Hyperdimensional Space Research Articles

Optical hyperdimensional soft sensing: speckle-based touch interface and tactile sensor.

Hyperdimensional computing (HDC) is an emerging computing paradigm that exploits the distributed representation of input data in a hyperdimensional space, the dimensions of which are typically between 1,000-10,000. The hyperdimensional distributed representation enables energy-efficient, low-latency, and noise-robust computations with low-precision and basic arithmetic operations. In this study, we propose optical hyperdimensional distributed representations based on laser speckles for adaptive, efficient, and low-latency optical sensor processing. In the proposed approach, sensory information is optically mapped into a hyperdimensional space with >250,000 dimensions, enabling HDC-based cognitive processing. We use this approach for the processing of a soft-touch interface and a tactile sensor and demonstrate to achieve high accuracy of touch or tactile recognition while significantly reducing training data amount and computational burdens, compared with previous machine-learning-based sensing approaches. Furthermore, we show that this approach enables adaptive recalibration to keep high accuracy even under different conditions.

An encoding framework for binarized images using hyperdimensional computing.

Hyperdimensional Computing (HDC) is a brain-inspired and lightweight machine learning method. It has received significant attention in the literature as a candidate to be applied in the wearable Internet of Things, near-sensor artificial intelligence applications, and on-device processing. HDC is computationally less complex than traditional deep learning algorithms and typically achieves moderate to good classification performance. A key aspect that determines the performance of HDC is encoding the input data to the hyperdimensional (HD) space. This article proposes a novel lightweight approach relying only on native HD arithmetic vector operations to encode binarized images that preserves the similarity of patterns at nearby locations by using point of interest selection and local linear mapping. The method reaches an accuracy of 97.92% on the test set for the MNIST data set and 84.62% for the Fashion-MNIST data set. These results outperform other studies using native HDC with different encoding approaches and are on par with more complex hybrid HDC models and lightweight binarized neural networks. The proposed encoding approach also demonstrates higher robustness to noise and blur compared to the baseline encoding.

Nonlinearity-enabled higher-order exceptional singularities with ultra-enhanced signal-to-noise ratio.

Higher-order exceptional points (HOEPs) with extraordinary responsivity are expected to exhibit a vastly improved performance in detection-related applications. However, over the past few years, such an approach has been questioned due to several potential drawbacks, including the stringent parameter requirements, fundamental resolution limits and noise. Here, exploring the consequence of nonlinear gain saturation in exceptional singularities of non-Hermitian systems, we offer a feasible scheme to overcome all the above difficulties. We provide a simple and intuitive example by demonstrating with both theory and circuit experiments an 'exceptional nexus' ('EX'), a HOEP with an ultra-enhanced signal-to-noise ratio (SNR), in only two coupled resonators with the aid of nonlinear gain. The tedious parameter tuning in a six-dimensional hyper-dimensional space is reduced to two dimensions. The feedback mechanism of nonlinear saturable gain can give a solution to the ongoing debate on the SNR of EPs in other linear systems. Our findings advance the fundamental understanding of the peculiar topology of nonlinear non-Hermitian systems, significantly reduce the practical difficulty in EP sensing and possibly open new avenues for applications.

Recognition of Active Deception Jamming for LFM Radar Based on Hyperdimensional Computing

Active deception jamming is one of the common means to jam radar signals. How to effectively recognize active deception jamming is a challenge of modern radar technology. To address the accuracy and real-time of radar active jamming recognition in practical applications, we propose a fast recognition method of radar active deception jamming based on hyperdimensional computing. First, to address the high feature dimensions, we use the sparse representation of time–frequency diagrams as the input, which time–frequency diagrams are constructed by the jamming plus echo signals in multiple consecutive pulse periods. Second, to achieve a high accuracy and real time of recognition, we employ the hyperdimensional computing to map the input to hyperdimensional space for training and recognition. Last, in the recognition stage, the Hamming distance is adopted to measure the similarity of samples. We validate our method on nine types of radar active deception jamming. The experimental results show that compared with the existing mainstream machine learning-based methods, the proposed method greatly shortens the training time on the premise of maintaining a high recognition accuracy.

