Redundant Representation Research Articles

Takagi–Sugeno fuzzy observer design for nonlinear descriptor systems with unmeasured premise variables and unknown inputs

AbstractThis article presents a new observer design framework for a class of nonlinear descriptor systems with unknown but bounded inputs. In the presence of unmeasured nonlinearities, that is, premise variables, designing nonlinear observers is known as particularly challenging. To solve this problem, we rewrite the nonlinear descriptor system in the form of a Takagi–Sugeno (TS) fuzzy model with nonlinear consequents. This model reformulation enables an effective use of the differential mean value theorem to deal with the mismatching terms involved in the estimation error dynamics. These nonlinear terms, issued from the unmeasured nonlinearities of the descriptor system, cause a major technical difficulty for TS fuzzy‐model‐based observer design. The descriptor form is treated through a singular redundancy representation. For observer design, we introduce into the Luenberger‐like observer structure a virtual variable aiming at estimating the one‐step ahead state. This variable introduction allows for free‐structure decision variables involved in the observer design to further reduce the conservatism. Using Lyapunov‐based arguments, the observer design is reformulated as an optimization problem under linear matrix inequalities with a single line search parameter. The estimation error bounds of both the state and the unknown input can be minimized by means of a guaranteed ℓ∞‐gain performance level. The interests of the new ℓ∞ TS fuzzy observer design are clearly illustrated with two physically motivated examples.

Non-power positional number representation systems, bijective numeration, and the Mesoamerican discovery of zero

Pre-Columbian Mesoamerica was a fertile crescent for the development of number systems. A form of vigesimal system seems to have been present from the first Olmec civilization onwards, to which succeeding peoples made contributions. We discuss the Maya use of the representational redundancy present in their Long Count calendar, a non-power positional number representation system with multipliers 1, 20, 18 × 20, …, 18 × 20n. We demonstrate that the Mesoamericans did not need to invent positional notation and discover zero at the same time because they were not afraid of using a number system in which the same number can be written in different ways. A Long Count number system with digits from 0 to 20 is seen later to pass to one using digits 0 to 19, which leads us to propose that even earlier there may have been an initial zeroless bijective numeration system whose digits ran from 1 to 20. Mesoamerica was able to make this conceptual leap to the concept of a cardinal zero to perform arithmetic owing to a familiarity with multiple and redundant number representation systems.

Reachable set bounding of output-feedback control for discrete-time large-scale IT-2 fuzzy descriptor systems using distributed event-based broadcasts

This paper studies the distributed event-based broadcasting of output-feedback control for discrete-time large-scale fuzzy descriptor systems subject to reachable set bounding. First, each nonlinear subsystem is represented by the interval type-2 fuzzy model, where fuzzy representation is assumed to be appearing not only in both the state and input matrices but also in the derivative matrix. By using a descriptor redundancy approach, the fuzzy representation in the derivative matrix is reformulated into the linear one. Then, we introduce an output-feedback fuzzy controller with distributed event-based broadcasting, where all subsystems communicate with each other via a distributed network, and each subsystem broadcasts its decision-making of transmission based on a prescribed event. Two event-based mechanisms (EBMs) are respectively proposed to examine when the system output and fuzzy premise variable should be transmitted to the controller. Moreover, by further employing a descriptor redundancy representation, combined with reachable set analysis method, it will be shown that the proposed fuzzy controller guarantees that the estimation error is bounded within the ellipsoidal boundary while communication data are transmitted to the controller as little as possible, and sufficient condition for designing the desired controller is derived in terms of linear matrix inequalities (LMIs). Finally, a simulation study is given to show the effectiveness of the proposed method.

A High-Performance and Low-Cost Montgomery Modular Multiplication Based on Redundant Binary Representation

In this brief, Redundant Binary Representation (RBR) is applied in Montgomery modular multiplication (MMM) to eliminate the long carry chain and realize parallel computation. A novel MMM algorithm based on RBR is proposed. Based on the proposed algorithm, different sizes of high-performance and low-cost Montgomery multipliers are implemented in TSMC CMOS process technology. The experimental results demonstrate that our design has significant advantages in terms of performance, area and Area-Time-Product over previous researches. It’s worth mentioning that our 8192-bit Montgomery multiplier (TMSC 65nm) with 603MHz working frequency and 878.1K equivalent gates can complete the MMM in only 3403ns.

