Efficient Reduction Algorithm Research Articles

Implementation of entropically secure encryption: Securing personal health data

AbstractEntropically secure encryption (ESE) offers unconditional security with shorter keys compared to the One‐Time Pad. Here, the first implementation of ESE for bulk encryption is presented. The main computational bottleneck for bulk ESE is a multiplication in a very large finite field. This involves multiplication of polynomials followed by modular reduction. A polynomial multiplication is implemented based on the gf2x library, with modifications that avoid inputs of vastly different length, thus improving speed. Additionally, a recently proposed efficient reduction algorithm that works for any polynomial degree is implemented. Two use cases are investigated: x‐ray images of patients and human genome data. Entropy estimation is conducted using compression methods whose results determine the key lengths required for ESE. The running times for all steps of the encryption are reported. The potential of ESE to be used in conjunction with quantum key distribution (QKD), in order to achieve full information‐theoretic security of QKD‐protected links for these use cases is discussed.

Wred: Workload Reduction for Scalable Index Tuning

Modern database systems offer index-tuning advisors that automatically identify a set of indexes to improve workload performance. Advisors leverage the optimizer's what-if API to optimize a query for a hypothetical index configuration. Because what-if calls constitute a major bottleneck of index tuning, existing techniques, such as workload compression, help reduce the number of what-if calls to speed up tuning. Unfortunately, even with small workloads and few what-if calls, tuning can still take hours due to the complexity of the queries (e.g., the number of joins, filters, group-by and order-by clauses), which increases their optimization time. This paper introduces workload reduction, a new complementary technique aimed at expediting index tuning by decreasing individual what-if call time without significantly affecting the quality of index tuning. We present an efficient workload reduction algorithm, called Wred, which rewrites each query in the original workload to eliminate column and table expressions unlikely to benefit from indexes, thereby accelerating what-if calls. We study its complexity and ability to maintain high index quality. We perform an extensive evaluation over industry benchmarks and real-world customer workloads, which shows that Wred results in a 3x median speedup in tuning efficiency over an industrial-strength state-of-the-art index advisor, with only a 3.7% median loss in improvement---where improvement is the total workload cost as estimated by the query optimizer---and results in up to 24.7x speedup with 1.8% improvement loss. Furthermore, combining Wred and Isum (a state-of-the-art workload compression technique for index tuning) results in higher speedups than either of the two techniques alone, with 10.5x median speedup and 5% median improvement loss.

Optimizing Storage and Computational Efficiency: An Efficient Algorithm for Whole Slide Image Size Reduction

ObjectiveTo efficiently store, transfer, and analyze whole slide imaging (WSI), we developed an image-processing algorithm to remove the unneeded background in a WSI and assemble tissue-containing parts into smaller WSIs without any change in tissue area image resolution. Patients and MethodsWe used histology slides of nondysplastic Barrett esophagus, low-grade dysplasia, and high-grade dysplasia, which were digitized using Aperio AT2 Scanner from January 1992 to September 2020. The algorithm involved converting color images to grayscale images, binarizing images by assigning zero to the background and 1 to the foreground, filling the holes and dilating the foreground masks, and extracting connected components. Using the coordinates of each component, the vertices of the smallest surrounding bounding box were calculated, and tissue-containing parts were cropped from the original slide. The smallest possible rectangle that encloses all bounding boxes containing tissue was found using the rectangle-packer package. ResultsThe algorithm resulted in a mean reduction of 7.11×. The performance of a previously developed deep learning model for the detection of Barrett esophagus dysplasia grade on the size-reduced WSIs was comparable with that on the original WSIs. ConclusionOur algorithm for WSI size reduction can assist researchers in storing, transferring, and analyzing WSIs while optimally using them in their workflow.

