Similarity Geometry

Abstract. In this paper, we propose a new approach to generate analogy questions of the form” A is to B as... is to?” from ontologies. Analogy questions are widely used in multiple-choice tests such as SATs and GREs and are used to assess student's higher cognitive abilities. The design, implementation and evaluation of the new approach are presented in this paper. The results show that mining ontologies for such questions is fruitful.

We address the problem of analysing the joint coherence of a number of concepts with respect to a background ontology. To address this problem, we explore the applicability of Paul Thagard’s computational theory of coherence, in combination with semantic similarity between concepts based on a generalisation operator. In particular, given the input concepts, our approach computes maximally coherent subsets of these concepts following Thagard’s partitioning approach, whilst returning a number of possible generalisations of these concepts as justification of why these concepts cohere.

Superspirals include a very broad family of monotonic curvature curves, whose radius of curvature is defined by a completely monotonic Gauss hypergeometric function. They are generalizations of log-aesthetic curves, and other curves whose radius of curvature is a particular case of a completely monotonic Gauss hypergeometric function. In this work, we study superspirals of confluent type via similarity geometry. Through a detailed investigation of the similarity curvatures of superspirals of confluent type, we find a new class of planar curves with monotone curvature in terms of Tricomi confluent hypergeometric function. Moreover, the proposed ideas will be our guide to expanding superspirals.

We present the Penn system for SemEval-2012 Task 6, computing the degree of semantic equivalence between two sentences. We explore the contributions of different vector models for computing sentence and word similarity: Collobert and Weston embeddings as well as two novel approaches, namely eigenwords and selectors. These embeddings provide different measures of distributional similarity between words, and their contexts. We used regression to combine the different similarity measures, and found that ...

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Many developments have taken place in the field of face-recognition and liveness analysis to improvise various device securities and attendance verification systems. Many approaches have incorporated 3D analysis of the face to predict the liveness of the person in front of it. Our method tries to account for this problem without using advanced 3D imaging techniques or hardware. This results in a solution that is both, more economical and also much easier to deploy. It consists of two parts; the former helps in face verification and the latter to check the liveness of the face. In the first part, we have used a model based on Google’s FaceNet Model which learns a mapping from face images to compact Euclidean space distances, which directly correspond to the measure of similarity of the images. Once the space has been produced, face verification can be easily implemented using standard techniques with embeddings as feature vectors. For the second part, we have employed a cascaded multi-task framework that extracts certain features from the facial image which are then used to check for liveness by tracking their relative displacements. These extracted features were used to check the liveness of the person’s face by asking them to perform some tasks in a random order like head and facial movements etc.

The COVID-19 pandemic has led to an unprecedented challenge to public health. It resulted in global efforts to understand, record, and alleviate the disease. This research serves the purpose of generating a relevant summary related to Coronavirus. The research uses the COVID-19 Open Research Dataset (CORD-19) provided by Allen Institute for AI. The dataset contains 236,336 academic full-text articles as of July 19, 2021. This paper introduces a web-based system to handle user questions over the Coronavirus full-text scholarly articles. The system periodically runs backend services to process such large amount article with basic Natural Language Processing (NLP) techniques that include tokenization, N-Grams extraction, and part-of-speech (PoS) tagging. It automatically identifies the keywords from the question and uses cosine similarity to summarize the associated content and present to the user. This research will possibly benefit researchers, health workers as well as other individuals. Moreover, the same service can be used to train with the datasets of different domains (e.g., education) to generate a relevant summary for other user groups (e.g., students). © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Over the last two decades, radiologists have been using multi-view images to detect tumors. Computer Tomography (CT) imaging is considered as one of the reliable imaging techniques. Many medical-image-processing techniques have been developed to diagnoses lung cancer at early or later stages through CT images; however, it is still a big challenge to improve the accuracy and sensitivity of the algorithms. In this paper, we propose an algorithm based on image fusion for lung segmentation to optimize lung cancer diagnosis. The image fusion technique was developed through Laplacian Pyramid (LP) decomposition along with Adaptive Sparse Representation (ASR). The suggested fusion technique fragments medical images into different sizes using the LP. After that, the LP is used to fuse the four decomposed layers. For the evaluation purposes of the proposed technique, the Lungs Image Database Consortium and Image Database Resource Initiative (LIDC-IDRI) was used. The results showed that the Di...

Development of technology in educational field brings the easier ways through the variety of facilitation for learning process, sharing files, giving assignment and assessment. Automated Essay Scoring (AES) is one of the development systems for determining a score automatically from text document source to facilitate the correction and scoring by utilizing applications that run on the computer. AES process is used to help the lecturers to score efficiently and effectively. Besides it can reduce the subjectivity scoring problem. However, implementation of AES depends on many factors and cases, such as language and mechanism of scoring process especially for essay scoring. A number of methods implemented for weighting the terms from document and reaching the solutions for handling comparative level between documents answer and expert's document still defined. In this research, we implemented the weighting of Term Frequency - Inverse Document Frequency (TF-IDF) method and Cosine Similarity with the measuring degree concept of similarity terms in a document. Tests carried out on a number of Indonesian text-based documents that have gone through the stage of pre-processing for data extraction purposes. This process results is in a ranking of the document weight that have closesness match level with expert's document.

Different binary similarity measures have been explored with different agglomerative hierarchical clustering approaches for software clustering, to make the software systems understandable and manageable. Similarity measures have strengths and weakness that results in improving and deteriorating clustering quality. Determine whether strengths of the similarity measures can be used to avoid their weaknesses for software clustering. This paper presents the strengths of some of the well known existing binary similarity measures. Using these strengths, this paper introduces an improved new binary similarity measure. A series of experiments, on five different test software systems, is presented to evaluate the effectiveness of our new binary similarity measure. The results indicate that our new measure show the combined strengths of the existing similarity measures by reducing the arbitrary decisions, increasing the number of clusters and thus improve the authoritativeness of the clustering.

Similarity and unitary equivalence can be shown to be of equivalence relations. We discuss a result showing that two similar operators have equal spectra (i.e. point and approximate point spectrum). More so, unitary equivalence results for invariant subspaces and normal operators are proved. For similar normal operators, we state the Fuglede – Putnam –Rosenblum theorem that makes proofs for similar normal operators more simplified. It is also noted that direct sums and summands are preserved under unitary equivalence. Furthermore, we show that the natural concept of equivalence between Hilbert Space operators is unitary equivalence which is stronger than similarity. By introducing the notion of quasisimilarity of operators which is the same as similarity in finite dimensional spaces, but in infinite dimensional spaces, it is a much weaker relation, we further show that quasisimilarity is an equivalence relation. We also link invariant subspaces and hyperinvariant subspaces with quasisimilarity where it is seen that similarity preserves nontrivial invariant subspaces while quasisimilarity preserves nontrivial hyperinvariant subspaces. 152 Mathematics Subject Classification: 47A10; 47A15; 47B15

Superspirals include a very broad family of monotonic curvature curves, whose radius of curvature is defined by a completely monotonic Gauss hypergeometric function. They are generalizations of log-aesthetic curves, and other curves whose radius of curvature is a particular case of a completely monotonic Gauss hypergeometric function. In this work, we study superspirals of confluent type via similarity geometry. Through a detailed investigation of the similarity curvatures of superspirals of confluent type, we find a new class of planar curves with monotone curvature in terms of Tricomi confluent hypergeometric function. Moreover, the proposed ideas will be our guide to expanding superspirals.