scholarly journals Integrated Embedding Approach for Knowledge Base Completion with CNN

2020 ◽  
Vol 49 (4) ◽  
pp. 622-642
Author(s):  
Samuel Chen ◽  
Shengyi Xie ◽  
Qingqiang Chen
Keyword(s):  
Computational Complexity ◽  
Knowledge Base ◽  
Scaling Up ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Feature Maps ◽  
Personalized Search ◽  
Input Channel ◽  
Dimensional Matrix ◽  
Low Dimensional

To tackle specific problems in knowledge base completion such as computational complexity and complex relations or nodes with high indegree or outdegree, an algorithm called IEAKBC(short for Integrated Embedding Approach for Knowledge Base Completion) is proposed, in which entities and relations from triplets are first mapped into low-dimensional vector spaces, each original triplet represented in the form of 3-column, k dimensional matrix; then features from different relations are integrated into head and tail entities thus forming fused triplet matrices used as another input channel for convolution. In CNN feature maps are extracted by filters, concatenated and weighted for output scores to discern whether the original triplet holds or not. Experiments show that IEAKBC holds certain advantages over other models; when scaling up to relatively larger datasets, signs of superiority of IEAKBC stand out especially on relations with high cardinalities. At last we apply IEAKBC to a personalized search application, comparing its performance with strong baselines to verify its practicality in real environments.     

scholarly journals Geometries arising from trilinear forms on low-dimensional vector spaces

2019 ◽  
Vol 19 (2) ◽  
pp. 269-290 ◽  
Author(s):  
Ilaria Cardinali ◽  
Luca Giuzzi
Keyword(s):  
Vector Space ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Low Dimension ◽  
Low Dimensional ◽  
Point Line

Abstract Let 𝓖k(V) be the k-Grassmannian of a vector space V with dim V = n. Given a hyperplane H of 𝓖k(V), we define in [3] a point-line subgeometry of PG(V) called the geometry of poles of H. In the present paper, exploiting the classification of alternating trilinear forms in low dimension, we characterize the possible geometries of poles arising for k = 3 and n ≤ 7 and propose some new constructions. We also extend a result of [6] regarding the existence of line spreads of PG(5, 𝕂) arising from hyperplanes of 𝓖3(V).

Model Based Defect Detection in Multi-Dimensional Vector Spaces

2011 ◽  
Vol 131 (9) ◽  
pp. 1633-1641
Author(s):  
Toshifumi Honda ◽  
Kenji Obara ◽  
Minoru Harada ◽  
Hajime Igarashi
Keyword(s):  
Defect Detection ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Model Based

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

scholarly journals TransET: Knowledge Graph Embedding with Entity Types

Electronics ◽  
2021 ◽  
Vol 10 (12) ◽  
pp. 1407
Author(s):  
Peng Wang ◽  
Jing Zhou ◽  
Yuzhang Liu ◽  
Xingchen Zhou
Keyword(s):  
Link Prediction ◽  
State Of The Art ◽  
Score Function ◽  
Graph Embedding ◽  
Vector Spaces ◽  
Knowledge Graph ◽  
Semantic Features ◽  
Knowledge Graphs ◽  
Real World Datasets ◽  
Low Dimensional

Knowledge graph embedding aims to embed entities and relations into low-dimensional vector spaces. Most existing methods only focus on triple facts in knowledge graphs. In addition, models based on translation or distance measurement cannot fully represent complex relations. As well-constructed prior knowledge, entity types can be employed to learn the representations of entities and relations. In this paper, we propose a novel knowledge graph embedding model named TransET, which takes advantage of entity types to learn more semantic features. More specifically, circle convolution based on the embeddings of entity and entity types is utilized to map head entity and tail entity to type-specific representations, then translation-based score function is used to learn the presentation triples. We evaluated our model on real-world datasets with two benchmark tasks of link prediction and triple classification. Experimental results demonstrate that it outperforms state-of-the-art models in most cases.

scholarly journals A note on extensions of multilinear maps defined on multilinear varieties

2021 ◽  
pp. 1-26
Author(s):  
W. T. Gowers ◽  
L. Milićević
Keyword(s):  
Finite Fields ◽  
Vector Spaces ◽  
Restriction Map ◽  
Zero Set ◽  
Dimensional Vector ◽  
Prime Field ◽  
Finite Dimensional ◽  
Multilinear Maps ◽  
Multilinear Map

Abstract Let $G_1, \ldots , G_k$ be finite-dimensional vector spaces over a prime field $\mathbb {F}_p$ . A multilinear variety of codimension at most $d$ is a subset of $G_1 \times \cdots \times G_k$ defined as the zero set of $d$ forms, each of which is multilinear on some subset of the coordinates. A map $\phi$ defined on a multilinear variety $B$ is multilinear if for each coordinate $c$ and all choices of $x_i \in G_i$ , $i\not =c$ , the restriction map $y \mapsto \phi (x_1, \ldots , x_{c-1}, y, x_{c+1}, \ldots , x_k)$ is linear where defined. In this note, we show that a multilinear map defined on a multilinear variety of codimension at most $d$ coincides on a multilinear variety of codimension $O_{k}(d^{O_{k}(1)})$ with a multilinear map defined on the whole of $G_1\times \cdots \times G_k$ . Additionally, in the case of general finite fields, we deduce similar (but slightly weaker) results.

