Rank Vector Research Articles

Higher rank Clifford indices of curves on a K3 surface

Let (X, H) be a polarized K3 surface with mathrm {Pic}(X) = mathbb {Z}H, and let Cin |H| be a smooth curve of genus g. We give an upper bound on the dimension of global sections of a semistable vector bundle on C. This allows us to compute the higher rank Clifford indices of C with high genus. In particular, when gge r^2ge 4, the rank r Clifford index of C can be computed by the restriction of Lazarsfeld–Mukai bundles on X corresponding to line bundles on the curve C. This is a generalization of the result by Green and Lazarsfeld for curves on K3 surfaces to higher rank vector bundles. We also apply the same method to the projective plane and show that the rank r Clifford index of a degree d(ge 5) smooth plane curve is d-4, which is the same as the Clifford index of the curve.

Ranking cities based on their smartness level using MADM methods

Urbanization and its consequent problems are urging cities to become smarter. Developing smart cities calls for a suitable while comprehensive assessment framework to assist city planners and decision-makers to suggest future directions for cities on how to become smarter by evaluating the smartness of cities. In this regard, this study follows two primary purposes. First, we investigate the concept of “smart city” and its pillars. Second, we develop a smartness assessment framework by considering both subjective and objective criteria and employing six effective multi-attribute decision making (MADM) methods. A linear assignment model is formulated to find an aggregated ranking vector using the ranking vectors obtained from these MADM methods. Then, as a case study, five out of the most important cities in Iran are compared and evaluated by adopting the proposed framework. Furthermore, different scenarios are introduced to investigate the sensitivity of results to the distribution of the importance weights amongst criteria. The results demonstrate the significance of the governmental, economic, and environmental indicators in evaluating the smartness of cities. Moreover, Tehran, the capital city of Iran, obtains the best ranking in all the methods and weighting scenarios, while Tabriz has the worst ranking among the cities under study.

Forecasting electric power consumption of technocenosis objects on the basis of values from transformed vector rank distribution

The article examines a technique for predicting the electric power consumption of technocenosis objects on the basis of the values of the transformed vector rank distribution. This technique includes the following stages: preparing data on electric power consumption, calculating an additional resource for technocenosis objects, forming transformed rank distribution and forecasting its values. The theoretical basis of the methodology was formed by the tenets of the theory of vector rank analysis, the methodology of functional rank analysis and the theory of mathematical statistics, as well as the concepts “technocenosis”, “MS-cenosis” and “bifurcation”. Its distinctive feature is the possibility to take into account the external control effect of a higher power system-MC-cenosis by adding or deducting an additional resource calculated using the system of transformed vector rank distributions. The additional resource is the difference between the values of the technocenosis located on the vector rank distribution of the higher MC-cenosis and the lower permissible value of the lower boundary of permissible values. The presented technique can be implemented in software and hardware complexes and situational centers for electric power consumption control in the area, energy system, transport network complex, large infrastructures and enterprises. The results will significantly supplement the methods of resource management for large infrastructure and energy facilities and form a resource consumption plan individually for each object.

The predictive power of popular sports ranking methods in the NFL, NBA, and NHL

Ideally, a ranking method for a sports tournament will be not only fair and comprehensive, but it will also possess strong predictive power. In a recent article, the $$(1, \alpha )$$ method was proposed as being fair and comprehensive in comparison with five other popular sports ranking methods. In this study, we will compare the predictive power of the $$(1, \alpha )$$ method against five popular sports ranking methods (Win-loss, Massey, Colley, Markov, and Elo) for the NFL, NBA, and NHL in the last two decades. We use regular season results to obtain the ranking vector, and then evaluate said ranking vector on its ability to predict playoff results using both a frequency count and McNemar’s test of statistical significance.

