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176 results on '"High dimensional space"'

1. Stochastic resonance in a high-dimensional space coupled bistable system and its application.

Author

Li, Mengdi, Shi, Peiming, Zhang, Wenyue, and Han, Dongying

Subjects
*STOCHASTIC resonance, *SIGNAL-to-noise ratio, *STOCHASTIC systems, *FAULT diagnosis, *SIGNAL detection
Abstract

• A high-dimensional space coupled bistable stochastic resonance system is proposed. • The influence of system parameters on signal to noise ratio is analyzed. • The proposed model has a higher signal to noise ratio than other stochastic resonance models. • The effectiveness of the proposed method is validated by experiments. As a noise-enhanced signal processing method, stochastic resonance has been widely applied in the field of condition detection and fault diagnosis. To further consummate the application of stochastic resonance in practical engineering, a high-dimensional space model based on coupled bistable stochastic resonance system is proposed in this paper. Firstly, taking the three-dimensional space coupled bistable stochastic resonance system as the research object, the influence of system parameters on the output signal-to-noise ratio is analyzed. Then, the output signal-to-noise ratio of the high-dimensional space coupled bistable stochastic resonance system are analyzed in different dimensions. It is found that the output signals of these coupling ends with the same system parameters are identical, and there is always an optimal dimension for a given input so that the output signal-to-noise ratio reaches the maximum. Moreover, simulation results indicate that the proposed model has good feature enhancement ability and anti-noise robustness. Finally, the proposed approach is employed to diagnose fault signals of two different bearing types. The optimal output of the system is determined by establishing the best dimension value. The bigger output signal-to-noise ratio demonstrates that the proposed method outperforms the one-dimensional bistable stochastic resonance and two-dimensional coupled bistable stochastic resonance in weak fault signal detection, which improves the engineering practicability of stochastic resonance theory. [ABSTRACT FROM AUTHOR]

Published
2023
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2. Framework of Meta-Heuristic Variable Length Searching for Feature Selection in High-Dimensional Data.

Author

Saraf, Tara Othman Qadir, Fuad, Norfaiza, and Taujuddin, Nik Shahidah Afifi Md

Subjects
METAHEURISTIC algorithms, FEATURE selection, MATHEMATICAL variables, PARTICLE swarm optimization, SEARCH algorithms, MATHEMATICAL functions, NP-hard problems
Abstract

Feature Selection in High Dimensional Space is a combinatory optimization problem with an NP-hard nature. Meta-heuristic searching with embedding information theory-based criteria in the fitness function for selecting the relevant features is used widely in current feature selection algorithms. However, the increase in the dimension of the solution space leads to a high computational cost and risk of convergence. In addition, sub-optimality might occur due to the assumption of a certain length of the optimal number of features. Alternatively, variable length searching enables searching within the variable length of the solution space, which leads to more optimality and less computational load. The literature contains various meta-heuristic algorithms with variable length searching. All of them enable searching in high dimensional problems. However, an uncertainty in their performance exists. In order to fill this gap, this article proposes a novel framework for comparing various variants of variable length-searching meta-heuristic algorithms in the application of feature selection. For this purpose, we implemented four types of variable length meta-heuristic searching algorithms, namely VLBHO-Fitness, VLBHO-Position, variable length particle swarm optimization (VLPSO) and genetic variable length (GAVL), and we compared them in terms of classification metrics. The evaluation showed the overall superiority of VLBHO over the other algorithms in terms of accomplishing lower fitness values when optimizing mathematical functions of the variable length type. [ABSTRACT FROM AUTHOR]

Published
2023
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3. Sampled Angles in High-Dimensional Spaces

Author

Connor, Richard, Dearle, Alan, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Satoh, Shin'ichi, editor, Vadicamo, Lucia, editor, Zimek, Arthur, editor, Carrara, Fabio, editor, Bartolini, Ilaria, editor, Aumüller, Martin, editor, Jónsson, Björn Þór, editor, and Pagh, Rasmus, editor

Published
2020
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4. A study on the critical Kirchhoff problem in high-dimensional space.