Performance limits of the single screw expander in organic Rankine cycle with ensemble learning and hyperdimensional evolutionary many-objective optimization algorithm intervention

The operating performance of the expander, as the core component of the ORC system, directly determines the comprehensive performance of the system. Single screw expander (SSE) has received widespread attention due to its advantages such as large single-stage expansion pressure ratio, insensitivity to liquid, wide working range, and balanced forces. This study fully considers the strong coupling, high nonlinearity, large time variability and uncertainty between SSE performance evaluation indexes and operating parameters. On this basis, a scatter–bilinear interpolation hybrid feature selection approach is proposed, and the feature selection and analysis of the correlation degree among SSE performance evaluation indexes are conducted. In the high-dimensional space, the influence of operating parameters on different performance evaluation indexes is analyzed. Then, this study proposes the ensemble learning-driven non-dominated sorting genetic algorithm-III (NSGA-III) approach. An ensemble learning-driven NSGA-III model for SSE performance limit optimization is constructed on the basis of the scatter–bilinear interpolation hybrid feature selection method and the ensemble learning-driven NSGA-III approach. In the hyperdimensional space, the performance limits of SSE are obtained. When the comprehensive performance of SSE reaches its limit, the shaft efficiency, expansion pressure ratio, and power output are 53.71%, 7.76, and 10.83 kW, respectively. This research provides a reliable reference for analyzing, designing, and optimizing the SSE performance limits, and it also provides a direct guidance for obtaining the SSE performance limits in the ORC system.

Training atomic neural networks using fragment-based data generated in virtual reality.

The ability to understand and engineer molecular structures relies on having accurate descriptions of the energy as a function of atomic coordinates. Here, we outline a new paradigm for deriving energy functions of hyperdimensional molecular systems, which involves generating data for low-dimensional systems in virtual reality (VR) to then efficiently train atomic neural networks (ANNs). This generates high-quality data for specific areas of interest within the hyperdimensional space that characterizes a molecule's potential energy surface (PES). We demonstrate the utility of this approach by gathering data within VR to train ANNs on chemical reactions involving fewer than eight heavy atoms. This strategy enables us to predict the energies of much higher-dimensional systems, e.g., containing nearly 100 atoms. Training on datasets containing only 15k geometries, this approach generates mean absolute errors around 2 kcal mol-1. This represents one of the first times that an ANN-PES for a large reactive radical has been generated using such a small dataset. Our results suggest that VR enables the intelligent curation of high-quality data, which accelerates the learning process.

Hardware Optimizations of Dense Binary Hyperdimensional Computing: Rematerialization of Hypervectors, Binarized Bundling, and Combinational Associative Memory

Brain-inspired hyperdimensional (HD) computing models neural activity patterns of the very size of the brain’s circuits with points of a hyperdimensional space, that is, with hypervectors . Hypervectors are D -dimensional (pseudo)random vectors with independent and identically distributed (i.i.d.) components constituting ultra-wide holographic words: D =10,000 bits, for instance. At its very core, HD computing manipulates a set of seed hypervectors to build composite hypervectors representing objects of interest. It demands memory optimizations with simple operations for an efficient hardware realization. In this article, we propose hardware techniques for optimizations of HD computing, in a synthesizable open-source VHDL library, to enable co-located implementation of both learning and classification tasks on only a small portion of Xilinx UltraScale FPGAs: (1) We propose simple logical operations to rematerialize the hypervectors on the fly rather than loading them from memory. These operations massively reduce the memory footprint by directly computing the composite hypervectors whose individual seed hypervectors do not need to be stored in memory. (2) Bundling a series of hypervectors over time requires a multibit counter per every hypervector component. We instead propose a binarized back-to-back bundling without requiring any counters. This truly enables on-chip learning with minimal resources as every hypervector component remains binary over the course of training to avoid otherwise multibit components. (3) For every classification event, an associative memory is in charge of finding the closest match between a set of learned hypervectors and a query hypervector by using a distance metric. This operator is proportional to hypervector dimension ( D ), and hence may take O( D ) cycles per classification event. Accordingly, we significantly improve the throughput of classification by proposing associative memories that steadily reduce the latency of classification to the extreme of a single cycle. (4) We perform a design space exploration incorporating the proposed techniques on FPGAs for a wearable biosignal processing application as a case study. Our techniques achieve up to 2.39× area saving, or 2,337× throughput improvement. The Pareto optimal HD architecture is mapped on only 18,340 configurable logic blocks (CLBs) to learn and classify five hand gestures using four electromyography sensors.

