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CubeSat formation architecture for small space debris surveillance and orbit determination 用于小空间碎片监视和轨道确定的立方体卫星编队结构
Q3 Mathematics Pub Date : 2021-09-13 DOI: 10.31799/1684-8853-2021-4-37-46
A. Afanasev, S. Biktimirov
Introduction: Satellites which face space debris cannot track it throughout the whole orbit due to natural limitations of their optical sensors, sush as field of view, Earth occultation, or solar illumination. Besides, the time of continuous observations is usually very short. Therefore, we are trying to offer the most effective configuration of optical sensors in order to provide short-arc tracking of a target piece of debris, using a scalable Extended Information Filter. Purpose: The best scenario for short-arc tracking of a space debris orbit using multipoint optical sensors. Results: We have found optimal configurations for groups of satellites with optical sensors which move along a sun-synchronous orbit.  Debris orbit determination using an Extended Information Filter and measurements from multipoint sensors was simulated, and mean squared errors of the target's position were calculated. Based on the simulation results for variouos configurations, inter-satellite distances and measurement time, the most reliable scenario (four satellites in tetrahedral configuration) was found and recommended for practical use in short-arc debris tracking.
引言:面对空间碎片的卫星由于其光学传感器的自然限制,如视野、地球掩星或太阳照明,无法在整个轨道上跟踪它。此外,连续观测的时间通常很短。因此,我们正试图提供最有效的光学传感器配置,以便使用可扩展的扩展信息过滤器对目标碎片进行短弧跟踪。目的:使用多点光学传感器对空间碎片轨道进行短弧跟踪的最佳方案。结果:我们发现了带有光学传感器的卫星组在太阳同步轨道上移动的最佳配置。模拟了使用扩展信息滤波器和多点传感器测量的碎片轨道确定,并计算了目标位置的均方误差。根据各种配置、卫星间距离和测量时间的模拟结果,找到了最可靠的场景(四面体配置的四颗卫星),并推荐在短弧碎片跟踪中实际使用。
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引用次数: 0
Evaluation of the union bound for the decoding error probability using characteristic functions 利用特征函数评估解码错误概率的并界
Q3 Mathematics Pub Date : 2021-09-13 DOI: 10.31799/1684-8853-2021-4-71-85
A. Trofimov, F. Taubin
Introduction: Since the exact value of a decoding error probability cannot usually be calculated, an upper bounding technique is used. The standard approach for obtaining the upper bound on the maximum likelihood decoding error probability is based on the use of the union bound and the Chernoff bound, as well as its modifications. For many situations, this approach is not accurate enough. Purpose: Development of a method for exact calculation of the union bound for a decoding error probability, for a wide class of codes and memoryless channels. Methods: Use of characteristic functions of logarithm of the likelihood ratio for an arbitrary pair of codewords, trellis representation of codes and numerical integration. Results: The resulting exact union bound on the decoding error probability is based on a combination of the use of characteristic functions and the product of trellis diagrams for the code, which allows to obtain the final expression in an integral form convenient for numerical integration. An important feature of the proposed procedure is that it allows one to accurately calculate the union bound using an approach based on the use of transfer (generating) functions. With this approach, the edge labels in the product of trellis diagrams for the code are replaced by their corresponding characteristic functions. The final expression allows, using the standard methods of numerical integration, to calculate the values of the union bound on the decoding error probability with the required accuracy. Practical relevance: The results presented in this article make it possible to significantly improve the accuracy of the bound of the error decoding probability, and thereby increase the efficiency of technical solutions in the design of specific coding schemes for a wide class of communication channels.
