Related papers: Group-theoretical vector space model
Using a deformable sheet to handle objects is convenient and found in many practical applications. For object manipulation through a deformable sheet that is held by multiple mobile robots, it is a challenging task to model the object-sheet…
Computational Group Theory is applied to indexed objects (tensors, spinors, and so on) with dummy indices. There are two groups to consider: one describes the intrinsic symmetries of the object and the other describes the interchange of…
Computers understand very little of the meaning of human language. This profoundly limits our ability to give instructions to computers, the ability of computers to explain their actions to us, and the ability of computers to analyse and…
In this work, we conduct a joint analysis of both Vector Space and Language Models for IR using the mathematical framework of Quantum Theory. We shed light on how both models allocate the space of density matrices. A density matrix is shown…
Support vector machine (SVM) is one of the most studied paradigms in the realm of machine learning for classification and regression problems. It relies on vectorized input data. However, a significant portion of the real-world data exists…
We present an end-to-end deep Convolutional Neural Network called Convolutional Relational Machine (CRM) for recognizing group activities that utilizes the information in spatial relations between individual persons in image or video. It…
When a three-dimensional object moves relative to an observer, a change occurs on the observer's image plane and in the visual representation computed by a learned model. Starting with the idea that a good visual representation is one that…
In group activity recognition, the temporal dynamics of the whole activity can be inferred based on the dynamics of the individual people representing the activity. We build a deep model to capture these dynamics based on LSTM (long-short…
Advances in statistical learning theory present the opportunity to develop statistical models of quantum many-body systems exhibiting remarkable predictive power. The potential of such ``theory-thin'' approaches is illustrated with the…
Modeling semantic information is helpful for scene text recognition. In this work, we propose to model semantic and visual information jointly with a Visual-Semantic Transformer (VST). The VST first explicitly extracts primary semantic…
The purpose of this report is in examining the generalization performance of Support Vector Machines (SVM) as a tool for pattern recognition and object classification. The work is motivated by the growing popularity of the method that is…
This study presents SALMON VR, a visualization program designed to visualize the time evolution of electronic density changes and vector potentials in virtual reality (VR) space. The time-series electronic density data computed by SALMON…
We introduce a translational and rotational invariant local representation for vector fields, which can be employed in the construction of machine-learning energy models of solids and molecules. This allows us to describe, on the same…
Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…
In this paper we consider the problem of group invariant subspace clustering where the data is assumed to come from a union of group-invariant subspaces of a vector space, i.e. subspaces which are invariant with respect to action of a given…
Motion is an important signal for agents in dynamic environments, but learning to represent motion from unlabeled video is a difficult and underconstrained problem. We propose a model of motion based on elementary group properties of…
This note is intended to reformulate the Dixmier-Malliavin theorem about smooth group representations in the language of bornological vector spaces, instead of topological vector spaces. This language turns out to allow a more general…
A visual type theory is a cognitive tool that has much in common with language, and may be regarded as an exceptional form of spatial text adjunct. A mathematical visual type theory, called NPM, has been under development that can be viewed…
A plethora of vector-space representations for words is currently available, which is growing. These consist of fixed-length vectors containing real values, which represent a word. The result is a representation upon which the power of many…
We present numerical simulations of a model of social influence, where the opinion of each agent is represented by a binary vector. Agents adjust their opinions as a result of random encounters, whenever the difference between opinions is…