Hyperdimensional Computing With Local Binary Patterns: One-Shot Learning of Seizure Onset and Identification of Ictogenic Brain Regions Using Short-Time iEEG Recordings.

We develop a fast learning algorithm combining symbolic dynamics and brain-inspired hyperdimensional computing for both seizure onset detection and identification of ictogenic (seizure generating) brain regions from intracranial electroencephalography (iEEG). Our algorithm first transforms iEEG time series from each electrode into symbolic local binary pattern codes, from which a holographic distributed representation of the brain state of interest is constructed across all the electrodes and over time in a hyperdimensional space. The representation is used to quickly learn from few seizures, detect their onset, and identify the spatial brain regions that generated them. We assess our algorithm on our dataset that contains 99 short-time iEEG recordings from 16 drug-resistant epilepsy patients being implanted with 36-100 electrodes. For the majority of the patients (ten out of 16), our algorithm quickly learns from one or two seizures and perfectly (100%) generalizes on novel seizures using k-fold cross-validation. For the remaining six patients, the algorithm requires three to six seizures for learning. Our algorithm surpasses the state-of-the-art including deep learning algorithms by achieving higher specificity (94.84% versus 94.77%) and macroaveraging accuracy (95.42% versus 94.96%), and 74× lower memory footprint, but slightly higher average latency in detection (15.9s versus 14.7s). Moreover, the algorithm can reliably identify (with a p-value ) the relevant electrodes covering an ictogenic brain region at two levels of granularity: cerebral hemispheres and lobes. Our algorithm provides: 1) a unified method for both learning and classification tasks with end-to-end binary operations; 2) one-shot learning from seizure examples; 3) linear computational scalability for increasing number of electrodes; and 4) generation of transparent codes that enables post-translational support for clinical decision making. Our source code and anonymized iEEG dataset are freely available at http://ieeg-swez.ethz.ch.

Classification of abinitio models of proteins restored from small-angle X-ray scattering.

In structure analyses of proteins in solution by using small-angle X-ray scattering (SAXS), the molecular models are restored by using abinitio molecular modeling algorithms. There can be variation among restored models owing to the loss of phase information in the scattering profiles, averaging with regard to the orientation of proteins against the direction of the incident X-ray beam, and also conformational fluctuations. In many cases, a representative molecular model is obtained by averaging models restored in a number of abinitio calculations, which possibly provide nonrealistic models inconsistent with the biological and structural information about the target protein. Here, a protocol for classifying predicted models by multivariate analysis to select probable and realistic models is proposed. In the protocol, each structure model is represented as a point in a hyper-dimensional space describing the shape of the model. Principal component analysis followed by the clustering method is applied to visualize the distribution of the points in the hyper-dimensional space. Then, the classification provides an opportunity to exclude nonrealistic models. The feasibility of the protocol was examined through the application to the SAXS profiles of four proteins.

Cucurbituril mediated single molecule detection and identification via recognition tunneling

Recognition tunneling (RT) is an emerging technique for investigating single molecules in a tunnel junction. We have previously demonstrated its capability of single molecule detection and identification, as well as probing the dynamics of intermolecular bonding at the single molecule level. Here by introducing cucurbituril as a new class of recognition molecule, we demonstrate a powerful platform for electronically investigating the host–guest chemistry at single molecule level. In this report, we first investigated the single molecule electrical properties of cucurbituril in a tunnel junction. Then we studied two model guest molecules, aminoferrocene and amantadine, which were encapsulated by cucurbituril. Small differences in conductance and lifetime can be recognized between the host–guest complexes with the inclusion of different guest molecules. By using a machine learning algorithm to classify the RT signals in a hyper dimensional space, the accuracy of guest molecule recognition can be significantly improved, suggesting the possibility of using cucurbituril molecule for single molecule identification. This work enables a new class of recognition molecule for RT technique and opens the door for detecting a vast variety of small molecules by electrical measurements.