A Modified Roger's Distance Algorithm for Mixed Quantitative-Qualitative Phenotypes to Establish a Core Collection for Taiwanese Vegetable Soybeans.

Vegetable soybeans [Glycine max (L.) Merr.] have characteristics of larger seeds, less beany flavor, tender texture, and green-colored pods and seeds. Rich in nutrients, vegetable soybeans are conducive to preventing neurological disease. Due to the change of dietary habits and increasing health awareness, the demand for vegetable soybeans has increased. To conserve vegetable soybean germplasms in Taiwan, we built a core collection of vegetable soybeans, with minimum accessions, minimum redundancy, and maximum representation. Initially, a total of 213 vegetable soybean germplasms and 29 morphological traits were used to construct the core collection. After redundant accessions were removed, 200 accessions were retained as the entire collection, which was grouped into nine clusters. Here, we developed a modified Roger’s distance for mixed quantitative–qualitative phenotypes to select 30 accessions (denoted as the core collection) that had a maximum pairwise genetic distance. No significant differences were observed in all phenotypic traits (p-values > 0.05) between the entire and the core collections, except plant height. Compared to the entire collection, we found that most traits retained diversities, but seven traits were slightly lost (ranged from 2 to 9%) in the core collection. The core collection demonstrated a small percentage of significant mean difference (3.45%) and a large coincidence rate (97.70%), indicating representativeness of the entire collection. Furthermore, large values in variable rate (149.80%) and coverage (92.5%) were in line with high diversity retained in the core collection. The results suggested that phenotype-based core collection can retain diversity and genetic variability of vegetable soybeans, providing a basis for further research and breeding programs.

3-D Relation Network for visual relation recognition in videos

Video visual relation recognition aims at mining the dynamic relation instances between objects in the form of 〈subject,predicate,object〉, such as “person1-towards-person2” and “person-ride-bicycle”. Existing solutions treat the problem as several independent sub-tasks, i.e., image object detection, video object tracking and trajectory-based relation prediction. We argue that such separation results in the lack of information flow between different sub-models, which creates redundant representation while each sub-task cannot share a common set of task-specific features. Toward this end, we connect these three sub-tasks in an end-to-end manner by proposing the 3-D relation proposal that serves as a bridge for relation feature learning. Specifically, we put forward a novel deep neural network, named 3DRN, to fuse the spatio-temporal visual characteristics, object label features, and spatial interactive features for learning the relation instances with multi-modal cues. In addition, a three-staged training strategy is also provided to facilitate large-scale parameter optimization. We conduct extensive experiments on two public datasets with different emphasis to demonstrate the effectiveness of the proposed end-to-end feature learning method for visual relation recognition in videos. Furthermore, we verify the potential of our approach by tackling the video relation detection task.

Characteristics of Parallel Carry-Free Three-Step MSD Additions

Since the modified signed digital (MSD) redundant representation was proposed in the 1950s, lots of achievements have been made in MSD arithmetic. By inspecting the processes of the parallel carry-free three-step MSD addition, the transformations for such additions are studied in detail in this paper. The characteristics for parallel carry-free three-step MSD addition are proposed and the correctness is proved. Then seven groups of transformations that have characteristics of three-step MSD addition are presented. These groups of transformations are dual or self-dual, and some of them have simpler forms than the typical transformations consisting of $T, W, T', W', T_{2}$ . The general design mode of parallel carry-free three-step MSD additions and its applications in ternary optical computer (TOC) are further proposed. At the same time, single adder (multi-adder) reconstruction mode, processor bits allocation strategy, and light path diagrams are given. The optical experiments of MSD additions for three groups of MSD addition transformations show that the results of these transformations are correct. This work provides the theoretical basis for the design of the ternary optical computer adder.

Research on N-grams feature selection methods for text classification

Text classification requires previously extraction of features describing the text documents in the collection. Usually these features are based on the occurrence frequency of words, N-grams of words in documents, i.e. the vector space model for document representation is built. Feature selection allows to reduce redundancy in high-dimensional representation of text data, which can significantly improve text classification performance. In the present paper, research on feature selection methods is performed in terms of the accuracy and F-measure of text classification with different number of selected attributes (N-grams of words) for different classifiers and different datasets. The obtained results can be used to apply further pre-processing steps, which include modifying the vector space model in order to achieve its improvement in terms of the text classification.

