The comparison of multiple (labeled) graphs with unrelated vertex sets is an important task in diverse areas of applications. Conceptually, it is often closely related to multiple sequence alignments since one aims to determine a correspondence, or more precisely, a multipartite matching between the vertex sets. There, the goal is to match vertices that are similar in terms of labels and local neighborhoods. Alignments of sequences and ordered forests, however, have a second aspect that does not seem to be considered for graph comparison, namely the idea that an alignment is a superobject from which the constituent input objects can be recovered faithfully as well-defined projections. Progressive alignment algorithms are based on the idea of computing multiple alignments as a pairwise alignment of the alignments of two disjoint subsets of the input objects. Our formal framework guarantees that alignments have compositional properties that make alignments of alignments well-defined. The various similarity-based graph matching constructions do not share this property and solve substantially different optimization problems. We demonstrate that optimal multiple graph alignments can be approximated well by means of progressive alignment schemes. The solution of the pairwise alignment problem is reduced formally to computing maximal common induced subgraphs. Similar to the ambiguities arising from consecutive indels, pairwise alignments of graph alignments require the consideration of ambiguous edges that may appear between alignment columns with complementary gap patterns. We report a simple reference implementation in Python/NetworkX intended to serve as starting point for further developments. The computational feasibility of our approach is demonstrated on test sets of small graphs that mimimc in particular applications to molecular graphs.
{"title":"Progressive Multiple Alignment of Graphs","authors":"Marcos E. González Laffitte, Peter F. Stadler","doi":"10.3390/a17030116","DOIUrl":"https://doi.org/10.3390/a17030116","url":null,"abstract":"The comparison of multiple (labeled) graphs with unrelated vertex sets is an important task in diverse areas of applications. Conceptually, it is often closely related to multiple sequence alignments since one aims to determine a correspondence, or more precisely, a multipartite matching between the vertex sets. There, the goal is to match vertices that are similar in terms of labels and local neighborhoods. Alignments of sequences and ordered forests, however, have a second aspect that does not seem to be considered for graph comparison, namely the idea that an alignment is a superobject from which the constituent input objects can be recovered faithfully as well-defined projections. Progressive alignment algorithms are based on the idea of computing multiple alignments as a pairwise alignment of the alignments of two disjoint subsets of the input objects. Our formal framework guarantees that alignments have compositional properties that make alignments of alignments well-defined. The various similarity-based graph matching constructions do not share this property and solve substantially different optimization problems. We demonstrate that optimal multiple graph alignments can be approximated well by means of progressive alignment schemes. The solution of the pairwise alignment problem is reduced formally to computing maximal common induced subgraphs. Similar to the ambiguities arising from consecutive indels, pairwise alignments of graph alignments require the consideration of ambiguous edges that may appear between alignment columns with complementary gap patterns. We report a simple reference implementation in Python/NetworkX intended to serve as starting point for further developments. The computational feasibility of our approach is demonstrated on test sets of small graphs that mimimc in particular applications to molecular graphs.","PeriodicalId":502609,"journal":{"name":"Algorithms","volume":"126 S2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140251485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Network on Chip (NoC) has emerged as a potential substitute for the communication model in modern computer systems with extensive integration. Among the numerous design challenges, application mapping on the NoC system poses one of the most complex and demanding optimization problems. In this research, we propose a hybrid improved whale optimization algorithm with enhanced genetic properties (IWOA-IGA) to optimally map real-time applications onto the 2D NoC Platform. The IWOA-IGA is a novel approach combining an improved whale optimization algorithm with the ability of a refined genetic algorithm to optimally map application tasks. A comprehensive comparison is performed between the proposed method and other state-of-the-art algorithms through rigorous analysis. The evaluation consists of real-time applications, benchmarks, and a collection of arbitrarily scaled and procedurally generated large-task graphs. The proposed IWOA-IGA indicates an average improvement in power reduction, improved energy consumption, and latency over state-of-the-art algorithms. Performance based on the Convergence Factor, which assesses the algorithm’s efficiency in achieving better convergence after running for a specific number of iterations over other efficiently developed techniques, is introduced in this research work. These results demonstrate the algorithm’s superior convergence performance when applied to real-world and synthetic task graphs. Our research findings spotlight the superior performance of hybrid improved whale optimization integrated with enhanced GA features, emphasizing its potential for application mapping in NoC-based systems.