Parallel implementation of hyper-dimensional dynamical particle system on CUDA

The presented paper deals with possible approaches to parallel implementation of solution of a hyper-dimensional dynamical particle system. The proposed implementation approaches are generally applicable for similar particle systems of interest in various research and engineering fields. The original motivation for the present work was a simulation of particles that represent a space-filling design to be optimized for further use in design of experiments. Due to the underlying purpose of this particle system, the dimension of the particle system of interest is considered to be entirely arbitrary. Such a hyper-dimensional space is further folded into a periodically repeated domain.The theoretical background of the proposed particle system is provided along with the derivation of equations of motion of the dynamical system. As the complexity of the system is not limited by the number of particles nor the number of dimensions, the possibilities of utilizing the GPGPU platform are more restricted in comparison with today’s fast parallel implementations of common particle systems.Two distinct approaches to parallel implementation are presented, one aiming at a generalized usage of the fast on-chip resources, the other entirely relying on the GPU’s on-board global memory. Despite unambiguous mutual differences in their performance, both parallel implementations deliver major speedup compared to the single-thread CPU solution as well as a better scaling of execution time when increasing both the number of particles and dimensions.

An Application of the Support Vector Machine for Attribute-By-Attribute Classification in Cognitive Diagnosis.

Cognitive diagnostic modeling in educational measurement has attracted much attention from researchers in recent years. Its applications in real-world assessments, however, have been lagging behind its theoretical development. Reasons include but are not limited to requirement of large sample size, computational complexity, and lack of model fit. In this article, the authors propose to use the support vector machine (SVM), a popular supervised learning method to make classification decisions on each attribute (i.e., if the student masters the attribute or not), given a training dataset. By using the SVM, the problem of fitting and calibrating a cognitive diagnostic model (CDM) is converted into a quadratic optimization problem in hyperdimensional space. A classification boundary is obtained from the training dataset and applied to new test takers. The present simulation study considers the training sample size, the error rate in the training sample, the underlying CDM, as well as the structural parameters in the underlying CDM. Results indicate that by using the SVM, classification accuracy rates are comparable with those obtained from previous studies at both the attribute and pattern levels with much smaller sample sizes. The method is also computationally efficient. It therefore has great promise to increase the usability of cognitive diagnostic modeling in educational assessments, particularly small-scale testing programs.

Classification of Graphene Islands Via Confocal Raman Spectra Cluster Analysis

Since it was first isolated in 2004, monolayer graphene has been studied for its unique optical, electrical, and thermal properties. Recently, interest is growing in the rich physics of twisted bilayer graphene, especially with optical tools such as Raman spectroscopy[1]. In this work, we study the micro-Raman spectra of bi- and tri-layer graphene islands, and develop methods to classify features of these spectra. Graphene islands were grown on monolayer graphene via the CVD method[2], and then transferred to a Si/SiO2 substrate. Micro-Raman hyperspectral maps were taken from bi- and tri- layer islands with a wide variety of shapes and sizes. Using homemade code we fit the spectra from each pixel in the maps and extract the peak parameters for all of the major graphene Raman features. These pixels define a coordinate manifold, with the peak parameters building a hyperdimensional space over these coordinates. Principal Component Analysis was used to find the vectors where the spectra vary most widely, and data clusters were identified along these principal vectors. These clusters were further decomposed using this method iteratively. When all reasonable clusters are identified, the clusters can be remapped to the individual islands, allowing one to classify distinct regions on the islands with similar spectral features. Correlations between the peak parameters can be extracted from each cluster, and then fitted to determine the relationships between them. These relationships reflect the unique physics of the few-layer graphene system, such as biaxial strain or doping level. By classifying regions with similar behavior, we can determine how this physics is influenced by the geometry of the system. Acknowledgement: This work was supported by: NSF ECCS-1509786

