlation analysis (CCA), we utilize the derived correlation subspace as a joint representation for associating data across different domains, and we advance reduced kernel techniques for kernel CCA (KCCA) if nonlinear correlation subspace are desirable. Such techniques not only makes KCCA computationally more efficient, potential over-fitting problems can be alleviated as well. Instead of directly performing recognition in the derived CCA subspace (as prior CCA-based domain adaptation methods did), we advocate the exploitation of domain transfer ability in this subspace, in which each dimension has a unique capability in associating cross-domain data. In particular, we propose a novel support vector machine (SVM) with a correlation regularizer, named correlation-transfer SVM, which incorporates the domain adaptation ability into classifier design for cross-domain recognition. We show that our proposed domain adaptation and classification approach can be successfully applied to a variety of cross-domain recognition tasks such as cross-view action recognition, handwritten digit recognition with different features, and image-to-text or text-to-image classification. From our empirical results, we verify that our proposed method outperforms state-of-the-art domain adaptation approaches in terms of recognition performance.