Scaling Vector Research Articles

Phoneme-by-Phoneme Speech Recognition as a Classification of Series on a Set of Sequences of Elements of Complex Objects Using an Improved Trie-Tree

Sequences, including vector sequences, are applicable in any subject domains. Sequences of scalar values or vectors (series) can be produced by higher-order sequences, for example: a series of states, or elements of complex objects. This academic paper is devoted to the application of an improved trie-tree in the classification of series on a set of sequences of elements of complex objects using the dynamic programming method. The implementation areas of dynamic programming have been considered. It has been shown that dynamic programming is adapted to multi-step operations of calculating additive (multiplicative) similarity/difference measures. It is argued that the improved trie-tree is applicable in the problem of classifying a series on a set of sequences of elements of complex objects using such similarity/difference measures. An analysis of hierarchical representations of sets of sequences has been performed. The advantages of the improved trie-tree over traditional representations of other highly branching trees have been described. A formal description of the improved trie-tree has been developed. An explanation has been given to the previously obtained data on a significant speed gain for operations of adding and deleting sequences in the improved trie-tree relative to the use of an array with an index table (24 and 380 times, respectively). The problem of phoneme-by-phoneme recognition of speech commands has been formulated as a problem of classifying series on a set of sequences of elements of complex objects and a method for its solving has been presented. A method for classifying a series on a set of sequences of elements of complex objects using the improved trie-tree is developed. The method has been studied using the example of phoneme-by-phoneme recognition with a hierarchical representation of the dictionary of speech command classes. In this method, recognition of speech commands is executed traversing the improved trie-tree that stores a set of transcriptions of speech commands – sequences of transcription symbols that denote classes of sounds. Numerical studies have shown that classifying a series as sequences of elements of complex objects increases the frequency of correct classification compared to classifying a series on a set of series, and using the improved trie-tree reduces the time spent on classification.

Efficient and effective ensemble broad learning system based on structural diversity

Ensemble Broad Learning Systems (ENBLS) have received considerable attention from researchers and experienced rapid development due to its outstanding performance in handling complex data. A study has revealed that when ENBLS is trained with multiple independent storages, the issue of memory consumption is inevitable. To address this issue, this paper proposes an Ensemble Broad Learning Systems based on structural diversity (EBLSSD). This method effectively reduces the model memory consumption while maintaining superior performance. In EBLSSD, the scaling vectors are trained by constraining the scaling vectors of the current model and those of other existing models. These vectors are used to search for hidden paths of subnetworks within the network, extracting different network structures for integration. By preserving the scaling vectors during the storage process, memory pressure is reduced. EBLSSD introduces diversity from the perspective of network structure, which reduces cooperation between nodes and the risk of model overfitting, thereby enhancing model performance. The feasibility and effectiveness of the proposed algorithm is validated by experimental results on public datasets.

Spatial Functional Data analysis: Irregular spacing and Bernstein polynomials

Spatial Functional Data (SFD) analysis is an emerging statistical framework that combines Functional Data Analysis (FDA) and spatial dependency modeling. Unlike traditional statistical methods, which treat data as scalar values or vectors, SFD considers data as continuous functions, allowing for a more comprehensive understanding of their behavior and variability. This approach is well-suited for analyzing data collected over time, space, or any other continuous domain. SFD has found applications in various fields, including economics, finance, medicine, environmental science, and engineering. This study proposes new functional Gaussian models incorporating spatial dependence structures, focusing on irregularly spaced data and reflecting spatially correlated curves. The model is based on Bernstein polynomial (BP) basis functions and utilizes a Bayesian approach for estimating unknown quantities and parameters. The paper explores the advantages and limitations of the BP model in capturing complex shapes and patterns while ensuring numerical stability. The main contributions of this work include the development of an innovative model designed for SFD using BP, the presence of a random effect to address associations between irregularly spaced observations, and a comprehensive simulation study to evaluate models’ performance under various scenarios. The work also presents one real application of Temperature in Mexico City, showcasing practical illustrations of the proposed model.