Quantum dimensionality reduction by linear discriminant analysis

The dimensionality reduction is generally used as the data preprocessing stage of many machine learning tasks and has become an essential branch of information processing. Due to the exponential growth of data, how constructing reasonable and efficient dimensionality reduction algorithms has been an open challenge recently. In this paper, we propose a quantum linear discriminant analysis algorithm for dimensionality reduction. In the proposed algorithm, the idea of quantum solving linear equations is utilized to obtain the shadow principal components and an intermediate state. After that, the special unitary operations are designed to assist in completing the dimensionality reduction. The theoretical analysis shows the proposed algorithm has exponential acceleration on the number of vectors and a quadratic speedup on the dimensionality of the original data space. Since this algorithm solves the restriction that the between-class scatter matrix must be reversible, it makes the algorithm more applicable. Moreover, instead of getting the quantum state in the projection direction, the algorithm obtains the corresponding quantum state of dimensionality reduction data so that the outputs can be directly applied to other quantum machine learning algorithms. To illustrate it, a simple example, quantum K-nearest Neighbor classification, is provided.

Efficient maximum k -plex computation over large sparse graphs

The k -plex model is a relaxation of the clique model by allowing every vertex to miss up to k neighbors. Designing exact and efficient algorithms for computing a maximum k -plex in a graph has been receiving increasing interest recently. However, the existing algorithms are still inefficient due to having major limitations. We in this paper design a new algorithm kPlexS for the maximum k -plex problem, with three novel contributions. Firstly, we propose a new framework for computing maximum k -plex over large sparse graphs, by iteratively extracting small dense subgraphs from it and then solving each of the extracted dense subgraphs by a branch-and-bound search. Secondly, we propose an efficient reduction algorithm CTCP to reduce the input graph size by exhaustively conducting vertex reduction and edge reduction. CTCP computes a smaller reduced graph and also has a lower time complexity than the existing techniques. Moreover, we iteratively invoke CTCP to reduce the input graph once a vertex has been processed and removed from it. Thirdly, we develop a branch-and-bound algorithm BBMatrix specifically targeting the dense subgraphs that are extracted from the input graph. BBMatrix represents its input graph by an adjacency matrix, and utilizes both first-order (i.e., individual vertices) and second-order information (i.e., pairs of vertices) for reduction and upper bounding. In addition, incremental techniques are proposed to efficiently apply the reduction and upper bounding during the recursion. Extensive empirical studies on large real graphs demonstrate that our algorithm kPlexS outperforms the state-of-the-art algorithms BnB, Maplex, and KpLeX.

Generating Very Large RNS Bases

Residue Number Systems (RNS) are proven to be effective in speeding up computations involving additions and products. For these representations, there exists efficient modular reduction algorithms that can be used in the context of arithmetic over finite fields or modulo large numbers, especially when used in the context of cryptographic engineering. Their independence allows random draws of bases, which also makes it possible to protect against side-channel attacks, or even to detect them using redundancy. These systems are easily scalable, however the existence of large bases for some specific uses remains a difficult question. In this article, we present four techniques to extract RNS bases from specific sets of integers, giving better performance and flexibility to previous works in the litterature. While our techniques do not allow to solve efficiently every possible case, we provide techniques to provably and efficiently find the largest possible available RNS bases in several cases, improving the state-of-the-art on various works of the recent literature.

Automatic model order reduction for systems with frequency-dependent material properties

The frequency response of vibro-acoustic systems can be improved by using various forms of damping materials. Their material properties are typically varying with the excitation frequency and are introduced by one or multiple complex-valued functions. Numerical models of such systems are typically large and require efficient solving strategies. In this contribution, a workflow to reduce the numerical complexity of systems containing frequency-dependent damping materials is presented. The functions modeling the material’s frequency-dependent behavior are approximated in rational form and the resulting transfer function is used in a Krylov based moment matching method. The approximation is performed automatically using the adaptive Antoulas–Anderson algorithm. As robust and efficient automatic reduction algorithms are vital for an efficient design process of vibro-acoustic structures, we also show an adaptive procedure to automatically find a reasonably sized reduced model for a given system under a certain tolerance. The algorithms are tested for two forms of damping materials common in vibro-acoustic systems: poroelastic materials following the Biot theory and a constrained layer damping material.