{"title":"IWO-IGA—A Hybrid Whale Optimization Algorithm Featuring Improved Genetic Characteristics for Mapping Real-Time Applications onto 2D Network on Chip","authors":"Sharoon Saleem, F. Hussain, N. K. Baloch","doi":"10.3390/a17030115","DOIUrl":"https://doi.org/10.3390/a17030115","url":null,"abstract":"Network on Chip (NoC) has emerged as a potential substitute for the communication model in modern computer systems with extensive integration. Among the numerous design challenges, application mapping on the NoC system poses one of the most complex and demanding optimization problems. In this research, we propose a hybrid improved whale optimization algorithm with enhanced genetic properties (IWOA-IGA) to optimally map real-time applications onto the 2D NoC Platform. The IWOA-IGA is a novel approach combining an improved whale optimization algorithm with the ability of a refined genetic algorithm to optimally map application tasks. A comprehensive comparison is performed between the proposed method and other state-of-the-art algorithms through rigorous analysis. The evaluation consists of real-time applications, benchmarks, and a collection of arbitrarily scaled and procedurally generated large-task graphs. The proposed IWOA-IGA indicates an average improvement in power reduction, improved energy consumption, and latency over state-of-the-art algorithms. Performance based on the Convergence Factor, which assesses the algorithm’s efficiency in achieving better convergence after running for a specific number of iterations over other efficiently developed techniques, is introduced in this research work. These results demonstrate the algorithm’s superior convergence performance when applied to real-world and synthetic task graphs. Our research findings spotlight the superior performance of hybrid improved whale optimization integrated with enhanced GA features, emphasizing its potential for application mapping in NoC-based systems.","PeriodicalId":502609,"journal":{"name":"Algorithms","volume":"58 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140255081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mohammadhossein Reshadi, Wen Li, Wenjie Xu, Precious Omashor, Albert Dinh, Scott Dick, Yuntong She, Michael G Lipsett
Anomaly detection in data streams (and particularly time series) is today a vitally important task. Machine learning algorithms are a common design for achieving this goal. In particular, deep learning has, in the last decade, proven to be substantially more accurate than shallow learning in a wide variety of machine learning problems, and deep anomaly detection is very effective for point anomalies. However, deep semi-supervised contextual anomaly detection (in which anomalies within a time series are rare and none at all occur in the algorithm’s training data) is a more difficult problem. Hybrid anomaly detectors (a “normal model” followed by a comparator) are one approach to these problems, but the separate loss functions for the two components can lead to inferior performance. We investigate a novel synthetic-example oversampling technique to harmonize the two components of a hybrid system, thus improving the anomaly detector’s performance. We evaluate our algorithm on two distinct problems: identifying pipeline leaks and patient-ventilator asynchrony.
{"title":"Deep-Shallow Metaclassifier with Synthetic Minority Oversampling for Anomaly Detection in a Time Series","authors":"Mohammadhossein Reshadi, Wen Li, Wenjie Xu, Precious Omashor, Albert Dinh, Scott Dick, Yuntong She, Michael G Lipsett","doi":"10.3390/a17030114","DOIUrl":"https://doi.org/10.3390/a17030114","url":null,"abstract":"Anomaly detection in data streams (and particularly time series) is today a vitally important task. Machine learning algorithms are a common design for achieving this goal. In particular, deep learning has, in the last decade, proven to be substantially more accurate than shallow learning in a wide variety of machine learning problems, and deep anomaly detection is very effective for point anomalies. However, deep semi-supervised contextual anomaly detection (in which anomalies within a time series are rare and none at all occur in the algorithm’s training data) is a more difficult problem. Hybrid anomaly detectors (a “normal model” followed by a comparator) are one approach to these problems, but the separate loss functions for the two components can lead to inferior performance. We investigate a novel synthetic-example oversampling technique to harmonize the two components of a hybrid system, thus improving the anomaly detector’s performance. We evaluate our algorithm on two distinct problems: identifying pipeline leaks and patient-ventilator asynchrony.","PeriodicalId":502609,"journal":{"name":"Algorithms","volume":"53 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140255332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper proposes a genetic algorithm-based Markov Chain approach that can be used for non-parametric estimation of regression coefficients and their statistical confidence bounds. The proposed approach can generate samples from an unknown probability density function if a formal functional form of its likelihood is known. The approach is tested in the non-parametric estimation of regression coefficients, where the least-square minimizing function is considered the maximum likelihood of a multivariate distribution. This approach has an advantage over traditional Markov Chain Monte Carlo methods because it is proven to converge and generate unbiased samples computationally efficiently.