Author

Xie, Qilin and Zhou, Ben-Xing

Subjects
*MULTIPLICITY (Mathematics)
Abstract

In this present paper, we consider the following critical Kirchhoff problem - (a + λ ∫ R N | ∇ u | 2 d x) Δ u + m u = μ | u | p - 2 u + | u | 2 ∗ - 2 u in R N , where a , λ ∈ R and m , μ ∈ R + ∪ { 0 } , N ≥ 3 and 2 < p < 2 ∗ . In this first part, a pure critical Kirchhoff problem ( m = μ = 0 ) has been considered for both a > 0 and a ≤ 0 . We obtain a series of fairly complete existence and multiplicity results and have a clear understand the solutions of this pure critical Kirchhoff problem. In particular, if N ≥ 5 , a > 0 and λ > 0 is suitable small, we obtain two positive solutions, in which one is a mountain pass solution and another one is a global (local) minimum solution. In the second part, the original perturbation problem with m , μ > 0 has been considered and two positive solutions also have been obtained for N ≥ 5 , which is rather different compared with the case that λ = 0 . [ABSTRACT FROM AUTHOR]

Published
2022
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5. Fast identifying redundant security constraints in SCUC in the presence of uncertainties

Author

Tao Ding, Ming Qu, Jiawen Bai, Wenhao Jia, Jiang Wu, Yuankang He, and Tianen Chen

Subjects
day‐ahead market, computational complexity, uncertain feasible region, SCUC, high dimensional space, fast identification method, Distribution or transmission of electric power, TK3001-3521, Production of electric energy or power. Powerplants. Central stations, TK1001-1841
Abstract

Security constrained unit commitment (SCUC), with renewable resources integrated into power grid, is one core function in the day‐ahead market. However, it confronts with critical challenges as the heavy complicated security constraints are considered. Usually, it is observed that lots of security constraints are redundant, which can be identified and eliminated, so as to reduce the computational complexity. In this study, the authors first lift the uncertain feasible region of SCUC into a high dimensional space. Furthermore, a fast identification method is proposed to relax the original feasible region, which thus can be solved by the classical greedy algorithm. In order to prevent the over‐relaxation and find more redundant constraints, an efficient feasible‐based bound tightening strategy is utilised to provide a tighter bound. Numerical results on large‐scale test systems verify the effectiveness of the proposed method.

Published
2020
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6. Framework of Meta-Heuristic Variable Length Searching for Feature Selection in High-Dimensional Data

Author

Tara Othman Qadir Saraf, Norfaiza Fuad, and Nik Shahidah Afifi Md Taujuddin

Subjects
feature selection, high dimensional space, meta-heuristic, solution space, variable length, Electronic computers. Computer science, QA75.5-76.95
Abstract

Feature Selection in High Dimensional Space is a combinatory optimization problem with an NP-hard nature. Meta-heuristic searching with embedding information theory-based criteria in the fitness function for selecting the relevant features is used widely in current feature selection algorithms. However, the increase in the dimension of the solution space leads to a high computational cost and risk of convergence. In addition, sub-optimality might occur due to the assumption of a certain length of the optimal number of features. Alternatively, variable length searching enables searching within the variable length of the solution space, which leads to more optimality and less computational load. The literature contains various meta-heuristic algorithms with variable length searching. All of them enable searching in high dimensional problems. However, an uncertainty in their performance exists. In order to fill this gap, this article proposes a novel framework for comparing various variants of variable length-searching meta-heuristic algorithms in the application of feature selection. For this purpose, we implemented four types of variable length meta-heuristic searching algorithms, namely VLBHO-Fitness, VLBHO-Position, variable length particle swarm optimization (VLPSO) and genetic variable length (GAVL), and we compared them in terms of classification metrics. The evaluation showed the overall superiority of VLBHO over the other algorithms in terms of accomplishing lower fitness values when optimizing mathematical functions of the variable length type.