Scaling High-Quality Pairwise Link-Based Similarity Retrieval on Billion-Edge Graphs

SimRank is an attractive link-based similarity measure used in fertile fields of Web search and sociometry. However, the existing deterministic method by Kusumoto et al. [ 24 ] for retrieving SimRank does not always produce high-quality similarity results, as it fails to accurately obtain diagonal correction matrix D . Moreover, SimRank has a “connectivity trait” problem: increasing the number of paths between a pair of nodes would decrease its similarity score. The best-known remedy, SimRank++ [ 1 ], cannot completely fix this problem, since its score would still be zero if there are no common in-neighbors between two nodes. In this article, we study fast high-quality link-based similarity search on billion-scale graphs. (1) We first devise a “varied- D ” method to accurately compute SimRank in linear memory. We also aggregate duplicate computations, which reduces the time of [ 24 ] from quadratic to linear in the number of iterations. (2) We propose a novel “cosine-based” SimRank model to circumvent the “connectivity trait” problem. (3) To substantially speed up the partial-pairs “cosine-based” SimRank search on large graphs, we devise an efficient dimensionality reduction algorithm, PSR # , with guaranteed accuracy. (4) We give mathematical insights to the semantic difference between SimRank and its variant, and correct an argument in [ 24 ] that “if D is replaced by a scaled identity matrix (1-Ɣ)I, their top-K rankings will not be affected much”. (5) We propose a novel method that can accurately convert from Li et al. SimRank ~{S} to Jeh and Widom’s SimRank S . (6) We propose GSR # , a generalisation of our “cosine-based” SimRank model, to quantify pairwise similarities across two distinct graphs, unlike SimRank that would assess nodes across two graphs as completely dissimilar. Extensive experiments on various datasets demonstrate the superiority of our proposed approaches in terms of high search quality, computational efficiency, accuracy, and scalability on billion-edge graphs.

An Efficient Adaptive and Steep-Convergent Sidelobes Simultaneous Reduction Algorithm for Massive Linear Arrays

Antenna arrays have become an essential part of most wireless communications systems. In this paper, the unwanted sidelobes in the symmetric linear array power pattern are reduced efficiently by utilizing a faster simultaneous sidelobes processing algorithm, which generates nulling sub-beams that are adapted to control and maintain steep convergence toward lower sidelobe levels. The proposed algorithm is performed using adaptive damping and heuristic factors which result in learning curve perturbations during the first few loops of the reduction process and is followed by a very steep convergence profile towards deep sidelobe levels. The numerical results show that, using the proposed adaptive sidelobes simultaneous reduction algorithm, a maximum sidelobe level of −50 dB can be achieved after only 10 iteration loops (especially for very large antenna arrays formed by 256 elements, wherein the processing time is reduced to approximately 25% of that required by the conventional fixed damping factor case). On the other hand, the generated array weights can be applied to practical linear antenna arrays under mutual coupling effects, which have shown very similar results to the radiation pattern of the isotropic antenna elements with very deep sidelobe levels and the same beamwidth.

Incremental Linear Discriminant Analysis Dimensionality Reduction and 3D Dynamic Hierarchical Clustering WSNs