引言:由于解码错误概率的确切值通常无法计算,因此使用了上界技术。获得最大似然解码错误概率上限的标准方法是基于并界和Chernoff界的使用及其修改。在许多情况下,这种方法不够准确。目的:开发一种精确计算解码错误概率并界的方法,用于广泛的代码和无记忆信道。方法:使用任意码字对的似然比对数的特征函数,代码的网格表示和数值积分。结果:解码错误概率的精确并集是基于特征函数的使用和代码的网格图的乘积的组合,这允许获得便于数值积分的积分形式的最终表达式。所提出的过程的一个重要特征是,它允许使用基于使用传递(生成)函数的方法来准确地计算并界。使用这种方法,代码的网格图乘积中的边缘标签被其相应的特征函数所取代。最后的表达式允许使用数字积分的标准方法,以所需的精度计算解码错误概率的并集值。实际相关性:本文提出的结果有可能显著提高错误解码概率界的准确性,从而提高为广泛的通信信道设计特定编码方案的技术解决方案的效率。
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引用次数: 1
Scenario model of intelligent decision support based user digital life models 基于智能决策支持的用户数字生活模型场景模型
Q3 Mathematics Pub Date : 2021-09-13 DOI: 10.31799/1684-8853-2021-4-47-60
A. Smirnov, T. Levashova
Introduction. In the decision support domain, the practice of using information from user digital traces has not been widespread so far. Earlier, the authors of this paper developed a conceptual framework of intelligent decision support based on user digital life models that was aimed at recommending decisions using information from the user digital traces. The present research is aiming at the development of a scenario model that implements this framework. Purpose: the development of a scenario model of intelligent decision support based on user digital life models and an approach to grouping users with similar preferences and decision-making behaviours. Results: A scenario model of intelligent decision support based on user digital life models has been developed. The model is intended to recommend to the user decisions based on the knowledge about the user decision-maker type, decision support problem, and problem domain. The scenario model enables to process incompletely formulated problems due to taking into account the preferences of users who have preferences and decision-making behaviour similar to the active user. An approach to grouping users with similar preferences and decision-making behaviours has been proposed. The approach enables to group users with similar preferences and decision-making behaviours based on the information about user behavioural segments that exist in various domains, behavioural segmentation rules, and user actions represented in their digital life models. Practical relevance: the research results are beneficial for the development of advanced recommendation systems expected to tracking digital traces.
介绍在决策支持领域,迄今为止,使用来自用户数字痕迹的信息的做法还不普遍。早些时候,本文作者开发了一个基于用户数字生活模型的智能决策支持概念框架,旨在使用来自用户数字轨迹的信息推荐决策。本研究旨在开发一个实现该框架的场景模型。目的:开发基于用户数字生活模型的智能决策支持场景模型,以及对具有相似偏好和决策行为的用户进行分组的方法。结果:建立了基于用户数字生活模型的智能决策支持场景模型。该模型旨在根据用户决策者类型、决策支持问题和问题领域的知识向用户推荐决策。由于考虑了具有与活跃用户相似的偏好和决策行为的用户的偏好,该场景模型能够处理不完全公式化的问题。已经提出了一种将具有相似偏好和决策行为的用户分组的方法。该方法能够根据不同领域中存在的用户行为细分信息、行为细分规则以及数字生活模型中代表的用户行为,对具有类似偏好和决策行为的用户进行分组。实际相关性:研究结果有利于开发用于跟踪数字痕迹的高级推荐系统。
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引用次数: 1
Training set formation in machine learning problems (review) 机器学习问题中的训练集形成(回顾)
Q3 Mathematics Pub Date : 2021-09-13 DOI: 10.31799/1684-8853-2021-4-61-70
A. Parasich, V. Parasich, I. Parasich
Introduction: Proper training set formation is a key factor in machine learning. In real training sets, problems and errors commonly occur, having a critical impact on the training result. Training set need to be formed in all machine learning problems; therefore, knowledge of possible difficulties will be helpful. Purpose: Overview of possible problems in the formation of a training set, in order to facilitate their detection and elimination when working with real training sets. Analyzing the impact of these problems on the results of the training.  Results: The article makes on overview of possible errors in training set formation, such as lack of data, imbalance, false patterns, sampling from a limited set of sources, change in the general population over time, and others. We discuss the influence of these errors on the result of the training, test set formation, and training algorithm quality measurement. The pseudo-labeling, data augmentation, and hard samples mining are considered the most effective ways to expand a training set. We offer practical recommendations for the formation of a training or test set. Examples from the practice of Kaggle competitions are given. For the problem of cross-dataset generalization in neural network training, we propose an algorithm called Cross-Dataset Machine, which is simple to implement and allows you to get a gain in cross-dataset generalization. Practical relevance: The materials of the article can be used as a practical guide in solving machine learning problems.