Detection of different voice diseases based on the nonlinear characterization of speech signals

This work describes a novel methodology to characterize voice diseases by using nonlinear dynamics, considering different complexity measures that are mainly based on the analysis of the time delay embedded space. The feature space is represented with a DHMM and a further transformation of the DHMM states to a hyperdimensional space is performed. The discrimination between healthy and pathological speech signals is peformed by using a RBF-SVM which is trained following a K-fold cross-validation strategy. Results of around 99% of accuracy are obtained for three different voice disorders, disphonia due to laryngeal pathologies, hypernasality due to cleft lip and palate, and dysarthria due to Parkinson's disease.

Informational Clustering of Hyperspectral Data

Hyperspectral remote sensing is recognized as a powerful tool for mineralogical mapping of exposed surfaces on Earth and planets, as well. It allows for more rigorous discrimination among materials than multispectral imaging. Nevertheless, the huge data volume that comes with single observations results in severe limitations to successful data exploitation. Many techniques of feature reduction that have been developed so far do not allow for the complete exploitation of the informational content of the hyper-dimensional space. The present investigation aims at providing a feature reduction technique that preserves the spectral information and improves the classification results. We accomplished the feature reduction of synthetic and real hypercubes through exponential Gaussian optimization (EGO) and compared the results of k-means, spectral angle mapper (SAM), support vector machines (SVMs), and CLUES clustering techniques. The results show that the k-means clustering of hyper-dimensional spaces is the most efficient technique, but it does not automatically retrieve the optimal number of clusters. The SAM and SVM techniques give discrete results in terms of data partitioning, although the process of endmembers' selection is challenging and the definition of model parameters is not trivial. The combination of EGO modeling and CLUES algorithm allows for correctly estimating the number of clusters and deriving the accurate partitions when the cluster separability lies on two variables, at least. With real data, the CLUES clustering in the reduced space allows for higher overall performances than the more conventional techniques, although it underestimates the number of categories.

Neutron spectrum unfolding using genetic algorithm in a Monte Carlo simulation

A spectrum unfolding technique GAMCD (Genetic Algorithm and Monte Carlo based spectrum Deconvolution) has been developed using the genetic algorithm methodology within the framework of Monte Carlo simulations. Each Monte Carlo history starts with initial solution vectors (population) as randomly generated points in the hyper dimensional solution space that are related to the measured data by the response matrix of the detection system. The transition of the solution points in the solution space from one generation to another are governed by the genetic algorithm methodology using the techniques of cross-over (mating) and mutation in a probabilistic manner adding new solution points to the population. The population size is kept constant by discarding solutions having lesser fitness values (larger differences between measured and calculated results). Solutions having the highest fitness value at the end of each Monte Carlo history are averaged over all histories to obtain the final spectral solution. The present method shows promising results in neutron spectrum unfolding for both under-determined and over-determined problems with simulated test data as well as measured data when compared with some existing unfolding codes. An attractive advantage of the present method is the independence of the final spectra from the initial guess spectra.

Fast learning complex-valued classifiers for real-valued classification problems

In this paper, we present two fast learning complex-valued, single hidden layer neural network classifiers namely, ‘bilinear branch-cut complex-valued extreme learning machine (BB-CELM)’ and ‘phase encoded complex-valued extreme learning machine (PE-CELM)’ to solve real-valued classification problems. BB-CELM and PE-CELM use the bilinear transformation with a branch-cut at 2π and the phase encoded transformation, respectively, at the input layer to transform the feature space from the real domain to complex domain ( $${\Re \rightarrow \mathbb{C}}$$ ). A complex-valued activation function of the type of hyperbolic secant employed at the hidden layer maps the complex-valued feature space to a hyper dimensional complex space ( $${\mathbb{C}^m \rightarrow \mathbb{C}^K\quad K > m}$$ ). BB-CELM and PE-CELM are trained by choosing the hidden layer parameters randomly and computing the output weights analytically. Therefore, these classifiers require minimal computational effort during the training process. The performances of these classifiers are evaluated on a set of benchmark classification problems from the UCI machine learning repository and a practical acoustic emission signal classification problem. The results of the performance study highlight the superior classification ability of BB-CELM and PE-CELM classifiers.