{"title":"A Markov Chain Genetic Algorithm Approach for Non-Parametric Posterior Distribution Sampling of Regression Parameters","authors":"P. Pendharkar","doi":"10.3390/a17030111","DOIUrl":"https://doi.org/10.3390/a17030111","url":null,"abstract":"This paper proposes a genetic algorithm-based Markov Chain approach that can be used for non-parametric estimation of regression coefficients and their statistical confidence bounds. The proposed approach can generate samples from an unknown probability density function if a formal functional form of its likelihood is known. The approach is tested in the non-parametric estimation of regression coefficients, where the least-square minimizing function is considered the maximum likelihood of a multivariate distribution. This approach has an advantage over traditional Markov Chain Monte Carlo methods because it is proven to converge and generate unbiased samples computationally efficiently.","PeriodicalId":502609,"journal":{"name":"Algorithms","volume":"3 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140258557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The principal component analysis is a well-known and widely used technique to determine the essential dimension of a data set. Broadly speaking, it aims to find a low-dimensional linear manifold that retains a large part of the information contained in the original data set. It may be the case that one cannot approximate the entirety of the original data set using a single low-dimensional linear manifold even though large subsets of it are amenable to such approximations. For these cases we raise the related but different challenge (problem) of locating subsets of a high dimensional data set that are approximately 1-dimensional. Naturally, we are interested in the largest of such subsets. We propose a method for finding these 1-dimensional manifolds by finding cliques in a purpose-built auxiliary graph.
{"title":"Exploratory Data Analysis and Searching Cliques in Graphs","authors":"András Hubai, Sándor Szabó, Bogdán Zaválnij","doi":"10.3390/a17030112","DOIUrl":"https://doi.org/10.3390/a17030112","url":null,"abstract":"The principal component analysis is a well-known and widely used technique to determine the essential dimension of a data set. Broadly speaking, it aims to find a low-dimensional linear manifold that retains a large part of the information contained in the original data set. It may be the case that one cannot approximate the entirety of the original data set using a single low-dimensional linear manifold even though large subsets of it are amenable to such approximations. For these cases we raise the related but different challenge (problem) of locating subsets of a high dimensional data set that are approximately 1-dimensional. Naturally, we are interested in the largest of such subsets. We propose a method for finding these 1-dimensional manifolds by finding cliques in a purpose-built auxiliary graph.","PeriodicalId":502609,"journal":{"name":"Algorithms","volume":"32 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140259536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work discusses the electric vehicle (EV) ordered charging planning (OCP) optimization problem. To address this issue, an improved dual-population genetic moth–flame optimization (IDPGMFO) is proposed. Specifically, to obtain an appreciative solution of EV OCP, the design for a dual-population genetic mechanism integrated into moth–flame optimization is provided. To enhance the global optimization performance, the adaptive nonlinear decreasing strategies with selection, crossover and mutation probability, as well as the weight coefficient, are also designed. Additionally, opposition-based learning (OBL) is also introduced simultaneously. The simulation results show that the proposed improvement strategies can effectively improve the global optimization performance. Obviously, more ideal optimization solution of the EV OCP optimization problem can be obtained by using IDPGMFO.