引言:正确的训练集形成是机器学习的一个关键因素。在真实的训练集中,问题和错误经常发生,对训练结果有着至关重要的影响。所有机器学习问题都需要形成训练集;因此,了解可能存在的困难将有所帮助。目的:概述训练集形成过程中可能存在的问题,以便于在使用真实训练集时发现和消除这些问题。分析这些问题对培训结果的影响。结果:本文概述了训练集形成中可能存在的错误,如数据缺乏、不平衡、错误模式、有限来源的抽样、一般人群随时间的变化等。我们讨论了这些误差对训练结果、测试集形成和训练算法质量测量的影响。伪标记、数据扩充和硬样本挖掘被认为是扩展训练集的最有效方法。我们为培训或测试集的形成提供实用的建议。文中列举了卡格尔比赛的实例。针对神经网络训练中的跨数据集泛化问题,我们提出了一种称为跨数据集机器的算法,该算法实现简单,可以在跨数据集的泛化中获得增益。实际相关性:文章的材料可以作为解决机器学习问题的实践指南。
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引用次数: 2
Finite field and group algorithms for orthogonal sequence search 正交序列搜索的有限域和群算法
Q3 Mathematics Pub Date : 2021-09-13 DOI: 10.31799/1684-8853-2021-4-2-17
N. A. Balonin, A. Sergeev, Olga Sinitshina
Introduction: Hadamard matrices consisting of elements 1 and –1 are an ideal object for a visual application of finite dimensional mathematics operating with a finite number of addresses for –1 elements. The notation systems of abstract algebra methods, in contrast to the conventional matrix algebra, have been changing intensively, without being widely spread, leading to the necessity to revise and systematize the accumulated experience. Purpose: To describe the algorithms of finite fields and groups in a uniform notation in order to facilitate the perception of the extensive knowledge necessary for finding orthogonal and suborthogonal sequences. Results: Formulas have been proposed for calculating relatively unknown algorithms (or their versions) developed by Scarpis, Singer, Szekeres, Goethal — Seidel, and Noboru Ito, as well as polynomial equations used to prove the theorems about the existence of finite-dimensional solutions. This replenished the significant lack of information both in the domestic literature (most of these issues are published here for the first time) and abroad. Practical relevance: Orthogonal sequences and methods for their effective finding via the theory of finite fields and groups are of direct practical importance for noise-immune coding, compression and masking of video data.
简介:由元素1和-1组成的阿达玛矩阵是一个理想的对象,用于有限维数学的视觉应用,操作与-1元素的有限数量的地址。与传统的矩阵代数方法不同,抽象代数方法的符号系统一直在剧烈地变化,但没有得到广泛的推广,这导致了对积累的经验进行修正和系统化的必要性。目的:用统一的符号描述有限域和群的算法,以便于理解寻找正交和次正交序列所必需的广泛知识。结果:已经提出了计算Scarpis, Singer, Szekeres, Goethal - Seidel和Noboru Ito开发的相对未知算法(或其版本)的公式,以及用于证明有限维解存在性定理的多项式方程。这补充了国内文献(这些问题大多数是第一次在这里发表)和国外资料严重缺乏的情况。实际意义:正交序列及其通过有限域和群理论有效发现正交序列的方法对视频数据的抗噪声编码、压缩和屏蔽具有直接的实际意义。
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引用次数: 1
Dataset segmentation considering the information about impact factors 考虑影响因子信息的数据集分割
Q3 Mathematics Pub Date : 2021-06-29 DOI: 10.31799/1684-8853-2021-3-29-38
I. Lebedev
Introduction: The application of machine learning methods involves the collection and processing of data which comes from the recording elements in the offline mode. Most models are trained on historical data and then used in forecasting, classification, search for influencing factors or impacts, and state analysis. In the long run, the data value ranges can change, affecting the quality of the classification algorithms and leading to the situation when the models should be constantly trained or readjusted taking into account the input data. Purpose: Development of a technique to improve the quality of machine learning algorithms in a dynamically changing and non-stationary environment where the data distribution can change over time. Methods: Splitting (segmentation) of multiple data based on the information about factors affecting the ranges of target variables. Results: A data segmentation technique has been proposed, based on taking into account the factors which affect the change in the data value ranges. Impact detection makes it possible to form samples based on the current and alleged situations. Using PowerSupply dataset as an example, the mass of data is split into subsets considering the effects of factors on the value ranges. The external factors and impacts are formalized based on production rules. The processing of the factors using the membership function (indicator function) is shown. The data sample is divided into a finite number of non-intersecting measurable subsets. Experimental values of the neural network loss function are shown for the proposed technique on the selected dataset. Qualitative indicators (Accuracy, AUC, F-measure) of the classification for various classifiers are presented. Practical relevance: The results can be used in the development of classification models of machine learning methods. The proposed technique can improve the classification quality in dynamically changing conditions of the functioning.