Augmenting the diversity of imbalanced datasets via multi-vector stochastic exploration oversampling

The problem of class imbalance is prevalent in many real-world data sets, causing learning models to skew towards the majority class and resulting in biased performance. Data augmentation methods, such as the well-known Synthetic Minority Over-sampling Technique (SMOTE), are commonly employed to address class imbalance by generating synthetic samples. However, the generation mechanism of SMOTE is relatively constrained resulting in insufficient diversity in synthetic samples. To overcome this limitation, this paper expands the classical SMOTE and introduces a novel generalized version, namely Multi-vector Stochastic Exploration Oversampling (MSEO). It broadens the set of mapping synthetic samples, originally formed by the determined direction vectors and scaling vectors through the neighboring samples, to a collection obtained through mappings with random direction vectors and scaling vectors. This allows the generated samples to escape the original linear interpolation region, facilitating a more flexible exploration of the sample space. We extensively evaluated the method on various types of datasets, including artificially generated datasets, multi-class real-world datasets, and the engineering dataset. The results indicate that MSEO exhibits significant advantages in enhancing classification performance and promoting diversity in synthetic samples.

Class-Balanced Deep Learning with Adaptive Vector Scaling Loss for Dementia Stage Detection.

Alzheimer's disease (AD) leads to irreversible cognitive decline, with Mild Cognitive Impairment (MCI) as its prodromal stage. Early detection of AD and related dementia is crucial for timely treatment and slowing disease progression. However, classifying cognitive normal (CN), MCI, and AD subjects using machine learning models faces class imbalance, necessitating the use of balanced accuracy as a suitable metric. To enhance model performance and balanced accuracy, we introduce a novel method called VS-Opt-Net. This approach incorporates the recently developed vector-scaling (VS) loss into a machine learning pipeline named STREAMLINE. Moreover, it employs Bayesian optimization for hyperparameter learning of both the model and loss function. VS-Opt-Net not only amplifies the contribution of minority examples in proportion to the imbalance level but also addresses the challenge of generalization in training deep networks. In our empirical study, we use MRI-based brain regional measurements as features to conduct the CN vs MCI and AD vs MCI binary classifications. We compare the balanced accuracy of our model with other machine learning models and deep neural network loss functions that also employ class-balanced strategies. Our findings demonstrate that after hyperparameter optimization, the deep neural network using the VS loss function substantially improves balanced accuracy. It also surpasses other models in performance on the AD dataset. Moreover, our feature importance analysis highlights VS-Opt-Net's ability to elucidate biomarker differences across dementia stages.

Security design for integrated communication and computation networks through cooperative cognitive radios

AbstractIn this letter, a novel integrated communication and computation framework is proposed through cooperative cognitive radios, which includes a communication primary network (PN) and a computing secondary network. Specifically, two primary communication users intend to exchange their confidential information with the relay assistance of cognitive access point (CAP), meanwhile, multiple sensors share the spectrum of PN to transmit their concurrent sensing data to CAP. The CAP is assumed to be a potential eavesdropper and to ensure the secure communication of primary users (PUs) and computational performance of the CAP, it is proposed to maximize the sum achievable secrecy rate of PUs by jointly designing the transmit precoding, relay beamforming matrix, transmit scaling factors and aggregation beamforming vector, while satisfying the constraint of the computational mean square error of the CAP. A weighted minimum mean square error (WMMSE)‐based block coordinate descent (BCD) algorithm is developed to solve the formulated problem, and simulation results are provided to validate the effectiveness of our proposed schemes.

Designing Learning Media Using Augmented Reality for Engineering Mechanics Course

The development of digital technology for education is continuously conducted to successfully integrate digital technology with people's lives. This study aimed to develop an Augmented Reality learning media application for the Engineering Mechanics course, which is considered challenging by some students. Engineering mechanics, a discipline that analyzes structural analysis in compensating for the loads that work on a particular machine in scalar quantities, motion forces, vectors, and moments that require physical structural forms to analyze them, is considered challenging by some students. The Augmented Reality application was created using the prototyping method, which consists of three steps: 1) listening to the customer, 2) building/ revising mock-up, and 3) customer test-drivers mock-up. The AR-based learning media application includes usage instructions, developer info, learning videos, 3D AR object animation simulations, and exercise and discussion menus, which were tested as expected. The results of the black box testing indicate that the Augmented Reality-based engineering mechanics learning media application ran successfully as expected. However, users suggested improving the navigation speed by streamlining page transitions. The application provides an accessible solution for students as an alternative to traditional distance education, offering anytime, anywhere access to learning materials with longer duration.