An Inexact Penalty Decomposition Method for Sparse Optimization.

The penalty decomposition method is an effective and versatile method for sparse optimization and has been successfully applied to solve compressed sensing, sparse logistic regression, sparse inverse covariance selection, low rank minimization, image restoration, and so on. With increase in the penalty parameters, a sequence of penalty subproblems required being solved by the penalty decomposition method may be time consuming. In this paper, an acceleration of the penalty decomposition method is proposed for the sparse optimization problem. For each penalty parameter, this method just finds some inexact solutions to those subproblems. Computational experiments on a number of test instances demonstrate the effectiveness and efficiency of the proposed method in accurately generating sparse and redundant representations of one-dimensional random signals.

Exploitation of image statistics with sparse coding in the case of stereo vision

The sparse coding algorithm has served as a model for early processing in mammalian vision. It has been assumed that the brain uses sparse coding to exploit statistical properties of the sensory stream. We hypothesize that sparse coding discovers patterns from the data set, which can be used to estimate a set of stimulus parameters by simple readout. In this study, we chose a model of stereo vision to test our hypothesis. We used the Locally Competitive Algorithm (LCA), followed by a naïve Bayes classifier, to infer stereo disparity. From the results we report three observations. First, disparity inference was successful with this naturalistic processing pipeline. Second, an expanded, highly redundant representation is required to robustly identify the input patterns. Third, the inference error can be predicted from the number of active coefficients in the LCA representation. We conclude that sparse coding can generate a suitable general representation for subsequent inference tasks.

Low-Latency ASIC Algorithms of Modular Squaring of Large Integers for VDF Evaluation

This study is an attempt in quest of the fastest hardware algorithms for the computation of the evaluation component of verifiable delay functions (VDFs), ${a^{2^{T}}}$ mod N, proposed for use in various distributed protocols, in which no party is assumed to compute it significantly faster than other participants. To this end, we propose a class of modular squaring algorithms suitable for low-latency ASIC implementations. The proposed algorithms aim to achieve highest levels of parallelization that have not been explored in previous works in the literature, which usually pursue more balanced optimization of speed and area. For this, we utilize redundant representations of integers and introduce three modular squaring algorithms that work with integers in redundant forms: i) Montgomery algorithm, ii) memory-based algorithm and iii) direct reduction algorithm for fixed moduli. All algorithms enable ${O(log k)}$ depth circuit implementations, where k is the bit-size of the modulus N in the VDF function. We analyze and compare gate level-circuits of the proposed algorithms and provide estimates for their critical path delay and gate count.

Richly Activated Graph Convolutional Network for Robust Skeleton-Based Action Recognition

Current methods for skeleton-based human action recognition usually work with complete skeletons. However, in real scenarios, it is inevitable to capture incomplete or noisy skeletons, which could significantly deteriorate the performance of current methods when some informative joints are occluded or disturbed. To improve the robustness of action recognition models, a multi-stream graph convolutional network (GCN) is proposed to explore sufficient discriminative features spreading over all skeleton joints, so that the distributed redundant representation reduces the sensitivity of the action models to non-standard skeletons. Concretely, the backbone GCN is extended by a series of ordered streams which is responsible for learning discriminative features from the joints less activated by preceding streams. Here, the activation degrees of skeleton joints of each GCN stream are measured by the class activation maps (CAM), and only the information from the unactivated joints will be passed to the next stream, by which rich features over all active joints are obtained. Thus, the proposed method is termed richly activated GCN (RA-GCN). Compared to the state-of-the-art (SOTA) methods, the RA-GCN achieves comparable performance on the standard NTU RGB+D 60 and 120 datasets. More crucially, on the synthetic occlusion and jittering datasets, the performance deterioration due to the occluded and disturbed joints can be significantly alleviated by utilizing the proposed RA-GCN.

Frames and Numerical Approximation II: Generalized Sampling

In a previous paper (Adcock and Huybrechs in SIAM Rev 61(3):443–473, 2019) we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but ill-conditioning often prevents the numerical computation of best approximations. We showed that, in spite of said ill-conditioning, approximations with regularization may still provide accuracy up to order $$\sqrt{\epsilon }$$ , where $$\epsilon $$ is a small truncation threshold. When using frames, i.e. complete systems that are generally redundant but which provide infinite representations with coefficients of bounded norm, this accuracy can actually be achieved for all functions in a space. Here, we generalize that setting in two ways. We assume information or samples from f from a wide class of linear operators acting on f, rather than inner products associated with the best approximation projection. This enables the analysis of fully discrete approximations based, for instance, on function values only. Next, we allow oversampling, leading to least-squares approximations. We show that this leads to much improved accuracy on the order of $$\epsilon $$ rather than $$\sqrt{\epsilon }$$ . Overall, we demonstrate that numerical function approximation using redundant representations may lead to highly accurate approximations in spite of having to solve ill-conditioned systems of equations.

