The projection graph of the augmented ribbon model is unique

Victor Nicholson; John P. Neuzil

doi:10.1007/bf01164625

Semi-supervised Label Distribution Learning via Projection Graph Embedding

Information Sciences ◽

10.1016/j.ins.2021.10.009 ◽

2021 ◽

Author(s):

Xiuyi Jia ◽

Tao Wen ◽

Weiping Ding ◽

Huaxiong Li ◽

Weiwei Li

Keyword(s):

Graph Embedding ◽

Label Distribution Learning ◽

Projection Graph ◽

Label Distribution

Pedestrian Attribute Recognition by Joint Visual-semantic Reasoning and Knowledge Distillation

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2019/117 ◽

2019 ◽

Cited By ~ 1

Author(s):

Qiaozhe Li ◽

Xin Zhao ◽

Ran He ◽

Kaiqi Huang

Keyword(s):

Large Scale ◽

Visual Space ◽

Model Potential ◽

Feature Representations ◽

Trained Teacher ◽

Knowledge Distillation ◽

Attribute Recognition ◽

Feature Projection ◽

Pose Variation ◽

Projection Graph

Pedestrian attribute recognition in surveillance is a challenging task in computer vision due to significant pose variation, viewpoint change and poor image quality. To achieve effective recognition, this paper presents a graph-based global reasoning framework to jointly model potential visual-semantic relations of attributes and distill auxiliary human parsing knowledge to guide the relational learning. The reasoning framework models attribute groups on a graph and learns a projection function to adaptively assign local visual features to the nodes of the graph. After feature projection, graph convolution is utilized to perform global reasoning between the attribute groups to model their mutual dependencies. Then, the learned node features are projected back to visual space to facilitate knowledge transfer. An additional regularization term is proposed by distilling human parsing knowledge from a pre-trained teacher model to enhance feature representations. The proposed framework is verified on three large scale pedestrian attribute datasets including PETA, RAP, and PA-100k. Experiments show that our method achieves state-of-the-art results.

Directed Projection Graph of N-Dimensional Hypercube and Subhypercube Decomposition of Balanced Linearly Separable Boolean Functions

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127421501388 ◽

2021 ◽

Vol 31 (09) ◽

pp. 2150138

Author(s):

Wei Jin ◽

Fangyue Chen ◽

Qinbin He

Keyword(s):

Neural Networks ◽

Artificial Neural Networks ◽

Boolean Function ◽

Planar Graph ◽

Boolean Functions ◽

Conformal Transformation ◽

Two Dimensional ◽

Induced Subgraph ◽

Projection Graph ◽

Enumeration Scheme

A directed projection graph of the [Formula: see text]-dimensional hypercube on the two-dimensional plane is successfully created. Any [Formula: see text]-variable Boolean function can be easily transformed to an induced subgraph of the projection. Therefore, the discussions on [Formula: see text]-variable Boolean functions only need to focus on a two-dimensional planar graph. Some mathematical theories on the projection graph and the induced subgraph are established, and some properties and characteristics of a balanced linearly separable Boolean function (BLSBF) are uncovered. In particular, the sub-hypercube decompositions of BLSBF is easily represented on the projection, and meanwhile, the enumeration scheme for counting the number of [Formula: see text]-variable BLSBFs is developed by using equivalence classification and conformal transformation. With the aid of the directed projection grap constructed in this paper, one can further study many difficult problems in some fields such as Boolean functions and artificial neural networks.

Successive Projection Graph Matching

Lecture Notes in Computer Science - Structural, Syntactic, and Statistical Pattern Recognition ◽

10.1007/3-540-70659-3_27 ◽

2002 ◽

pp. 263-271 ◽

Cited By ~ 3

Author(s):

Barend Jacobus van Wyk ◽

Michaël Antonie van Wyk ◽

Hubert Edward Hanrahan

Keyword(s):

Graph Matching ◽

Successive Projection ◽

Projection Graph

AN EXTENSION OF THE JONES POLYNOMIAL OF CLASSICAL KNOTS

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216506004294 ◽

2006 ◽

Vol 15 (01) ◽

pp. 81-100 ◽

Cited By ~ 3

Author(s):

BLERTA SHTYLLA ◽

LOUIS ZULLI

Keyword(s):

Isomorphism Class ◽

Topological Property ◽

Jones Polynomial ◽

Algebraic Extension ◽

Jones Polynomials ◽

Projection Graph ◽

Projection Matrices

We define a linear algebraic extension of the Jones polynomial of classical knots, and prove that certain key properties of the classical Jones polynomial are properties of the extension. This shows that these properties are linear algebraic in nature, not topological. We identify a topological property of the classical Jones polynomial, that is, a property of the classical Jones polynomial that the extension does not possess. We discuss ortho-projection matrices, ortho-projection graphs, and their Jones polynomials. We classify, up to isomorphism, the connected ortho-projection graphs with at most eight vertices, and show that each such isomorphism class corresponds to a prime alternating classical knot diagram. We give an example of a connected ortho-projection graph with nine vertices that does not correspond to such a diagram.