Published
2022
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7. Efficient similarity search on multidimensional space of biometric databases.

Author

Jayaraman, Umarani and Gupta, Phalguni

Subjects
*APPROXIMATION algorithms, *BIOMETRY, *SEARCH algorithms, *FEATURE extraction, *DECISION making, *K-nearest neighbor classification
Abstract

The problem of pursuing the data items of a large database whose distances to a query item are the least is known as Similarity Search (Nearest Neighbor Search) problem. There exist various algorithms to address this problem. Some of the well known algorithms are i) exact algorithms ii) approximation algorithms and iii) randomized algorithms. This paper has made study only on exact and approximation algorithms because randomized algorithm produces approximate results with some probability. Recently, there are several approximation algorithms are proposed by the researchers because this type of algorithms minimizes the problem of Curse of Dimensionality. This paper mainly has two major sections. In first section, various methods under exact and approximation algorithms are discussed with regard to storage, preprocessing and query time. In the second section, efficient algorithms for similarity search suitable for certain physiological characteristics based biometric systems are considered. Biometric system has five main steps viz acquisition of Image, pre-processing, extraction of features, matching and making final decision. In this paper, indexing algorithms for similarity search suitable for iris trait based on different features are discussed in detail. Since the nature of features are distinct and different in biometric traits, there does not exist a universal (one unique) solution which can apply to all traits of biometric systems. Various performance measures like Penetration Rate and Hit Rate are used to determine the correct recognition rate with top best match (rank-1 accuracy). [ABSTRACT FROM AUTHOR]

Published
2021
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8. Optimal Spherical Separability: Artificial Neural Networks

Author

Garimella, Rama Murthy, Yaparla, Ganesh, Singh, Rhishi Pratap, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Rojas, Ignacio, editor, Joya, Gonzalo, editor, and Catala, Andreu, editor

Published
2017
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9. UAV route planning based on improved dynamic weighted A* algorithm

Author

Yan HE

Subjects
mechatronics technology, UAV, route planning, dynamic weighting, high dimensional space, complex environment, A* algorithm, Technology
Abstract

With the expansion of high dimensional space in UAV trajectory planning, the flying environment of UAV is very complex, and the external threat of UAV is no longer a simple two-dimensional static threat. The traditional ant colony algorithm and artificial potential field algorithm cannot meet the requirements of real-time and high complex environment. To solve the above problems, a new dynamic programming algorithm based on dynamic weighted A* algorithm is proposed. Firstly, the flight environment of UAV is modeled. By studying the constraints such as the turning radius, the length of track section and the limit of the maximum range, the safe flight of UAV is ensured, thus reducing the crash rate and the threat probability. Secondly, a new navigation mode is designed by studying the track and external threat parameters of the UAV, which can reduce the danger of navigation and reduce the loss. Then, the potential energy of the vertex can be expanded. The dynamic weight of the overall change of location and grid graph is obtained, and the cost function in dynamic environment is obtained, which increases the speed, accuracy and evasion degree of obstacle avoidance search. Finally, the simulation results show that under the same application environment, the proposed algorithm has the best path, the least threat cost and the shortest execution time compared with the ant colony algorithm and artificial potential field algorithm. To sum up, the dynamic weighted A* algorithm can be well applied to UAV trajectory planning, reducing the cost of UAV track, shortening the completion time of the algorithm and improving the search speed and precision of unmanned aerial vehicle trajectory planning in complex environment.

Published
2018
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10. Fast identifying redundant security constraints in SCUC in the presence of uncertainties.