Entropy information‐based heterogeneous deep selective fused features using deep convolutional neural network for sketch recognition

An effective feature representation can boost recognition tasks in the sketch domain. Due to an abstract and diverse structure of the sketch relatively with a natural image, it is complex to generate a discriminative features representation for sketch recognition. Accordingly, this article presents a novel scheme for sketch recognition. It generates a discriminative features representation as a result of integrating asymmetry essential information from deep features. This information is kept as an original feature-vector space for making a final decision. Specifically, five different well-known pre-trained deep convolutional neural networks (DCNNs), namely, AlexNet, VGGNet-19, Inception V3, Xception, and InceptionResNetV2 are fine-tuned and utilised for feature extraction. First, the high-level deep layers of the networks were used to get multi-features hierarchy from sketch images. Second, an entropy-based neighbourhood component analysis was employed to optimise the fusion of features in order of rank from multiple different layers of various deep networks. Finally, the ranked features vector space was fed into the support vector machine (SVM) classifier for sketch classification outcomes. The performance of the proposed scheme is evaluated on two different sketch datasets such as TU-Berlin and Sketchy for classification and retrieval tasks. Experimental outcomes demonstrate that the proposed scheme brings substantial improvement over human recognition accuracy and other state-of-the-art algorithms.

A Combination of Query Expansion Ranking and GA-SVM for Improving Indonesian Sentiment Classification Performance

The sentiment classification method is a research field that is proliferating in Indonesia since it is fast in extracting public opinion and provides essential and valuable information for stakeholders. Of the best-performing sentiment classification approaches, machine learning is one of them that has excellent performance. However, the method has several problems, such as noisy features and high dimensionality of features that significantly affect the sentiment classification performance. Therefore, to overcome the problems, this paper presents a novel feature selection using a combination of Query Expansion Ranking (QER) and Genetic Algorithm-Support Vector Machine (GA-SVM) for improving sentiment classification performance. Based on the experimental results, the proposed method could significantly improve sentiment classification performance, outperform all state-of-the-art algorithms, and decrease computational time. The method achieved the best performance in average precision, recall, and f-measure with the value of 96.78%, 96.76%, and 96.75%, respectively.

Modeling and Identification of Low Rank Vector Processes

Abstract We study modeling and identification of processes with a spectral density matrix of low rank. Equivalently, we consider processes having an innovation of reduced dimension for which Prediction Error Methods (PEM) algorithms are not directly applicable. We show that these processes admit a special feedback structure with a deterministic feedback channel which can be used to split the identification in two steps, one of which can be based on standard algorithms while the other is based on a deterministic least squares fit.

Improved Smartphone-Based Indoor Localization System Using Lightweight Fingerprinting and Inertial Sensors

The existing radio frequency-based positioning approaches widely used for indoor localization-based service (LBS) are fingerprinting and trilateration and their integration with the inertial sensors-based dead reckoning system. However, these localization methods have practical limits and challenges due to unstable signal strength, the cost of offline workload, computational complexity, terminal device heterogeneity, and accumulated sensor error. We propose a smartphone-based indoor localization system using weighted Spearman’s foot-rule (WSF)-based probabilistic fingerprinting for reliable smartphone localization service. This localization system adopts a real-time fingerprinting position error estimation approach realizing an adaptive extended Kalman filter (AEKF) to integrate the proposed fingerprinting localization with inertial measurement unit (IMU)-based localization. This proposed WSF-based smartphone localization uses a Gaussian process regression (GPR)-based signal prediction module to deal with fingerprinting localization’s offline workload. Furthermore, the smartphone localization system’s expected high computational complexity is controlled by employing a data-clustering module. The proposed WSF also employs a rank vector that helps mitigate the effect of terminal device heterogeneity. The proposed localization system is experimentally evaluated at two different representative indoor environments. Experimental results obtained by real field deployment show that the mean error is 2.06 m in an elongated hallway corridor and 3.47 m in the crowded and well-furnished wide area.

A generalized permutation entropy for noisy dynamics and random processes.

Permutation entropy measures the complexity of a deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or simply permutations. Reasons for the increasing popularity of this entropy in time series analysis include that (i) it converges to the Kolmogorov-Sinai entropy of the underlying dynamics in the limit of ever longer permutations and (ii) its computation dispenses with generating and ad hoc partitions. However, permutation entropy diverges when the number of allowed permutations grows super-exponentially with their length, as happens when time series are output by dynamical systems with observational or dynamical noise or purely random processes. In this paper, we propose a generalized permutation entropy, belonging to the class of group entropies, that is finite in that situation, which is actually the one found in practice. The theoretical results are illustrated numerically by random processes with short- and long-term dependencies, as well as by noisy deterministic signals.

Insights into protease sequence similarities by comparing substrate sequences and phylogenetic dynamics.