Optimizing the sensor energy is one of the most important concern in Three-Dimensional (3D) Wireless Sensor Networks (WSNs). An improved dynamic hierarchical clustering has been used in previous works that computes optimum clusters count and thus, the total consumption of energy is optimal. However, the computational complexity will be increased due to data dimension, and this leads to increase in delay in network data transmission and reception. For solving the above-mentioned issues, an efficient dimensionality reduction model based on Incremental Linear Discriminant Analysis (ILDA) is proposed for 3D hierarchical clustering WSNs. The major objective of the proposed work is to design an efficient dimensionality reduction and energy efficient clustering algorithm in 3D hierarchical clustering WSNs. This ILDA approach consists of four major steps such as data dimension reduction, distance similarity index introduction, double cluster head technique and node dormancy approach. This protocol differs from normal hierarchical routing protocols in formulating the Cluster Head (CH) selection technique. According to node’s position and residual energy, optimal cluster-head function is generated, and every CH is elected by this formulation. For a 3D spherical structure, under the same network condition, the performance of the proposed ILDA with Improved Dynamic Hierarchical Clustering (IDHC) is compared with Distributed Energy-Efficient Clustering (DEEC), Hybrid Energy Efficient Distributed (HEED) and Stable Election Protocol (SEP) techniques. It is observed that the proposed ILDA based IDHC approach provides better results with respect to Throughput, network residual energy, network lifetime and first node death round.

A size-reduction algorithm for the order scheduling problem with total tardiness minimization

We investigated a variant of the customer order scheduling problem taking into consideration due dates to minimize the total tardiness. Since the problem under study is NP-hard, we propose an efficient size reduction algorithm (SR). We perform an extensive computational experience and compare our proposition with JPO-20 matheuristic, the best existing algorithm for the problem under study. We use the Relative Deviation Index (RDI) and the Success Rate (SRa) as the statistical indicators for the performance measure. We must emphasize that SR presented the lowest average RDI (around 15.5 %), whereas the JPO-20 presented an average RDI approximately three times higher (around 52.5 %). Furthermore, the proposed SR presented a higher average SRa (around 66.9%), whereas the JPO-20 presented a lower average success (around 25.7%). Our proposal used a lower computational effort, resulting in a reduction for the computation times of approximately 22%. The obtained results point to the superiority of the proposed SR in comparison with the JPO-20.

Robust nonlinear aggregation operator for ECG powerline interference reduction

ObjectiveNowadays, the most effective methods for ElectroCardioGraphic (ECG) PowerLine (PL) interference suppression, based on the subtraction operation, require the determination of signal fragments with a low electrical activity of the heart. Any errors in searching for these fragments result in a loss of effectiveness of interference suppression and an increase in signal distortion. This article proposes a method that does not need to determine such signal fragments. MethodsThe robust nonlinear aggregation operator is used for the PL disturbance estimation. This results in an automatic reduction (or elimination) of the influence of the ECG signal fragments with an increased electrical activity of the heart. In other words, the samples with the lowest electrical activity of the heart will be used for the PL interference estimation. ResultsThe method leads to a significant reduction of the ECG signal distortions, unattainable for other methods, leaving the residual noise of the order of single micro-volts, regardless of the PL interference level tackled. The method can be applied using an algorithm that is computationally very efficient, which can help to reduce the total cost of ECG signal processing. The new method proposed is experimentally compared to the traditional ones using signals from the Physikalisch-Technische Bundesanstalt (PTB) diagnostic ECG database. ConclusionThe method proposed is an accurate, robust and computationally efficient algorithm for reduction of PL interference disturbing ECG signals. SignificanceNew prospects emerge for systems processing the ECG signal, it is possible to analyze traces with a more unfavorable signal-to-noise ratio. This applies to monitoring and exercise systems as well as to a special advanced analysis of e.g. cardiac micro-potentials.