The genus of graphs associated with vector spaces

2019 ◽  
Vol 19 (05) ◽  
pp. 2050086 ◽  
Author(s):  
T. Tamizh Chelvam ◽  
K. Prabha Ananthi
Keyword(s):  
Finite Field ◽  
Vector Space ◽  
Undirected Graph ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Vertex Connectivity ◽  
Dimensional Vector Space ◽  
Nonzero Component ◽  
Vertex Set ◽  
Component Graph

Let [Formula: see text] be a k-dimensional vector space over a finite field [Formula: see text] with a basis [Formula: see text]. The nonzero component graph of [Formula: see text], denoted by [Formula: see text], is a simple undirected graph with vertex set as nonzero vectors of [Formula: see text] such that there is an edge between two distinct vertices [Formula: see text] if and only if there exists at least one [Formula: see text] along which both [Formula: see text] and [Formula: see text] have nonzero scalars. In this paper, we find the vertex connectivity and girth of [Formula: see text]. We also characterize all vector spaces [Formula: see text] for which [Formula: see text] has genus either 0 or 1 or 2.

An Improved and Low-dimensional Fingerprint-based Localization Method in Collocated Massive MIMO-OFDM Systems

2021 ◽  
Author(s):  
Seyedeh Samira Moosavi ◽  
Paul Fortier
Keyword(s):  
Computational Complexity ◽  
Gaussian Process ◽  
Massive Mimo ◽  
High Reliability ◽  
Gaussian Process Regression ◽  
Location Estimation ◽  
Ofdm Systems ◽  
Process Data ◽  
Localization Method ◽  
Low Dimensional

Abstract Localization has drawn significant attention in 5G due to the fast-growing demand for location-based service (LBS). Massive multiple-input multiple-output (M-MIMO) has been introduced in 5G as a powerful technology due to its evident potentials for communication performance enhancement and localization in complicated environments. Fingerprint-based (FP) localization are promising methods for rich scattering environments thanks to their high reliability and accuracy. The Gaussian process regression (GPR) method could be used as an FP-based localization method to facilitate localization and provide high accuracy. However, this method has high computational complexity, especially in large-scale environments. In this study, we propose an improved and low-dimensional FP-based localization method in collocated massive MIMO orthogonal frequency division multiplexing (OFDM) systems using principal component analysis (PCA), the affinity propagation clustering (APC) algorithm, and Gaussian process regression (GPR) to estimate the user's location. Fingerprints are first extracted based on instantaneous channel state information (CSI) by taking full advantage of the high-resolution angle and delay domains. First, PCA is used to pre-process data and reduce the feature dimension. Then, the training fingerprints are clustered using the APC algorithm to increase prediction accuracy and reduce computation complexity. Finally, each cluster's data distribution is accurately modelled using GPR to provide support for further localization. Simulation results reveal that the proposed method improves localization performance significantly by reducing the location estimation error. Additionally, it reduces the matching complexity and computational complexity.

scholarly journals Deep CNNs with Robust LBP Guiding Pooling for Face Recognition

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 3876 ◽  
Author(s):  
Zhongjian Ma ◽  
Yuanyuan Ding ◽  
Baoqing Li ◽  
Xiaobing Yuan
Keyword(s):  
Neural Networks ◽  
Face Recognition ◽  
Computational Complexity ◽  
Local Binary Pattern ◽  
Weighted Average ◽  
Sliding Window ◽  
Performance Gain ◽  
Feature Maps ◽  
Input Feature ◽  
Noise Impact

Pooling layer in Convolutional Neural Networks (CNNs) is designed to reduce dimensions and computational complexity. Unfortunately, CNN is easily disturbed by noise in images when extracting features from input images. The traditional pooling layer directly samples the input feature maps without considering whether they are affected by noise, which brings about accumulated noise in the subsequent feature maps as well as undesirable network outputs. To address this issue, a robust Local Binary Pattern (LBP) Guiding Pooling (G-RLBP) mechanism is proposed in this paper to down sample the input feature maps and lower the noise impact simultaneously. The proposed G-RLBP method calculates the weighted average of all pixels in the sliding window of this pooling layer as the final results based on their corresponding probabilities of being affected by noise, thus lowers the noise impact from input images at the first several layers of the CNNs. The experimental results show that the carefully designed G-RLBP layer can successfully lower the noise impact and improve the recognition rates of the CNN models over the traditional pooling layer. The performance gain of the G-RLBP is quite remarkable when the images are severely affected by noise.

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