本研究讨论了电动汽车（EV）有序充电规划（OCP）优化问题。针对这一问题，提出了一种改进的双种群遗传蛾焰优化（IDPGMFO）。具体来说，为了获得电动汽车 OCP 的优化解，设计了一种集成到蛾焰优化中的双种群遗传机制。为了提高全局优化性能，还设计了具有选择、交叉和变异概率以及权重系数的自适应非线性递减策略。此外，还同时引入了基于对立面的学习（OBL）。仿真结果表明，所提出的改进策略能有效提高全局优化性能。显然，使用 IDPGMFO 可以获得更理想的 EV OCP 优化问题的优化解。
{"title":"Electric Vehicle Ordered Charging Planning Based on Improved Dual-Population Genetic Moth–Flame Optimization","authors":"Shuang Che, Yan Chen, Longda Wang, Chuanfang Xu","doi":"10.3390/a17030110","DOIUrl":"https://doi.org/10.3390/a17030110","url":null,"abstract":"This work discusses the electric vehicle (EV) ordered charging planning (OCP) optimization problem. To address this issue, an improved dual-population genetic moth–flame optimization (IDPGMFO) is proposed. Specifically, to obtain an appreciative solution of EV OCP, the design for a dual-population genetic mechanism integrated into moth–flame optimization is provided. To enhance the global optimization performance, the adaptive nonlinear decreasing strategies with selection, crossover and mutation probability, as well as the weight coefficient, are also designed. Additionally, opposition-based learning (OBL) is also introduced simultaneously. The simulation results show that the proposed improvement strategies can effectively improve the global optimization performance. Obviously, more ideal optimization solution of the EV OCP optimization problem can be obtained by using IDPGMFO.","PeriodicalId":502609,"journal":{"name":"Algorithms","volume":"25 24","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140262894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Jeng, Alvir Nobel, Vinayak Jha, David Levy, Dylan Kneidel, Manu Chaudhary, Ishraq Islam, Evan Baumgartner, Eade Vanderhoof, Audrey Facer, Manish Singh, Abina Arshad, E. El-Araby
Convolutional neural networks (CNNs) have proven to be a very efficient class of machine learning (ML) architectures for handling multidimensional data by maintaining data locality, especially in the field of computer vision. Data pooling, a major component of CNNs, plays a crucial role in extracting important features of the input data and downsampling its dimensionality. Multidimensional pooling, however, is not efficiently implemented in existing ML algorithms. In particular, quantum machine learning (QML) algorithms have a tendency to ignore data locality for higher dimensions by representing/flattening multidimensional data as simple one-dimensional data. In this work, we propose using the quantum Haar transform (QHT) and quantum partial measurement for performing generalized pooling operations on multidimensional data. We present the corresponding decoherence-optimized quantum circuits for the proposed techniques along with their theoretical circuit depth analysis. Our experimental work was conducted using multidimensional data, ranging from 1-D audio data to 2-D image data to 3-D hyperspectral data, to demonstrate the scalability of the proposed methods. In our experiments, we utilized both noisy and noise-free quantum simulations on a state-of-the-art quantum simulator from IBM Quantum. We also show the efficiency of our proposed techniques for multidimensional data by reporting the fidelity of results.
事实证明，卷积神经网络（CNN）是一类非常高效的机器学习（ML）架构，可通过保持数据局部性来处理多维数据，尤其是在计算机视觉领域。数据池是 CNN 的主要组成部分，在提取输入数据的重要特征和降低其维度方面发挥着至关重要的作用。然而，现有的 ML 算法并不能有效地实现多维池化。特别是，量子机器学习（QML）算法倾向于通过将多维数据表示/扁平化为简单的一维数据来忽略高维数据的局部性。在这项工作中，我们提出利用量子哈尔变换（QHT）和量子部分测量对多维数据执行广义池化操作。我们为所提出的技术提出了相应的退相干优化量子电路，并对电路进行了理论深度分析。我们使用从一维音频数据到二维图像数据再到三维高光谱数据的多维数据进行了实验工作，以证明所提方法的可扩展性。在实验中，我们利用 IBM Quantum 公司最先进的量子模拟器进行了有噪声和无噪声量子模拟。我们还通过报告结果的保真度，展示了我们提出的多维数据技术的效率。
{"title":"Optimizing Multidimensional Pooling for Variational Quantum Algorithms","authors":"M. Jeng, Alvir Nobel, Vinayak Jha, David Levy, Dylan Kneidel, Manu Chaudhary, Ishraq Islam, Evan Baumgartner, Eade Vanderhoof, Audrey Facer, Manish Singh, Abina Arshad, E. El-Araby","doi":"10.3390/a17020082","DOIUrl":"https://doi.org/10.3390/a17020082","url":null,"abstract":"Convolutional neural networks (CNNs) have proven to be a very efficient class of machine learning (ML) architectures for handling multidimensional data by maintaining data locality, especially in the field of computer vision. Data pooling, a major component of CNNs, plays a crucial role in extracting important features of the input data and downsampling its dimensionality. Multidimensional pooling, however, is not efficiently implemented in existing ML algorithms. In particular, quantum machine learning (QML) algorithms have a tendency to ignore data locality for higher dimensions by representing/flattening multidimensional data as simple one-dimensional data. In this work, we propose using the quantum Haar transform (QHT) and quantum partial measurement for performing generalized pooling operations on multidimensional data. We present the corresponding decoherence-optimized quantum circuits for the proposed techniques along with their theoretical circuit depth analysis. Our experimental work was conducted using multidimensional data, ranging from 1-D audio data to 2-D image data to 3-D hyperspectral data, to demonstrate the scalability of the proposed methods. In our experiments, we utilized both noisy and noise-free quantum simulations on a state-of-the-art quantum simulator from IBM Quantum. We also show the efficiency of our proposed techniques for multidimensional data by reporting the fidelity of results.","PeriodicalId":502609,"journal":{"name":"Algorithms","volume":"376 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139835615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper provides a comprehensive overview of approaches to the determination of isocontours and isosurfaces from given data sets. Different algorithms are reported in the literature for this purpose, which originate from various application areas, such as computer graphics or medical imaging procedures. In all these applications, the challenge is to extract surfaces with a specific isovalue from a given characteristic, so called isosurfaces. These different application areas have given rise to solution approaches that all solve the problem of isocontouring in their own way. Based on the literature, the following four dominant methods can be identified: the marching cubes algorithms, the tessellation-based algorithms, the surface nets algorithms and the ray tracing algorithms. With regard to their application, it can be seen that the methods are mainly used in the fields of medical imaging, computer graphics and the visualization of simulation results. In our work, we provide a broad and compact overview of the common methods that are currently used in terms of isocontouring with respect to certain criteria and their individual limitations. In this context, we discuss the individual methods and identify possible future research directions in the field of isocontouring.