Data Visualization for Kansei Analysis

Kansei data are multi-dimensional data. It is difficult for an analyzer to interpret data whose dimensionality is higher than three because his/her vision is used only to one -- three dimensions. Visualization by reducing the dimensionality of Kansei data to less than or equal to three dimensions could help the analyzer to understand the data. For an effective visualization, definition of distances between data is important. For the definition, axes that form a space of Kansei data should be determined first. The choice could be questions or objects. A questionnaire uses several objects and many questions. Respondents are asked to answer each question one by one by marking on a rating scale. Questions are usually used as axes for multivariate analysis. Objects are another choice for the axes. By changing our viewpoint from different axes, new relationships between questions/objects could be found. One of the most popular visualization methods is PCA (Principal Component Analysis). By applying PCA to questionnaire data on question axes, relationships between objects can be visualized. If the method is applied to the data on object axes, relationships between questions can be seen. The distance used in PCA is usually Euclidean distance. If some features can be extracted by a nonlinear transformation from original data, distances can be defined between the features. Kernel PCA[1] can be applied and kernel trick would work for dealing with multi-dimensional features. MDS (Multi-Dimensional Scaling)[2][3] is also an effective visualization method. This method is to reduce the dimensionality of data while preserving the distances or dissimilarities between data in the original space. The weights on the differences between the distances in the visualized space and those in the original hyper-space make MDS a flexible tool for the visualization. These weights can be set to determine distances to be preserved or ignored. In exploratory visual data analysis, interactive manifold unfolding can be carried out by setting these weights. ISOMAP[4] is an extension of MDS in which Euclidean distance is replaced with geodesic distance. Kansei data on manifold embedded in a hyper-dimensional space could be measured by their geodesic, or shortest path, distances and the manifold can be unfolded and visualized.

N -Dimensional Nonuniform Rational B-Splines for Metamodeling

Nonuniform rational B-splines (NURBs) have unique properties that make them attractive for engineering metamodeling applications. NURBs are known to accurately model many different continuous curve and surface topologies in one- and two-variate spaces. However, engineering metamodels of the design space often require hypervariate representations of multidimensional outputs. In essence, design space metamodels are hyperdimensional constructs with a dimensionality determined by their input and output variables. To use NURBs as the basis for a metamodel in a hyperdimensional space, traditional geometric fitting techniques must be adapted to hypervariate and hyperdimensional spaces composed of both continuous and discontinuous variable types. In this paper, we describe the necessary adaptations for the development of a NURBs-based metamodel called a hyperdimensional performance model or HyPerModel. HyPerModels are capable of accurately and reliably modeling nonlinear hyperdimensional objects defined by both continuous and discontinuous variables of a wide variety of topologies, such as those that define typical engineering design spaces. We demonstrate this ability by successfully generating accurate HyPerModels of ten trial functions laying the foundation for future work with N-dimensional NURBs in design space applications.

Job shop scheduling optimization through multiple independent particle swarms

Purpose – The purpose of this paper is to develop an effective and efficient approach to exploit meta‐heuristic in particle swarm optimization (PSO) for the job shop scheduling problem (JSP), a class of NP‐hard optimization problems. The approach is to be built on a PSO with multiple independent swarms. PSO was inspired by bird flocking and animal social behaviors. The particles operate collectively like a swarm that flies through the hyperdimensional space to search for possible optimal solutions. The behavior of the particles is influenced by their tendency to learn from their personal past experience and from the success of their peers to adjust their flying speed and direction. Research in fusing the multiple‐swarm concept into PSO is well‐established in solving single objective optimization problems and multimodal problems.Design/methodology/approach – This study examines the optimization of the JSP via a search space division scheme and use of the meta‐heuristic method of PSO by assigning each machi...