An Efficient Fast and Convergence-Controlled Algorithm for Sidelobes Simultaneous Reduction (SSR) and Spatial Filtering

In this paper, an efficient sidelobe levels (SLL) reduction and spatial filtering algorithm is proposed for linear one-dimensional arrays. In this algorithm, the sidelobes are beamspace processed simultaneously based on its orientation symmetry to achieve very deep SLL at much lower processing time compared with recent techniques and is denoted by the sidelobes simultaneous reduction (SSR) algorithm. The beamwidth increase due to SLL reduction is found to be the same as that resulting from the Dolph-Chebyshev window but at considerably lower average SLL at the same interelement spacing distance. The convergence of the proposed SSR algorithm can be controlled to guarantee the achievement of the required SLL with almost steady state behavior. On the other hand, the proposed SSR algorithm has been examined for spatial selective sidelobe filtering and has shown the capability to effectively reduce any angular range of the radiation pattern effectively. In addition, the controlled convergence capability of the proposed SSR algorithm allows it to work at any interelement spacing distance, which ranges from tenths to a few wavelength distances, and still provide very low SLL.

Montgomery-friendly primes and applications to cryptography

This paper deals with Montgomery-friendly primes designed for the modular reduction algorithm of Montgomery. These numbers are scattered in the literature and their properties are partially exploited. We exhibit a large family of Montgomery-friendly primes which give rise to efficient modular reduction algorithms. We develop two main outcomes. The first one is dedicated directly to cryptography, in particular for isogeny-based approaches and more generally to elliptic curves cryptography (ECC). We suggest more appropriate finite fields and curves in terms of complexity for the recommended security levels, for both isogeny-based cryptography and ECC. The second issue is mainly arithmetic (even if its main use is cryptography), and we propose families of alternative RNS bases. We show that, for dedicated architectures with word operators, we can reach, for a same or better complexity, larger RNS bases with Montgomery-friendly pairwise co-primes than the RNS bases generally used in the literature with pseudo-Mersenne numbers.

Non-negative matrix factorization via adaptive sparse graph regularization

Non-negative matrix factorization (NMF), as an efficient and intuitive dimension reduction algorithm, has been successfully applied to clustering tasks. However, there are still two dominating limitations. First, the original NMF only pays attention to the global data structure, ignoring the intrinsic geometry of the original higher-dimensional data. Second, the traditional pairwise distance-based graph construction is sensitive to noise and outliers, and the nearest neighbor graph obtained is not optimal. As a result, the clustering performance will be reduced. To solve the aforementioned problems and increase the cluster accuracy, a non-negative matrix factorization via adaptive sparse graph (NMF_ASGR) is proposed in this paper. More precisely, this paper assembles the sparse representation and manifold learning into a framework to get the l1 sparse robust graph. The l1 sparse robust graph not only can adaptively discover the potential manifold structure of the data, but also has strong robustness to noise and outliers, which makes the structure of the graph can be learned automatically in the process of matrix decomposition. Moreover, an adaptive sparse graph is learned to batter regularize the NMF. Finally, the effectiveness and superiority of the proposed algorithm are illustrated by lots of image clustering experiments.

Efficient Data Reduction at the Edge of Industrial Internet of Things for PMSM Bearing Fault Diagnosis

An efficient data reduction algorithm is designed and implemented on an industrial Internet of Things (IIoT) node for permanent magnet synchronous motor (PMSM) bearing fault diagnosis in variable speed conditions. Leakage flux and vibration signals are, respectively, acquired by a magnetic sensor and an accelerometer on the IIoT node in a noninvasive manner. These two signals are processed and mixed on the IIoT and transmitted to a server. The received signal is separated, the cumulative rotation angle is calculated, and the vibration signal is resampled for bearing fault identification. The proposed method can reduce about 95% of the transmission data while maintaining sufficient precision in bearing fault diagnosis in comparison to a traditional method. The proposed method based on edge computing reduces the power consumption, and hence it is suitable to use on a battery-supplied IIoT node for remote PMSM condition monitoring and fault diagnosis.