简介:机器学习方法的应用涉及到数据的收集和处理,这些数据来自离线模式下的记录元素。大多数模型都是在历史数据上训练的,然后用于预测、分类、搜索影响因素或影响以及状态分析。从长期来看,数据值的范围会发生变化,从而影响分类算法的质量,并导致模型需要根据输入数据不断训练或重新调整。目的:开发一种在数据分布随时间变化的动态变化和非平稳环境中提高机器学习算法质量的技术。方法:根据影响目标变量范围的因素信息,对多个数据进行拆分(分割)。结果:在考虑影响数据值范围变化因素的基础上,提出了一种数据分割技术。冲击检测可以根据当前和所谓的情况形成样品。以PowerSupply数据集为例,考虑因素对数值范围的影响,将大量数据划分为子集。外部因素和影响是基于生产规则形式化的。给出了利用隶属函数(指标函数)对各因素进行处理的过程。数据样本被划分为有限个不相交的可测量子集。给出了所选数据集上神经网络损失函数的实验值。给出了各种分类器分类的定性指标(准确率、AUC、F-measure)。实际意义:研究结果可用于开发机器学习方法的分类模型。该方法可以在功能动态变化的条件下提高分类质量。
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引用次数: 3
Suppression of correlated interference by adaptive notch filters under pulse repetition period modulation 脉冲重复周期调制下自适应陷波滤波器对相关干扰的抑制
Q3 Mathematics Pub Date : 2021-06-29 DOI: 10.31799/1684-8853-2021-3-53-60
S. Ziatdinov, L. Osipov
 Introduction: We discuss the problem of correlated noise suppression by adaptive complex notch filters of various orders. In order to eliminate the dependence of the transmission coefficient of the useful signal on its frequency, the pulse repetition period is modulated. Purpose: Studying the influence of pulse repetition period modulation on the correlated noise suppression coefficient. Methods: The notch filter parameters were optimized with the criterion of minimum average dispersion of correlated noise at the output of the filters during the repetition period modulation. Results: Expressions are obtained for the variance of correlated noise at the output of complex adaptive filters of various orders when the repetition period is modulated. Relationships are given for finding the optimal values ​​of the tuning frequency and coefficients of the notch filters which minimize the correlated noise level at their output. Expressions are obtained for the coefficients of correlated noise suppression by notch filters in the context of pulse repetition period modulation. The graphs are presented showing how the correlated noise suppression coefficient depends on the relative value of the probing signal repetition period deviation for various values ​​of the correlated noise spectral density width at optimal or non-optimal values ​​of the tuning frequency and coefficients of the notch filters. It is shown that the use of probing pulse repetition period modulation leads to a decrease in the correlated noise suppression coefficient. On the other hand, the adaptation of the weighting coefficients for the adopted models of notch filters and correlated interference provides an increase in the suppression coefficient. Practical relevance: When developing or studying correlated noise suppression systems, the obtained results make it possible, taking into account the permissible losses of the suppression coefficient, to reasonably choose the input pulse repetition period deviation value in order to eliminate the effect of “blind” frequencies.