Synthesizing Shaped-Beam Cylindrical Conformal Array Considering Mutual Coupling Using Refined Rotation/Phase Optimization

A novel method of synthesizing shaped-beam cylindrical conformal array by rotating the antenna elements and optimizing their excitation phases is presented. Rotation of antennas on curved surface is mathematically described by rotating its vectorial active element pattern (VAEP) in its local coordinate system (LCS). Then the scalar patterns and polarization unit vectors of all the rotated VAEPs are properly transformed and then interpolated at a unified angle sampling grid in a common coordinate system, where they are summed to obtain an approximated array expression. With this expression, element rotations and phases can be optimized using the constriction factor particle swarm optimization (CF-PSO) to synthesize desired shaped-beam pattern with controlled sidelobe level (SLL) and cross-polarization level (XPL). However, since rotations on curved surface introduce considerable variations to the element curvature and mutual coupling (MC), the synthesized array pattern would have considerable errors. A refined strategy is adopted then to improve the synthesis accuracy. The proposed method uses uniform amplitude weighting, thus saving many unequal power dividers. Three typical shaped pattern synthesis examples are provided to show the effectiveness of the proposed method. A cylindrical array prototype with 24 rotated U-slot loaded patch antennas is fabricated and measured for practical validation.

Joint Optimization for Multi-Antenna AF-Relay Aided Over-the-Air Computation

Benefiting from exploiting the waveform superposition property in the multi-access channels, over-the-air computation (AirComp) has emerged as a promising technique to swiftly compute functions of data from a large number of sensors. To enlarge the wireless coverage area, a two-phase multi-antenna amplify-and-forward (AF)-relay aided AirComp system is considered, where all the sensors transmit sensing data during both two phases in a half-duplex AF relay system with direct links. We present efficient designs for optimizing the transmit scalar vectors at the sensors, the AF matrix at the relay, and the aggregation vector at the access point, which aims to minimize the mean-square-error (MSE) subject to the transmit power budgets at the relay and the sensors, respectively. To solve the resultant multiple variables coupled non-convex optimization problem efficiently, we develop an alternating optimization-based algorithm to obtain locally optimal solutions. Specifically, in each iteration, closed-form expressions are derived for each optimizing variable. Finally, the computation distortion improvement of our proposed design over baseline schemes is demonstrated via simulations.

Structure of a finite non-commutative algebra set by a sparse multiplication table

Four-dimensional finite non-commutative associative algebras represent practical interest as algebraic support of post-quantum digital signature algorithms, especially algebras with two sided global unit, set by sparse basis vectors multiplication tables. A new algebra of the latter type, set over the field GF(p), is proposed and its structure is investigated. The studied algebra is described as a set of p2 + p + 1 commutative subalgebras of three different types. All subalgebras intersect strictly in the subset of scalar vectors. Formulas are derived for the number of subalgebras of each type.

Music information visualization and classical composers discovery: an application of network graphs, multidimensional scaling, and support vector machines

This article illustrates different information visualization techniques applied to a database of classical composers and visualizes both the macrocosm of the Common Practice Period and the microcosms of twentieth century classical music. It uses data on personal (composer-to-composer) musical influences to generate and analyze network graphs. Data on style influences and composers ‘ecological’ data are then combined to composer-to-composer musical influences to build a similarity/distance matrix, and a multidimensional scaling analysis is used to locate the relative position of composers on a map while preserving the pairwise distances. Finally, a support-vector machines algorithm is used to generate classification maps. This article falls into the realm of an experiment in music education, not musicology. The ultimate objective is to explore parts of the classical music heritage and stimulate interest in discovering composers. In an age offering either inculcation through lists of prescribed composers and compositions to explore, or music recommendation algorithms that automatically propose works to listen to next, the analysis illustrates an alternative path that might promote the active rather than passive discovery of composers and their music in a less restrictive way than inculcation through prescription.

A Novel Method for Developing Post-quantum Digital Signature Algorithms on Non-commutative Associative Algebras