Author

Ding, Tao, Qu, Ming, Bai, Jiawen, Jia, Wenhao, Wu, Jiang, He, Yuankang, and Chen, Tianen

Abstract

Security constrained unit commitment (SCUC), with renewable resources integrated into power grid, is one core function in the day‐ahead market. However, it confronts with critical challenges as the heavy complicated security constraints are considered. Usually, it is observed that lots of security constraints are redundant, which can be identified and eliminated, so as to reduce the computational complexity. In this study, the authors first lift the uncertain feasible region of SCUC into a high dimensional space. Furthermore, a fast identification method is proposed to relax the original feasible region, which thus can be solved by the classical greedy algorithm. In order to prevent the over‐relaxation and find more redundant constraints, an efficient feasible‐based bound tightening strategy is utilised to provide a tighter bound. Numerical results on large‐scale test systems verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Published
2020
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11. Gauge fields with respect to $$d=(3+1)$$ d = ( 3 + 1 ) in the Kaluza–Klein theories and in the spin-charge-family theory

Author

Dragan Lukman and Norma Susana Mankoč Borštnik

Subjects
Scalar Field, Yukawa Coupling, Gauge Field, High Dimensional Space, Spin Connection, Astrophysics, QB460-466, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Abstract

Abstract It is shown that in the spin-charge-family theory (Mankoč Borštnik in arXiv:1607.01618v2 , 2016, Phys Rev D 91:065004. arxiv:1409.7791 , 2015, J Mod Phys 6:2244. doi: 10.4236/jmp.2015.615230 . arXiv: 1409.4981 , 2015, J Mod Phys 4:823. doi: 10.4236/jmp.2013.46113 . arxiv:1312.1542 , 2013, arxiv:1409.4981 , 2014) as well as in all the Kaluza–Klein like theories (Blagojević in Gravitation and gauge symmetries, IoP Publishing, Bristol, 2002, An introduction to Kaluza–Klein theories, World Scientific, Singapore, 1983), vielbeins and spin connections manifest in $$d=(3+1)$$ d = ( 3 + 1 ) space equivalent vector gauge fields, when space with $$d\ge 5$$ d ≥ 5 has a large enough symmetry. The authors demonstrate this equivalence in spaces with the symmetry of the metric tensor in the space out of $$d=(3+1)-g^{\sigma \tau } = \eta ^{\sigma \tau } f^{2}$$ d = ( 3 + 1 ) - g σ τ = η σ τ f 2 – for any scalar function f of the coordinates $$x^{\sigma }$$ x σ , where $$x^{\sigma }$$ x σ denotes the coordinates of space out of $$d=(3+1).$$ d = ( 3 + 1 ) . Also the connection between vielbeins and scalar gauge fields in $$d=(3+1)$$ d = ( 3 + 1 ) (offering the explanation for the Higgs scalar) is discussed.

Published
2017
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12. Guarding a Subspace in High-Dimensional Space With Two Defenders and One Attacker

Author

Yisheng Zhong, Zongying Shi, and Rui Yan

Subjects
Computer Science::Computer Science and Game Theory, Current (mathematics), Theoretical computer science, Degree (graph theory), Computer science, Plane (geometry), Systems and Control (eess.SY), Construct (python library), Space (commercial competition), Electrical Engineering and Systems Science - Systems and Control, Computer Science Applications, Human-Computer Interaction, Game Theory, Control and Systems Engineering, FOS: Electrical engineering, electronic engineering, information engineering, Electrical and Electronic Engineering, Software, Subspace topology, High dimensional space, Information Systems
Abstract

This paper considers a subspace guarding game in high-dimensional space which consists of a play subspace and a target subspace. Two faster defenders cooperate to protect the target subspace by capturing an attacker which strives to enter the target subspace from the play subspace without being captured. A closed-form solution is provided from the perspectives of kind and degree. Contributions of the work include the use of the attack subspace (AS) method to construct the barrier, by which the game winner can be perfectly predicted before the game starts. In addition to this inclusion, with the priori information about the game result, a critical payoff function is designed when the defenders can win the game. Then, the optimal strategy for each player is explicitly reformulated as a saddle-point equilibrium. Finally, we apply these theoretical results to a half-space guarding game in three-dimensional space. Since the whole achieved developments are analytical, they require a little memory without computational burden and allow for real-time updates, beyond the capacity of traditional Hamilton-Jacobi-Isaacs method. It is worth noting that this is the first time in the current work to consider the target guarding games for arbitrary high-dimensional space, and in a fully analytical form., Comment: 12 pages, 2 figures