A Fast Attribute Reduction Algorithm Based on a Positive Region Sort Ascending Decision Table

Attribute reduction is one of the challenging problems in rough set theory. To accomplish an efficient reduction algorithm, this paper analyzes the shortcomings of the traditional methods based on attribute significance, and suggests a novel reduction way where the traditional attribute significance calculation is replaced by a special core attribute calculation. A decision table called the positive region sort ascending decision table (PR-SADT) is defined to optimize some key steps of the novel reduction method, including the special core attribute calculation, positive region calculation, etc. On this basis, a fast reduction algorithm is presented to obtain a complete positive region reduct. Experimental tests demonstrate that the novel reduction algorithm achieves obviously high computational efficiency.

Improved general attribute reduction algorithms

Attribute reduction is a critical issue in rough sets theory. In recent years, there are many kinds of attribute reduction proposed, such as positive region preservation reduction, generalized decision preservation reduction, distribution preservation reduction, maximum distribution preservation reduction, and relative discernibility relation preservation reduction. General reduction approaches to obtaining various types of reducts also have been explored, but they are computationally time-consuming in the condition of large-scale data processing. In this study, we focus on the efficient general reduction algorithm to obtain five typical reducts mentioned above. At first, we introduce a concept called granularity space to establish a unified representation of five typical reducts. Based on the unified representation, we construct two quick general reduction algorithms by extending the positive region approximation to the granularity space. Then, we conduct a series of comparisons with existing reduction algorithms in aspects of theoretical analysis and experiments to evaluate the performance of the proposed algorithms. The results of analysis and experiments indicate that the proposed algorithms are effective and efficient.

A Parallel Grid Optimization of SVM Hyperparameter for Big Data Classification using Spark Radoop

The big data phenomenon is currently a challenge to the process of relevant knowledge extraction using classical machine learning technique. This is due to the need for efficient data reduction and new fast-distributed machine learning algorithms for such process on big data. The extensive application of SVM demands efficient methods of constructing the classifier to be suitable for big data and high classification capability. In reality, the efficiency of SVM relies on the efficient derivation of the optimal feature subset and the algorithmic parameters. The grid search optimization method usually presents global optima and high learning accuracy compared to PSO and GA, but its larger computation takes much time. The grid search is more attractive because it can simultaneously take part in the learning of every SVM since they do not rely on each other. A novel parallel implementation of grid optimization using Spark Radoop is proposed in this paper to minimize the great computation load and make it suitable for big data processing issues. A major contribution of this study is a significant reduction in the algorithmic computational time when compared to the serial version of gridSVM, as well as the high classification accuracy compared to the other parallel optimization techniques.

Feature selection using neighborhood entropy-based uncertainty measures for gene expression data classification

Gene expression data classification is an important technology for cancer diagnosis in bioinformatics and has been widely researched. Due to the large number of genes and the small sample size in gene expression data, feature selection based on neighborhood rough sets is a key step for improving the performance of gene expression data classification. However, some quantitative measures of feature sets may be nonmonotonic in neighborhood rough sets, and many feature selection methods based on evaluation functions yield high cardinality and low predictive accuracy. Therefore, investigating effective and efficient heuristic reduction algorithms is necessary. In this paper, a novel feature selection method based on neighborhood rough sets using neighborhood entropy-based uncertainty measures for cancer classification from gene expression data is proposed. First, some neighborhood entropy-based uncertainty measures are investigated for handling the uncertainty and noise of neighborhood decision systems. Then, to fully reflect the decision-making ability of attributes, the neighborhood credibility and neighborhood coverage degrees are defined and introduced into decision neighborhood entropy and mutual information, which are proven to be nonmonotonic. Moreover, some of the properties and relationships among these measures are derived, which is helpful for understanding the essence of the knowledge content and the uncertainty of neighborhood decision systems. Finally, the Fisher score method is employed to preliminarily eliminate irrelevant genes to significantly reduce complexity, and a heuristic feature selection algorithm with low computational complexity is presented to improve the performance of cancer classification using gene expression data. Experiments on ten gene expression datasets show that our proposed algorithm is indeed efficient and outperforms other related methods in terms of the number of selected genes and the classification accuracy, especially as the size of the genes increases.