{"title":"A Comprehensive Survey of Isocontouring Methods: Applications, Limitations and Perspectives","authors":"Keno Jann Büscher, J. P. Degel, J. Oellerich","doi":"10.3390/a17020083","DOIUrl":"https://doi.org/10.3390/a17020083","url":null,"abstract":"This paper provides a comprehensive overview of approaches to the determination of isocontours and isosurfaces from given data sets. Different algorithms are reported in the literature for this purpose, which originate from various application areas, such as computer graphics or medical imaging procedures. In all these applications, the challenge is to extract surfaces with a specific isovalue from a given characteristic, so called isosurfaces. These different application areas have given rise to solution approaches that all solve the problem of isocontouring in their own way. Based on the literature, the following four dominant methods can be identified: the marching cubes algorithms, the tessellation-based algorithms, the surface nets algorithms and the ray tracing algorithms. With regard to their application, it can be seen that the methods are mainly used in the fields of medical imaging, computer graphics and the visualization of simulation results. In our work, we provide a broad and compact overview of the common methods that are currently used in terms of isocontouring with respect to certain criteria and their individual limitations. In this context, we discuss the individual methods and identify possible future research directions in the field of isocontouring.","PeriodicalId":502609,"journal":{"name":"Algorithms","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139774429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Jeng, Alvir Nobel, Vinayak Jha, David Levy, Dylan Kneidel, Manu Chaudhary, Ishraq Islam, Evan Baumgartner, Eade Vanderhoof, Audrey Facer, Manish Singh, Abina Arshad, E. El-Araby
Convolutional neural networks (CNNs) have proven to be a very efficient class of machine learning (ML) architectures for handling multidimensional data by maintaining data locality, especially in the field of computer vision. Data pooling, a major component of CNNs, plays a crucial role in extracting important features of the input data and downsampling its dimensionality. Multidimensional pooling, however, is not efficiently implemented in existing ML algorithms. In particular, quantum machine learning (QML) algorithms have a tendency to ignore data locality for higher dimensions by representing/flattening multidimensional data as simple one-dimensional data. In this work, we propose using the quantum Haar transform (QHT) and quantum partial measurement for performing generalized pooling operations on multidimensional data. We present the corresponding decoherence-optimized quantum circuits for the proposed techniques along with their theoretical circuit depth analysis. Our experimental work was conducted using multidimensional data, ranging from 1-D audio data to 2-D image data to 3-D hyperspectral data, to demonstrate the scalability of the proposed methods. In our experiments, we utilized both noisy and noise-free quantum simulations on a state-of-the-art quantum simulator from IBM Quantum. We also show the efficiency of our proposed techniques for multidimensional data by reporting the fidelity of results.