Published
2022
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14. List of Clustered Permutations for Proximity Searching

Author

Figueroa, Karina, Paredes, Rodrigo, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Brisaboa, Nieves, editor, Pedreira, Oscar, editor, and Zezula, Pavel, editor

Published
2013
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15. Differentially-Private Learning of Low Dimensional Manifolds

Author

Choromanska, Anna, Choromanski, Krzysztof, Jagannathan, Geetha, Monteleoni, Claire, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Goebel, Randy, editor, Siekmann, Jörg, editor, Wahlster, Wolfgang, editor, Jain, Sanjay, editor, Munos, Rémi, editor, Stephan, Frank, editor, and Zeugmann, Thomas, editor

Published
2013
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17. CMMB Image Sequences Measurement Based on Computation in High-Dimension Space

Author

Yang, Jun, Zhu, Shi-jiao, Bi, Zhong-qin, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Goebel, Randy, editor, Siekmann, Jörg, editor, Wahlster, Wolfgang, editor, Lei, Jingsheng, editor, Wang, Fu Lee, editor, Deng, Hepu, editor, and Miao, Duoqian, editor

Published
2012
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18. An Axiomatic Approach to Computer Arithmetic with an Appendix on Interval Hardware

Author

Kulisch, Ulrich, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Wyrzykowski, Roman, editor, Dongarra, Jack, editor, Karczewski, Konrad, editor, and Waśniewski, Jerzy, editor

Published
2012
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19. Face feature point detection based on nonlinear high-dimensional space

Author

Faez M. Hassan, Lokanayaki Karnan, and Guoyong Wang

Subjects
Nonlinear system, Feature (computer vision), Computer science, business.industry, Strategy and Management, Face (geometry), Point (geometry), Computer vision, Artificial intelligence, Safety, Risk, Reliability and Quality, business, High dimensional space
Published
2021
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20. Video Frame Quality Assessment Using Points Calculation in High Dimensional Space

Author

Zhu, Shi-jiao, Yang, Jun, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Goebel, Randy, editor, Siekmann, Jörg, editor, Wahlster, Wolfgang, editor, Deng, Hepu, editor, Miao, Duoqian, editor, Lei, Jingsheng, editor, and Wang, Fu Lee, editor

Published
2011
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21. Image Denoising Using Bilateral Filter in High Dimensional PCA-Space

Author

Do, Quoc Bao, Beghdadi, Azeddine, Luong, Marie, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Real, Pedro, editor, Diaz-Pernil, Daniel, editor, Molina-Abril, Helena, editor, Berciano, Ainhoa, editor, and Kropatsch, Walter, editor

Published
2011
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22. High Dimensional Correspondences from Low Dimensional Manifolds – An Empirical Comparison of Graph-Based Dimensionality Reduction Algorithms

Author

Roscher, Ribana, Schindler, Falko, Förstner, Wolfgang, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Koch, Reinhard, editor, and Huang, Fay, editor

Published
2011
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24. Immune Inspired Information Filtering in a High Dimensional Space

Author

Nanas, Nikolaos, Kodovas, Stefanos, Vavalis, Manolis, Houstis, Elias, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Hart, Emma, editor, McEwan, Chris, editor, Timmis, Jon, editor, and Hone, Andy, editor

Published
2010
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25. Extract Interesting Skyline Points in High Dimension

Author

Cheong Fung, Gabriel Pui, Lu, Wei, Yang, Jing, Du, Xiaoyong, Zhou, Xiaofang, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Kitagawa, Hiroyuki, editor, Ishikawa, Yoshiharu, editor, Li, Qing, editor, and Watanabe, Chiemi, editor

Published
2010
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27. 基于动态加权A* 算法的无人机航迹规划.