COMBINED MODELLING OF MULTIPLE TRANSPORTATION INFRASTRUCTURE WITHIN 3D CITY MODELS AND ITS IMPLEMENTATION IN CITYGML 3.0

Abstract. The development of digital urban twins has led to efforts of multiple cities to gather detailed and highly accurate data on many parts of urban environments, including road and railway infrastructure as well as areas used by pedestrians. This paper presents concepts for representing and segmenting this data semantically, geometrically and topologically ensuring usability for various multimodal applications in the context of digital 3D city models. First, methods for modelling multiple transportation types of several standards such as OpenDRIVE, GDF and INSPIRE are examined, including a discussion of different types of information integration such as functional and topographical representations. Then, concepts proposed to the CityGML Standards Working Group for the CityGML 3.0 Transportation model are presented. This includes detailed methods for modelling multiple transportation modes within a common city model while avoiding redundant geometric representations. A section / intersection concept in combination with links used to model these relations is described. Linear as well as areal models of level crossings, pedestrian crosswalks or areas shared by multiple transportation infrastructure at the same time (e.g. a tramway within a road) are presented. Subsequently, examples and applications that benefit from accurate representations of multiple transportation types are described.

UNIVARIATE AND MULTIVARIATE POLYNOMIAL REGRESSION CONSTRUCTION FROM A REDUNDANT REPRESENTATION USING AN ACTIVE EXPERIMENT

We consider the problem of a multidimensional polynomial regression construction from a given redundant representation based on the results of an active experiment. Redundant representation means inclusion in it the members which are possibly absent in the structure of the studied regression. Thus, we have a problem not only to estimate the values of the unknown coefficients of multidimensional polynomial regression from the results of an active experiment, but also to eliminate the redundant members from its redundant representation. The solution to this problem is based on: (a) obtaining new properties of the coefficients of normalized orthogonal polynomials of Forsythe; (b) possibility of reducing the problem of estimating the unknown coefficients for nonlinear members of multivariate polynomial regression to the problem of estimating the coefficients for the set of univariate polynomial regressions and solving the corresponding systems of linear equalities; (c) using the method to eliminate the redundant members of multidimensional nonlinear polynomial regression which organically includes both the methodology of cluster analysis and the main idea of the group method of data handling – dividing the experimental data into two sets, one of which is not used to estimate unknown coefficients of multidimensional polynomial regression given by a redundant representation.

Learning Document Image Features With SqueezeNet Convolutional Neural Network

The classification of various document image classes is considered an important step towards building a modern digital library or office automation system. Convolutional Neural Network (CNN) classifiers trained with backpropagation are considered to be the current state of the art model for this task. However, there are two major drawbacks for these classifiers: the huge computational power demand for training, and their very large number of weights. Previous successful attempts at learning document image features have been based on training very large CNNs. SqueezeNet is a CNN architecture that achieves accuracies comparable to other state of the art CNNs while containing up to 50 times less weights, but never before experimented on document image classification tasks. In this research we have taken a novel approach towards learning these document image features by training on a very small CNN network such as SqueezeNet. We show that an ImageNet pretrained SqueezeNet achieves an accuracy of approximately 75 percent over 10 classes on the Tobacco-3482 dataset, which is comparable to other state of the art CNN. We then visualize saliency maps of the gradient of our trained SqueezeNet's output to input, which shows that the network is able to learn meaningful features that are useful for document classification. Previous works in this field have made no emphasis on visualizing the learned document features. The importance of features such as the existence of handwritten text, document titles, text alignment and tabular structures in the extracted saliency maps, proves that the network does not overfit to redundant representations of the rather small Tobacco-3482 dataset, which contains only 3482 document images over 10 classes.

Descriptors representing two- and three-body atomic distributions and their effects on the accuracy of machine-learned inter-atomic potentials.