Based on substrate sequences, we proposed a novel method for comparing sequence similarities among 68 proteases compiled from the MEROPS online database. The rank vector was defined based on the frequencies of amino acids at each site of the substrate, aiming to eliminate the different order variances of magnitude between proteases. Without any assumption on homology, a protease specificity tree is constructed with a striking clustering of proteases from different evolutionary origins and catalytic types. Compared with other methods, almost all the homologous proteases are clustered in small branches in our phylogenetic tree, and the proteases belonging to the same catalytic type are also clustered together, which may reflect the genetic relationship among the proteases. Meanwhile, certain proteases clustered together may play a similar role in key pathways categorized using the Kyoto Encyclopedia of Genes and Genomes (KEGG) database. Consequently, this method can provide new insights into the shared similarities among proteases. This may inspire the design and development of targeted drugs that can specifically regulate protease activity.

Machine learning based quantitative texture analysis of CT images for diagnosis of renal lesions

Renal cancer is among the prominent causes of an upsurge in death rates around the globe that can be minimized by premature diagnosis. Computed tomography (CT) is the first-line imaging technique employed for analysis of renal lesions in clinical practice. Moreover, it is difficult for the radiologist to analyze a large number of medical images which may lead to misclassification of renal lesions that eventually results in cancer evolution or needless chemotherapy. Thus, there is a requirement to propose machine learning based techniques for classification of renal tissue based on their texture, and these techniques can be considered as a promising second opinion for the clinicians to minimize false-negative results. The present study aims to estimate the diagnosis performance of machine-learning based quantifiable texture examination of CT images to distinguish renal lesions. Texture analysis is performed to quantify the renal parenchyma tissues by employing different texture models, and the paper suggests a feature vector for the categorization of benign and malignant renal lesions based on their texture analysis. Further, dimensionality reduction is performed to recognize the discriminative features using distinct statistical, similarity and information knowledge-based techniques. The effectiveness of the resultant ranked feature vector is evaluated by using a Support vector machine (SVM), naive Bayes, Sequential minimal optimization (SMO), random forest, and K nearest neighbour (KNN) classifiers. The classification accuracy equivalent to 84% is observed by KNN with 5-fold cross-validation. Additionally, the practical implications, generalizability issues along with certain open challenges are highlighted that may open avenues for further research.

Large-Scale Group Decision-Making and Rank Clustering

Large-scale group decision-making (GDM) arises when a large group of decision-makers aims to compare several given options by ranking them or assigning scores to those options, for example, determining a ranking for five finalist papers in a best-paper competition, based on a large number of votes submitted by scholars. We study two classes of GDM problems where the submitted votes as well as the final decisions are in the form of ranking (respectively, score) vectors, denoted by PR (respectively, PS). Because a group of decision-makers usually consists of clusters (subgroups) that are essentially different in how they evaluate options, identifying the clusters and their centroids (representative ranking/score vectors) is necessary. We show the single-cluster cases of PR and PS are solvable in polynomial time. We present a general framework for deriving sufficient conditions on the number of decision-makers who propose a ranking/score vector to ensure their proposal is selected as the final decision. We prove that if a 'weak majority' (i.e., at least half) of the decision-makers vote for a ranking vector, and they are in 'extreme disagreement' (i.e., propose the most dissimilar ranking vectors) with the rest of the decision-makers, their proposal is an optimal decision of the group. Inconsistent with intuition, we show that ensuring optimality of a ranking vector requires fewer votes if the decision-makers are in extreme disagreement. Additionally, ensuring optimality of a score vector requires more votes than a ranking vector. We prove the optimal value of the classical k-means clustering problem is a lower bound that is within 50% of that of PR and PS. Interestingly, we establish the tightness of this worst-case gap for PR and PS with any number of clusters. We demonstrate the generalizability of this worst-case gap beyond PR and PS. We prove PR and PS are NP-hard, using a reduction from the hypercube clustering problem. Consequently, we present heuristic algorithms for finding good solutions for PR and PS in a reasonable amount of time. Our heuristic algorithms perform two major steps at each iteration: an assignment step that assigns vectors to clusters and an update step that determines the centroids of clusters. We propose six heuristic variations that use different assignment and update procedures, and show each iteration of these heuristic algorithms is polynomial. According to our numerical experiments, a heuristic variation that determines the optimal centroids using our proposed polynomial procedures demonstrates a remarkable performance and outperforms the other five variations.