引言:我们讨论了用不同阶数的自适应复数陷波滤波器抑制相关噪声的问题。为了消除有用信号的传输系数对其频率的依赖性,对脉冲重复周期进行调制。目的:研究脉冲重复周期调制对相关噪声抑制系数的影响。方法:以重复周期调制过程中滤波器输出处相关噪声的最小平均色散为准则,对陷波滤波器参数进行优化。结果:得到了调制重复周期时不同阶数的复自适应滤波器输出处相关噪声的方差表达式。给出了寻找最优值的关系式​​陷波滤波器的调谐频率和系数使其输出处的相关噪声电平最小化。在脉冲重复周期调制的背景下,获得了陷波滤波器的相关噪声抑制系数的表达式。图表显示了相关噪声抑制系数如何取决于不同值的探测信号重复周期偏差的相对值​​最佳或非最佳值下的相关噪声频谱密度宽度​​陷波滤波器的调谐频率和系数。结果表明,探测脉冲重复周期调制的使用导致相关噪声抑制系数的降低。另一方面,陷波滤波器和相关干扰的所采用的模型的加权系数的自适应提供了抑制系数的增加。实际相关性:在开发或研究相关噪声抑制系统时,所获得的结果使得在考虑抑制系数的允许损耗的情况下,合理选择输入脉冲重复周期偏差值,以消除“盲”频率的影响成为可能。
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引用次数: 1
Information-theoretic problems of DNA-based storage systems 基于dna存储系统的信息理论问题
Q3 Mathematics Pub Date : 2021-06-29 DOI: 10.31799/1684-8853-2021-3-39-52
S. Kruglik, G. Kucherov, Kamilla Nazirkhanova, Mikhail Filitov
Introduction: Currently, we witness an explosive growth in the amount of information produced by humanity. This raises new fundamental problems of its efficient storage and processing. Commonly used magnetic, optical, and semiconductor information storage devices have several drawbacks related to small information density and limited durability. One of the promising novel approaches to solving these problems is DNA-based data storage. Purpose: An overview of modern DNA-based storage systems and related information-theoretic problems. Results: The current state of the art of DNA-based storage systems is reviewed. Types of errors occurring in them as well as corresponding error-correcting codes are analized. The disadvantages of these codes are shown, and possible pathways for improvement are mentioned. Proposed information-theoretic models of DNA-based storage systems are analyzed, and their limitation highlighted. In conclusion, main obstacles to practical implementation of DNA-based storage systems are formulated, which can be potentially overcome using information-theoretic methods considered in this overview.
引言:目前,我们目睹了人类产生的信息量的爆炸性增长。这就提出了其有效存储和处理的新的基本问题。常用的磁性、光学和半导体信息存储设备具有与小的信息密度和有限的耐久性有关的几个缺点。解决这些问题的一种有前途的新方法是基于DNA的数据存储。目的:综述现代基于DNA的存储系统及其相关的信息理论问题。结果:综述了基于DNA的存储系统的现状。分析了它们中出现的错误类型以及相应的纠错码。显示了这些代码的缺点,并提到了可能的改进途径。分析了所提出的基于DNA的存储系统的信息论模型,并强调了它们的局限性。总之,列出了实际实现基于DNA的存储系统的主要障碍,使用本综述中考虑的信息论方法可以潜在地克服这些障碍。
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引用次数: 0
Coding and robustness of signal processing in streaming recurrent neural networks 流递归神经网络中信号处理的编码与鲁棒性
Q3 Mathematics Pub Date : 2021-06-29 DOI: 10.31799/1684-8853-2021-3-9-18
V. Osipov, Viktor Nikiforov
Introduction: When substantiating promising architectures of streaming recurrent neural networks, it becomes necessary to assess their stability in processing various input signals. For this, stability diagrams are constructed containing the results of simulation for each of the nodes of these diagrams. Such an estimation can be time-consuming and computationally intensive, especially when analyzing large neural networks. Purpose: Search for methods of quick construction of such diagrams and assessing the stability of streaming recurrent neural networks. Results: Analysis of the features of the stability diagrams under study showed that the nodes of the diagrams are grouped into continuous zones with the same ratio characteristics of the input signal processing defects. With this in mind, the article proposes a method for constructing these diagrams based on bypassing the boundaries of their zones. With this approach, you do not have to perform simulation for the interior nodes of each zone. The simulation should be performed only for the nodes adjacent to zone boundaries. Due to this, the number of nodes for which you need to perform simulation sessions is reduced by an order of magnitude. The influence of the input signal coding types on the streaming recurrent neural network stability has been investigated. It is shown that the representation of input signals in the form of sequences of single pulses with intersecting elements can provide greater stability as compared to pulses without any intersection.