Introduction: Development of practical post-quantum signature algorithms is a current challenge in the area of cryptography. Recently, several candidates on post-quantum signature schemes, in which the exponentiation operations in a hidden commutative group contained in a non-commutative algebra is used, were proposed. Search for new mechanisms of using a hidden group, while developing signature schemes resistant to quantum attacks, is of significant practical interest. Purpose: Development of a new method for designing post-quantum signature algorithms on finite non-commutative associative algebras. Results: A novel method for developing digital signature algorithms on non-commutative algebras. A new four-dimensional finite non-commutative associative algebra set over the ground field GF(p) have been proposed as algebraic support of the signature algorithms. To provide a higher performance of the algorithm, in the introduced algebra the vector multiplication is defined by a sparse basis vector multiplication table. Study of the algebra structure has shown that it can be represented as a set of commutative subalgebras of three different types, which intersect exactly in the set of scalar vectors. Using the proposed method and introduced algebra, a new post-quantum signature scheme has been designed. The introduced method is characterized in using one of the elements of the signature (e, S) in form of the four-dimensional vector S that is computed as a masked product of two exponentiated elements G and H of a hidden commutative group: S = B-1GnHmC-1, where non-permutable vectors B and C are masking multipliers; the natural numbers n and m are calculated depending on the signed document M and public key. The pair <G, H> composes a minimum generator systems of the hidden group. The signature verification equation has the form R = (Y1SZ1)e(Y2SZ2)e2, where pairwise non-permutable vectors Y1, Z1, Y2, and Z2 are element of the public key and natural number e that is computed depending on the value M and the vector R. Practical relevance: Due to sufficiently small size of public key and signature and high, the developed digital signature scheme represents interest as a practical post-quantum signature algorithm. The introduced method is very attractive to develop a post-quantum digital signature standard.

Emotion Recognition with Capsule Neural Network

For human-machine communication to be as effective as human-to-human communication, research on speech emotion recognition is essential. Among the models and the classifiers used to recognize emotions, neural networks appear to be promising due to the network’s ability to learn and the diversity in configuration. Following the convolutional neural network, a capsule neural network (CapsNet) with inputs and outputs that are not scalar quantities but vectors allows the network to determine the part-whole relationships that are specific 6 for an object. This paper performs speech emotion recognition based on CapsNet. The corpora for speech emotion recognition have been augmented by adding white noise and changing voices. The feature parameters of the recognition system input are mel spectrum images along with the characteristics of the sound source, vocal tract and prosody. For the German emotional corpus EMO-DB, the average accuracy score for 4 emotions, neutral, boredom, anger and happiness, is 99.69%. For Vietnamese emotional corpus BKEmo, this score is 94.23% for 4 emotions, neutral, sadness, anger and happiness. The accuracy score is highest when combining all the above feature parameters, and this score increases significantly when combining mel spectrum images with the features directly related to the fundamental frequency.

Approximation of Complex-Valued Functions by Fractal Functions

Fractal approximants developed through iterated function systems (IFS) prove more versatile than classical approximants. In this paper, we introduce a new class of fractal approximants using the suitable bounded linear operators defined on the space C(I) of continuous functions and concept of $$$\alpha$$$-fractal functions. The convergence of the proposed fractal approximants towards the original continuous function does not need any condition on the scaling factors. The fractal approximants proposed in this paper possess fractality and convergence simultaneously. Without imposing any condition on the scaling vector, we establish the constrained approximation by the proposed fractal approximants. Existence of Schauder basis of fractal polynomials for the space of continuous functions C(I) is investigated. Using the proposed class of fractal approximants, we develop complex fractal approximants for representation of the square integrable complex-valued functions defined on a real compact interval.

Bayesian Effect Selection in Structured Additive Distributional Regression Models

We propose a novel spike and slab prior specification with scaled beta prime marginals for the importance parameters of regression coefficients to allow for general effect selection within the class of structured additive distributional regression. This enables us to model effects on all distributional parameters for arbitrary parametric distributions, and to consider various effect types such as non-linear or spatial effects as well as hierarchical regression structures. Our spike and slab prior relies on a parameter expansion that separates blocks of regression coefficients into overall scalar importance parameters and vectors of standardised coefficients. Hence, we can work with a scalar quantity for effect selection instead of a possibly high-dimensional effect vector, which yields improved shrinkage and sampling performance compared to the classical normal-inverse-gamma prior. We investigate the propriety of the posterior, show that the prior yields desirable shrinkage properties, propose a way of eliciting prior parameters and provide efficient Markov Chain Monte Carlo sampling. Using both simulated and three large-scale data sets, we show that our approach is applicable for data with a potentially large number of covariates, multilevel predictors accounting for hierarchically nested data and non-standard response distributions, such as bivariate normal or zero-inflated Poisson.