Modeling of false information on microblog with block matching and fuzzy neural network

The detection method of microblog false information has been constructed based on block matching and fuzzy neural network to improve the detection accuracy of microblog false information effectively. With this method, we can calculate the rank distance and sample entropy of microblog data according to the evaluation word rank vector of microblog false information, carry out the block matching of false information in fuzzy data set and input the characteristic quantity of microblog false information extracted into the fuzzy neural network classifier for data classification and recognition. So that it has achieved the optimized detection of false information and improved the judgment ability of false information. Finally, the key factors that affect the algorithm are deeply studied through simulation experiments according to the real data of Sina microblog, and the performance state between the proposed algorithm and Fuzzy C-means and Spectral Analysis algorithms is compared and analyzed correspondingly. The results show that the algorithm has good adaptability.

A bipartite matching-based feature selection for multi-label learning

Many real-world data have multiple class labels known as multi-label data, where the labels are correlated with each other, and as such, they are not independent. Since these data are usually high-dimensional, and the current multi-label feature selection methods have not been precise enough, then a new feature selection method is necessary. In this paper, for the first time, we have modeled the problem of multi-label feature selection to a bipartite graph matching process. The proposed method constructs a bipartite graph of features (as the left vertices) and labels (as the right vertices), called Feature-Label Graph (FLG), where each feature is connected to the set of labels, where the weight of the edge between each feature and label is equal to their correlation. Then, the Hungarian algorithm estimates the best matching in FLG. The selected features in each matching are sorted by weighted correlation distance and added to the ranking vector. To select the discriminative features, the proposed method considers both the redundancy of features and the relevancy of each feature to the class labels. The results indicate the superiority of the proposed method against the other methods in classification measures.

MFS-MCDM: Multi-label feature selection using multi-criteria decision making

In this paper, for the first time, a feature selection procedure is modeled as a multi-criteria decision making (MCDM) process. This method is applied to a multi-label data and we have used the TOPSIS (Technique of Order Preference by Similarity to Ideal Solution) method as a famous MCDM algorithm to evaluate the features based on their relationship with multiple labels as different criteria. Our proposed method, Multi-label Feature Selection using Multi-Criteria Decision Making (MFS-MCDM) which treated the multi-label feature selection as an information fusion process, first obtains a decision matrix using the ridge regression algorithm and then calculates the weight of each column of this matrix based on the entropy of each label. Then, the TOPSIS approach is used to assign a score to each feature based on the weighted decision matrix. Finally, a rank vector for the features is generated as output which the user can select a desired number of features. The superiority of the proposed method is shown in experimental results comparing to other similar methods in terms of all evaluation metrics.

Learning sequential and general interests via a joint neural model for session-based recommendation

Session-based recommendation is to predict the next action of a user based on his current behavior session. Recent studies have focused on designing recurrent neural networks to capture representation of users sequential behaviors from a large number of anonymous sessions. Although these neural models have greatly improved recommendation performance compared with traditional approaches, they have overemphasized the sequential information of sessions, that is, the order of items in each browsing session. We argue that besides the order of items, the set of items in each session can also reflect the general interests of current session and can also be exploited to augment recommendations. To this end, this paper proposes a joint neural model, called SGINM, for jointly learning sequential and general interests of each session for session-based recommendation. In SGINM, we design an attentive recurrent neural network which not only captures self-adaptive weighed representation of each subsequence in a session but also learns a global representation for the whole session. Furthermore, the SGINM adopts a multi-layer neural network with residual connections to learn the general interests of each session. The SGINM uses a softmax layer to jointly decode the two types of interests and output a ranking vector of recommended items for each new session. The proposed model has been extensively experimented with the benchmark datasets from the RecSys Challenge 2015 and CIKM Cup 2016. Compared with the state-of-the-art models, the proposed SGINM achieves better recommendation performance in terms of higher predicative accuracy and mean reciprocal rank in almost all experiment cases.