引言:在证明流式递归神经网络有前景的架构时,有必要评估其在处理各种输入信号时的稳定性。为此,构建了稳定性图,其中包含这些图中每个节点的模拟结果。这种估计可能耗时且计算密集,尤其是在分析大型神经网络时。目的:寻找快速构建此类图并评估流式递归神经网络稳定性的方法。结果:对所研究的稳定性图的特征分析表明,图的节点被分组为连续区域,具有相同的输入信号处理缺陷比率特征。考虑到这一点,本文提出了一种基于绕过其区域边界来构建这些图的方法。使用这种方法,不必对每个分区的内部节点执行模拟。应仅对分区边界附近的节点执行模拟。因此,需要执行模拟会话的节点数量会减少一个数量级。研究了输入信号编码类型对流递归神经网络稳定性的影响。与没有任何交叉的脉冲相比,以具有交叉元素的单个脉冲序列形式的输入信号的表示可以提供更大的稳定性。
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引用次数: 0
Interpretation of a trained neural network based on genetic algorithms 基于遗传算法的训练神经网络的解释
Q3 Mathematics Pub Date : 2020-12-15 DOI: 10.31799/1684-8853-2020-6-12-20
V. Pimenov, I. Pimenov
Introduction: Artificial intelligence development strategy involves the use of deep machine learning algorithms in order to solve various problems. Neural network models trained on specific data sets are difficult to interpret, which is due to the “black box” approach when knowledge is formed as a set of interneuronal connection weights. Purpose: Development of a discrete knowledge model which explicitly represents information processing patterns encoded by connections between neurons. Methods: Adaptive quantization of a feature space using a genetic algorithm, and construction of a discrete model for a multidimensional OLAP cube with binary measures. Results: A genetic algorithm extracts a discrete knowledge carrier from a trained neural network. An individual's chromosome encodes a combination of values of all quantization levels for the measurable object properties. The head gene group defines the feature space structure, while the other genes are responsible for setting up the quantization of a multidimensional space, where each gene is responsible for one quantization threshold for a given variable. A discrete model of a multidimensional OLAP cube with binary measures explicitly represents the relationships between combinations of object feature values and classes. Practical relevance: For neural network prediction models based on a training sample, genetic algorithms make it possible to find the effective value of the feature space volume for the combinations of input feature values not represented in the training sample whose volume is usually limited. The proposed discrete model builds unique images of each class based on rectangular maps which use a mesh structure of gradations. The maps reflect the most significant integral indicators of classes that determine the location and size of a class in a multidimensional space. Based on a convolution of the constructed class images, a complete system of production decision rules is recorded for the preset feature gradations.
简介:人工智能的发展策略涉及到使用深度机器学习算法来解决各种问题。在特定数据集上训练的神经网络模型很难解释,这是由于当知识被形成为一组神经元间连接权重时的“黑箱”方法。目的:开发一种离散知识模型,该模型明确表示由神经元之间的连接编码的信息处理模式。方法:利用遗传算法对特征空间进行自适应量化,并对具有二值测度的多维OLAP多维数据集构建离散模型。结果:遗传算法从训练好的神经网络中提取离散的知识载体。个体的染色体编码了可测量物体属性的所有量化水平值的组合。头部基因组定义特征空间结构,其他基因负责建立多维空间的量化,其中每个基因负责给定变量的一个量化阈值。具有二元度量的多维OLAP多维数据集的离散模型显式地表示对象特征值和类的组合之间的关系。实际意义:对于基于训练样本的神经网络预测模型,遗传算法可以为体积通常有限的训练样本中未表示的输入特征值的组合找到特征空间体积的有效值。所提出的离散模型基于矩形地图构建每个类别的独特图像,矩形地图使用渐变网格结构。这些地图反映了类的最重要的整体指标,这些指标决定了类在多维空间中的位置和规模。基于构造的类图像的卷积,记录了一个完整的生产决策规则系统,用于预设的特征层次。
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引用次数: 1
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