When determining machine-learning models for inter-atomic potentials, the potential energy surface is often described as a non-linear function of descriptors representing two- and three-body atomic distribution functions. It is not obvious how the choice of the descriptors affects the efficiency of the training and the accuracy of the final machine-learned model. In this work, we formulate an efficient method to calculate descriptors that can separately represent two- and three-body atomic distribution functions, and we examine the effects of including only two- or three-body descriptors, as well as including both, in the regression model. Our study indicates that non-linear mixing of two- and three-body descriptors is essential for an efficient training and a high accuracy of the final machine-learned model. The efficiency can be further improved by weighting the two-body descriptors more strongly. We furthermore examine a sparsification of the three-body descriptors. The three-body descriptors usually provide redundant representations of the atomistic structure, and the number of descriptors can be significantly reduced without loss of accuracy by applying an automatic sparsification using a principal component analysis. Visualization of the reduced descriptors using three-body distribution functions in real-space indicates that the sparsification automatically removes the components that are less significant for describing the distribution function.

Two-level fusion big data compression and reconstruction framework combining second-generation wavelet and lossless compression

In view of the characteristics of big data, fuzziness, and real time of data acquisition and transmission in the fuzzy information system faced by aircraft health management, to reduce the load of airborne data processing and transmission system under the condition of limited airborne computing resources and strong time constraints, the data collected by the airborne system are first compressed, and the amount of data are reduced before transmission and reconstructed after transmission. In view of the situation that the compression ratio of primary data compression is too small and the compression time is too long for large-scale fuzzy systems to meet the transmission requirements of the system, this paper combines the advantages of lossy compression method which consumes less time and lossless compression method which has higher compression ratio, and innovatively proposes a two-level data compression and reconstruction framework combining lossy compression and lossless compression. The optimization analysis is carried out. Taking a real aero-engine health sample as an example, the validity, scientificity, and robustness of the proposed framework are verified by comparing with data compression and reconstruction algorithm based on redundant sparse representation and compressed sensing.

Data hiding in virtual bit-plane using efficient Lucas number sequences

This paper introduces a steganography technique using the concept of virtual bit-plane. Purposely another number system has been used in this technique instead of binary to hide the target data. After that embedding of target data is done on different bit-planes. Here for conversion, Lucas Number system is used. The Lucas sequence is almost similar to Fibonacci, instead 1 and 2 it starts with 2 and 1. It helps to increase robustness by embedding data at the second bit-plane with a slight change of ±1. Here for embedding target data, Blue and Green channels of RGB color image are used. Red channel is used as indicator for proper extraction of target data at the receiver side. The indicator is used to avoid lexicographically higher order to consider for number representation. It may seem that the use of two channels for embedding reduces the capacity. But it does not really happen. The skip of pixel to follow Zekendrof’s rule for handling redundant representation by other existing methods, make the proposed one more capacitive than other. In order to establish its efficiency over the state-of-art-works the proposed method is analyzed by using different parameters and compared with relevant techniques. It has been found from the tested result that the proposed one is better. The stego quality of the method is also maintained along with the robustness and capacity. The PSNR of the proposed method is within the acceptable range, even in the highest embedding capacity.

Accurate and robust neural networks for face morphing attack detection

Artificial neural networks tend to use only what they need for a task. For example, to recognize a rooster, a network might only considers the rooster’s red comb and wattle and ignores the rest of the animal. This makes them vulnerable to attacks on their decision making process and can worsen their generality. Thus, this phenomenon has to be considered during the training of networks, especially in safety and security related applications. In this paper, we propose neural network training schemes, which are based on different alternations of the training data, to increase robustness and generality. Precisely, we limit the amount and position of information available to the neural network for the decision making process and study their effects on the accuracy, generality, and robustness against semantic and black box attacks for the particular example of face morphing attacks. In addition, we exploit layer-wise relevance propagation (LRP) to analyze the differences in the decision making process of the differently trained neural networks. A face morphing attack is an attack on a biometric facial recognition system, where the system is fooled to match two different individuals with the same synthetic face image. Such a synthetic image can be created by aligning and blending images of the two individuals that should be matched with this image. We train neural networks for face morphing attack detection using our proposed training schemes and show that they lead to an improvement of robustness against attacks on neural networks. Using LRP, we show that the improved training forces the networks to develop and use reliable models for all regions of the analyzed image. This redundancy in representation is of crucial importance to security related applications.