Author

何 燕

Abstract

Copyright of Journal of Hebei University of Science & Technology is the property of Hebei University of Science & Technology, Journal of Hebei University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Published
2018
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30. Indexing the Function: An Efficient Algorithm for Multi-dimensional Search with Expensive Distance Functions

Author

Chen, Hanxiong, Liu, Jianquan, Furuse, Kazutaka, Xu Yu, Jeffrey, Ohbo, Nobuo, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Goebel, Randy, editor, Siekmann, Jörg, editor, Wahlster, Wolfgang, editor, Huang, Ronghuai, editor, Yang, Qiang, editor, Pei, Jian, editor, Gama, João, editor, Meng, Xiaofeng, editor, and Li, Xue, editor

Published
2009
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31. A Versatile Hyper-Ellipsoidal Basis Function for Function Approximation in High Dimensional Space

Author

Jaiyen, Saichon, Lursinsap, Chidchanok, Phimoltares, Suphakant, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Yu, Wen, editor, He, Haibo, editor, and Zhang, Nian, editor

Published
2009
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32. Principal Component Hashing: An Accelerated Approximate Nearest Neighbor Search

Author

Matsushita, Yusuke, Wada, Toshikazu, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Wada, Toshikazu, editor, Huang, Fay, editor, and Lin, Stephen, editor

Published
2009
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35. Neural networks trained with high-dimensional functions approximation data in high-dimensional space

Author

Wenlong Zhong, Wenling Wu, Jian Zheng, Jianfeng Wang, Yanping Chen, Shuping Chen, and Jingjin Chen

Subjects
0301 basic medicine, Statistics and Probability, Artificial neural network, Computer science, General Engineering, 02 engineering and technology, High dimensional, Topology, 03 medical and health sciences, 030104 developmental biology, Artificial Intelligence, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, High dimensional space
Abstract

Neural networks can approximate data because of owning many compact non-linear layers. In high-dimensional space, due to the curse of dimensionality, data distribution becomes sparse, causing that it is difficulty to provide sufficient information. Hence, the task becomes even harder if neural networks approximate data in high-dimensional space. To address this issue, according to the Lipschitz condition, the two deviations, i.e., the deviation of the neural networks trained using high-dimensional functions, and the deviation of high-dimensional functions approximation data, are derived. This purpose of doing this is to improve the ability of approximation high-dimensional space using neural networks. Experimental results show that the neural networks trained using high-dimensional functions outperforms that of using data in the capability of approximation data in high-dimensional space. We find that the neural networks trained using high-dimensional functions more suitable for high-dimensional space than that of using data, so that there is no need to retain sufficient data for neural networks training. Our findings suggests that in high-dimensional space, by tuning hidden layers of neural networks, this is hard to have substantial positive effects on improving precision of approximation data.

Published
2021
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36. Effective approximation of high-dimensional space using neural networks

Author

Jian Zheng, Jianfeng Wang, Wenlong Zhong, Wenling Wu, Shuping Chen, Jingjin Chen, and Yanping Chen

Subjects
Dependency (UML), Artificial neural network, Computer science, Function (mathematics), Lipschitz continuity, Space (mathematics), Theoretical Computer Science, Task (computing), Hardware and Architecture, Algorithm, Software, High dimensional space, Information Systems, Curse of dimensionality
Abstract

Because of the curse of dimensionality, the data in high-dimensional space hardly afford sufficient information for neural networks training. Hence, this is a tough task to approximate the high-dimensional space using neural networks. To address this, here proposes the method that neural networks approximate a high-dimensional function that can effectively approach the high-dimensional space, rather than using neural networks to directly approximate the high-dimensional space. Hence, two boundaries were derived by Lipschitz condition, i.e., the one is that neural networks approximate a high-dimensional function, and the other is that a high-dimensional function approaches the high-dimensional space. Experimental results on synthetic and real-world datasets show that our method is effective and outperforms the competing methods in the performance to approximate the high-dimensional space. We find that this manner of using neural networks to approximate a high-dimensional function that can effectively approach the high-dimensional space is more resistance to the curse of dimensionality. In addition, the ability of the proposed method to approximate the high-dimensional space is related to the number of hidden layers and the choice of high-dimensional functions, but more relies on the latter. Our findings demonstrate that it is no obvious dependency between the number of hidden layers respecting the proposed method and the choice for high-dimensional functions.