事实证明，卷积神经网络（CNN）是一类非常高效的机器学习（ML）架构，可通过保持数据局部性来处理多维数据，尤其是在计算机视觉领域。数据池是 CNN 的主要组成部分，在提取输入数据的重要特征和降低其维度方面发挥着至关重要的作用。然而，现有的 ML 算法并不能有效地实现多维池化。特别是，量子机器学习（QML）算法倾向于通过将多维数据表示/扁平化为简单的一维数据来忽略高维数据的局部性。在这项工作中，我们提出利用量子哈尔变换（QHT）和量子部分测量对多维数据执行广义池化操作。我们为所提出的技术提出了相应的退相干优化量子电路，并对电路进行了理论深度分析。我们使用从一维音频数据到二维图像数据再到三维高光谱数据的多维数据进行了实验工作，以证明所提方法的可扩展性。在实验中，我们利用 IBM Quantum 公司最先进的量子模拟器进行了有噪声和无噪声量子模拟。我们还通过报告结果的保真度，展示了我们提出的多维数据技术的效率。
{"title":"Optimizing Multidimensional Pooling for Variational Quantum Algorithms","authors":"M. Jeng, Alvir Nobel, Vinayak Jha, David Levy, Dylan Kneidel, Manu Chaudhary, Ishraq Islam, Evan Baumgartner, Eade Vanderhoof, Audrey Facer, Manish Singh, Abina Arshad, E. El-Araby","doi":"10.3390/a17020082","DOIUrl":"https://doi.org/10.3390/a17020082","url":null,"abstract":"Convolutional neural networks (CNNs) have proven to be a very efficient class of machine learning (ML) architectures for handling multidimensional data by maintaining data locality, especially in the field of computer vision. Data pooling, a major component of CNNs, plays a crucial role in extracting important features of the input data and downsampling its dimensionality. Multidimensional pooling, however, is not efficiently implemented in existing ML algorithms. In particular, quantum machine learning (QML) algorithms have a tendency to ignore data locality for higher dimensions by representing/flattening multidimensional data as simple one-dimensional data. In this work, we propose using the quantum Haar transform (QHT) and quantum partial measurement for performing generalized pooling operations on multidimensional data. We present the corresponding decoherence-optimized quantum circuits for the proposed techniques along with their theoretical circuit depth analysis. Our experimental work was conducted using multidimensional data, ranging from 1-D audio data to 2-D image data to 3-D hyperspectral data, to demonstrate the scalability of the proposed methods. In our experiments, we utilized both noisy and noise-free quantum simulations on a state-of-the-art quantum simulator from IBM Quantum. We also show the efficiency of our proposed techniques for multidimensional data by reporting the fidelity of results.","PeriodicalId":502609,"journal":{"name":"Algorithms","volume":"29 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139775992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper provides a comprehensive overview of approaches to the determination of isocontours and isosurfaces from given data sets. Different algorithms are reported in the literature for this purpose, which originate from various application areas, such as computer graphics or medical imaging procedures. In all these applications, the challenge is to extract surfaces with a specific isovalue from a given characteristic, so called isosurfaces. These different application areas have given rise to solution approaches that all solve the problem of isocontouring in their own way. Based on the literature, the following four dominant methods can be identified: the marching cubes algorithms, the tessellation-based algorithms, the surface nets algorithms and the ray tracing algorithms. With regard to their application, it can be seen that the methods are mainly used in the fields of medical imaging, computer graphics and the visualization of simulation results. In our work, we provide a broad and compact overview of the common methods that are currently used in terms of isocontouring with respect to certain criteria and their individual limitations. In this context, we discuss the individual methods and identify possible future research directions in the field of isocontouring.
{"title":"A Comprehensive Survey of Isocontouring Methods: Applications, Limitations and Perspectives","authors":"Keno Jann Büscher, J. P. Degel, J. Oellerich","doi":"10.3390/a17020083","DOIUrl":"https://doi.org/10.3390/a17020083","url":null,"abstract":"This paper provides a comprehensive overview of approaches to the determination of isocontours and isosurfaces from given data sets. Different algorithms are reported in the literature for this purpose, which originate from various application areas, such as computer graphics or medical imaging procedures. In all these applications, the challenge is to extract surfaces with a specific isovalue from a given characteristic, so called isosurfaces. These different application areas have given rise to solution approaches that all solve the problem of isocontouring in their own way. Based on the literature, the following four dominant methods can be identified: the marching cubes algorithms, the tessellation-based algorithms, the surface nets algorithms and the ray tracing algorithms. With regard to their application, it can be seen that the methods are mainly used in the fields of medical imaging, computer graphics and the visualization of simulation results. In our work, we provide a broad and compact overview of the common methods that are currently used in terms of isocontouring with respect to certain criteria and their individual limitations. In this context, we discuss the individual methods and identify possible future research directions in the field of isocontouring.","PeriodicalId":502609,"journal":{"name":"Algorithms","volume":"432 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139833889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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