An Attention Mechanism Based Algorithm of Identifying Vulnerable Spots of the Internet Data Center Power Systems

With the rapid development of Mobile Internet and Big Data in recent years, the demand for data centers is increasing. The number of super large data centers (more than 1000 counters) has increased. This paper focus on the distribution system, who is responsible for providing a continuous, stable and uninterrupted power supply for the data center. In the event of a large-scale power outage, all business in the data center will be interrupted. Therefore, identifying which electrical equipment in the data center paly the key role in a large-scale power outage is extremely important. Considering the computational complexity of the algorithm, the validity of the vulnerable nodes, the intelligence of the algorithm, this paper proposes a two-layer fragile node identification method based on attention mechanism. The algorithm selects the topology structure and electrical parameters of the data center power distribution system, and considers the flow load of the nodes around each electrical device to form an expression vector. After the vulnerability ranking of the candidate node expression vectors, the k most vulnerable nodes are selected. The outline of the two-layer node identification method is as follows, the first layer calculates an alternative node sequence through a variety of graph-based fragile node identification methods, and the second layer re-calibrates the expression vector of each candidate node based on the attention mechanism and then sorts all candidate nodes. Through the simulation test of a real data center power distribution system, we can see that the proposed algorithm in this paper identifies the effectiveness of the vulnerable nodes in the data center power distribution system.

An Integration Framework on Cloud for Cyber-Physical-Social Systems Big Data

A tremendous challenge in the development of Cyber-Physical-Social Systems (CPSS) is to integrate the growing volume and wide variety of data generated from multiple sources. To address the challenge, this paper presents an integration framework on cloud consisting of five functionally complementary processes, namely data representation, dimensionality reduction, relation establishment, data rank and data retrieval. The unstructured, semi-structured and structured data in the cyber, physical and social space are first represented as low-order data tensors, and then transformed to a three-order feature tensor for relation establishment. A similarity-based multi-linear data rank approach is proposed to measure the importance of the CPSS big data, and an incremental method is explored to rapidly and accurately update the rank vector. This paper, through a smart home case study, illustrates a practical application of the proposed integration framework, and evaluates the performance of the multi-linear data rank approach as well as the incremental rank update method. The results reveal that the proposed framework is feasible and competitive to integrate the CPSS big data on cloud.

Characterization Of sampling patterns for low-tt-rank tensor retrieval

In this paper, we analyze the fundamental conditions for low-rank tensor completion given the separation or tensor-train (TT) rank, i.e., ranks of TT unfoldings. We exploit the algebraic structure of the TT decomposition to obtain the deterministic necessary and sufficient conditions on the locations of the samples to ensure finite completability. Specifically, we propose an algebraic geometric analysis on the TT manifold that can incorporate the whole rank vector simultaneously in contrast to the existing approach based on the Grassmannian manifold that can only incorporate one rank component. Our proposed technique characterizes the algebraic independence of a set of polynomials defined based on the sampling pattern and the TT decomposition, which is instrumental to obtaining the deterministic condition on the sampling pattern for finite completability. In addition, based on the proposed analysis, assuming that the entries of the tensor are sampled independently with probability p, we derive a lower bound on the sampling probability p, or equivalently, the number of sampled entries that ensures finite completability with high probability. Moreover, we also provide the deterministic and probabilistic conditions for unique completability.

E-LEARNING EDUCATION SYSTEMS EFFICIENCY RATING MODEL

E-learning support system is a mandatory attribute of the modern educational process. What criteria laid down in its development depends largely on the effectiveness of further applications of the entire system. The evaluation of the training effect depends on various factors, each of which is determined by many interrelated criteria. In conditions when there are resource constraints (financial or time), the actual becomes the problem of determining the factors (criteria) that have the most significant impact on the effectiveness of e-learning system. The article offers step-by-step method of constructing a model that allows to represent the original set of criteria of evaluation of the training effect of the use of e-learning system in the form of appropriate level of influence grades. Introduces the concept of configuration vector and weight vector configuration, ranking models and based on them describe the procedure of finding the most substantive relationship between the criteria. Provides formulas to calculate appropriate weighting factors for current connections. An indicator of the importance of communication is the change of vector configuration, ranking models, and quantitative characterization of the dominant relations is defined as the difference between the weight coefficients of the respective vectors of the configuration options ranking of the analyzed models. The obtained results can be applied when developing holarchical models, support systems, e-learning, which allow us to quantitatively justify decisions regarding the choice of appropriate alternatives.