Published
2021
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38. Robust Multi-Objective Optimization in High Dimensional Spaces

Author

Sülflow, André, Drechsler, Nicole, Drechsler, Rolf, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Rangan, C. Pandu, editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Obayashi, Shigeru, editor, Deb, Kalyanmoy, editor, Poloni, Carlo, editor, Hiroyasu, Tomoyuki, editor, and Murata, Tadahiko, editor

Published
2007
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39. Acquisition of Articulated Human Body Models Using Multiple Cameras

Author

Sundaresan, Aravind, Chellappa, Rama, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Perales, Francisco J., editor, and Fisher, Robert B., editor

Published
2006
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40. A Multiclass Classification Method Based on Output Design

Author

Qiang, Qi, He, Qinming, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Dough, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Carbonell, Jaime G., editor, Siekmann, Jörg, editor, Ng, Wee-Keong, editor, Kitsuregawa, Masaru, editor, Li, Jianzhong, editor, and Chang, Kuiyu, editor

Published
2006
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42. View Independent Video-Based Face Recognition Using Posterior Probability in Kernel Fisher Discriminant Space

Author

Hotta, Kazuhiro, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Singh, Sameer, editor, Singh, Maneesha, editor, Apte, Chid, editor, and Perner, Petra, editor

Published
2005
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43. Robust Kernel Fuzzy Clustering

Author

Du, Weiwei, Inoue, Kohei, Urahama, Kiichi, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Carbonell, Jaime G., editor, Siekmann, Jörg, editor, Wang, Lipo, editor, and Jin, Yaochu, editor

Published
2005
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44. Enhanced Supervised Principal Component Analysis for Cancer Classification

Author

Mundher A. Khaleel, Ghadeer Jm Mahdi, and Bayda Atiya Kalaf

Subjects
0303 health sciences, Cancer classification, General Computer Science, Computer science, business.industry, Small number, Cancer, Pattern recognition, 02 engineering and technology, General Chemistry, medicine.disease, General Biochemistry, Genetics and Molecular Biology, 03 medical and health sciences, Stochastic gradient descent, Principal component analysis, 0202 electrical engineering, electronic engineering, information engineering, medicine, 020201 artificial intelligence & image processing, Artificial intelligence, business, High dimensional space, 030304 developmental biology
Abstract

In this paper, a new hybridization of supervised principal component analysis (SPCA) and stochastic gradient descent techniques is proposed, and called as SGD-SPCA, for real large datasets that have a small number of samples in high dimensional space. SGD-SPCA is proposed to become an important tool that can be used to diagnose and treat cancer accurately. When we have large datasets that require many parameters, SGD-SPCA is an excellent method, and it can easily update the parameters when a new observation shows up. Two cancer datasets are used, the first is for Leukemia and the second is for small round blue cell tumors. Also, simulation datasets are used to compare principal component analysis (PCA), SPCA, and SGD-SPCA. The results show that SGD-SPCA is more efficient than other existing methods.

Published
2021
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46. An Effective EM Algorithm for PCA Mixture Model

Author

Jin, Zhong, Davoine, Franck, Lou, Zhen, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Fred, Ana, editor, Caelli, Terry M., editor, Duin, Robert P. W., editor, Campilho, Aurélio C., editor, and de Ridder, Dick, editor

Published
2004
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49. Fast Outlier Detection in High Dimensional Spaces

Author

Angiulli, Fabrizio, Pizzuti, Clara, Goos, Gerhard, editor, Hartmanis, Juris, editor, van Leeuwen, Jan, editor, Carbonell, Jaime G., editor, Siekmann, Jörg, editor, Elomaa, Tapio, editor, Mannila, Heikki, editor, and Toivonen, Hannu, editor

Published
2002
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