Variational Metric Scaling for Metric-Based Meta-Learning

Metric-based meta-learning has attracted a lot of attention due to its effectiveness and efficiency in few-shot learning. Recent studies show that metric scaling plays a crucial role in the performance of metric-based meta-learning algorithms. However, there still lacks a principled method for learning the metric scaling parameter automatically. In this paper, we recast metric-based meta-learning from a Bayesian perspective and develop a variational metric scaling framework for learning a proper metric scaling parameter. Firstly, we propose a stochastic variational method to learn a single global scaling parameter. To better fit the embedding space to a given data distribution, we extend our method to learn a dimensional scaling vector to transform the embedding space. Furthermore, to learn task-specific embeddings, we generate task-dependent dimensional scaling vectors with amortized variational inference. Our method is end-to-end without any pre-training and can be used as a simple plug-and-play module for existing metric-based meta-algorithms. Experiments on miniImageNet show that our methods can be used to consistently improve the performance of existing metric-based meta-algorithms including prototypical networks and TADAM.

Approximation by Hidden Variable Fractal Functions: A Sequential Approach

The hidden variable fractal approximation is more diverse than classical fractal approximation. The main goal of the article is to establish new kind of hidden variable fractal approximants which possess convergence and non-differentiability simultaneously for any choice of the scaling factors. Without imposing any condition on the scaling vector, we establish the constrained approximation by the proposed hidden variable fractal approximants. By imposing suitable conditions on the scaling factors, we study the calculus of proposed hidden variable fractal approximants. We identify the suitable conditions for the parameters of hidden variable iterated function system so that the proposed hidden variable fractal functions preserve fundamental shape properties such as monotonicity and convexity in addition to the smoothness of the original function in the given compact interval.

Affine zipper fractal interpolation functions

This paper introduces a univariate interpolation scheme using a binary parameter called signature such that the graph of the interpolant—which we refer to as affine zipper fractal interpolation function—is obtained as an attractor of a suitable affine zipper. The scaling vector function is identified so that the graph of the corresponding affine zipper fractal interpolation function can be inscribed within a prescribed rectangle. Convergence analysis of the proposed affine zipper fractal interpolant is carried out. It is observed that for a fixed choice of discrete scaling factors, the box counting dimension of the graph of an affine zipper fractal interpolant is independent of the choice of a signature. Several examples of affine zipper fractal interpolants are presented to supplement our theory.

A Differential Accelerometer System: Offline Calibration and State Estimation

Accelerometers are used in a wide variety of applications including inertial navigation systems and activity monitors. In order to reduce systematic and random errors and improve accuracy and precision, this paper proposes a differential accelerometer system where two triaxial accelerometers are combined in opposite directions. The differential system allows to create additional constraints that can be used for improving calibration and estimation. Calibration methods based on nonlinear optimization are suggested to determine the offset and the scaling vectors. The differential system also permits to determine and update the offset and the scaling factors dynamically based on the system’s constraints. Sensor fusion is accomplished using a weighted least squares method. Experiments are carried out to evaluate and validate the system and the proposed methods including comparison with a single accelerometer system. It is shown that the differential system facilitates and improves acceleration estimation in terms of accuracy and precision.

A Novel Multichannel Internet of Things Based on Dynamic Spectrum Sharing in 5G Communication

The shortage of spectrum resources has limited the development of Internet of Things (IoT). Fifth generation (5G) network can flexibly support a variety of devices and services, which makes it possible to combine 5G with IoT. In this paper, a novel multichannel IoT is proposed to dynamically share the spectrum with 5G communication, where an IoT node including transmitter and receiver is designed to perform 5G communication and IoT communication simultaneously. The subchannel sets allocated for 5G communication and IoT communication are defined by two complementary spectrum marker vectors, respectively. Two independent spectrum sequences are generated by calculating the inner products of spectrum marker vectors, presudo-random phases and power scaling vectors. Two time-domain fundamental modulation waveforms generated by the inverse fast Fourier transform of the spectrum sequences are used to modulate 5G data and IoT data, respectively. The receiver can detect the data using the same spectrum marker vectors as the transmitter. The BER performances of the system using binary modulation and cyclic code shift keying modulation in the cases of spectrum marker error and multiple access are analyzed, respectively. A subchannel and power optimization unit is formulated as a joint optimization problem, which seeks to maximize the 5G throughput under the constraints of minimal IoT throughput, maximal power, and maximal interference. An alternative optimization problem is proposed to maximize the IoT throughput while guaranteeing the minimal 5G throughput. A joint optimization algorithm based on Lagrange dual decomposition is proposed to achieve the optimal solution. Simulation results indicate that the proposed IoT can improve the 5G throughput significantly while the IoT throughput is guaranteed.