Complex-valued Representation Research Articles

ComPoint: Can Complex-Valued Representation Benefit Point Cloud Place Recognition?

ComPoint: Can Complex-Valued Representation Benefit Point Cloud Place Recognition?

A Quantum-inspired Complex-valued Representation for Encoding Sentiment Information (Student Abstract)

Recently, a Quantum Probability Drive Network (QPDN) is proposed to model different levels of semantic units by extending word embedding to complex-valued representation (CR). The extended complex-valued embeddings are still insensitive to polarity causing that they generalize badly in sentiment analysis (SA). To solve it, we propose a method of encoding sentiment information into sentiment words for SA. Attention mechanism and an auxiliary task are introduced to help learn the CR of sentiment words with the help of the sentiment lexicon. We use the amplitude part to represent the distributional information and the phase part to represent the sentiment information of the language. Experiments on three popular SA datasets show that our method is effective.

Model-Based Resonance Tracking of Linear Systems

This article develops recursive algorithms to track shifts in the resonance frequency of linear systems in real time. To date, automatic resonance tracking has been limited to nonmodel-based approaches, which relies solely on the phase difference between a specific input and output of the system. Instead, we propose a transformation of the system into a complex-valued representation, which allows us to abstract the resonance shifts as an exogenous disturbance acting on the excitation frequency, perturbing the excitation frequency from the natural frequency of the plant. We then discuss the resonance-tracking task in two parts: recursively identifying the frequency disturbance and incorporating an update of the excitation frequency in the algorithm. The complex representation of the system simplifies the design of resonance-tracking algorithms due to the applicability of well-established techniques. We discuss the stability of the proposed scheme, even in cases that seriously challenge current phase-based approaches, such as nonmonotonic phase differences and multiple-input multiple-output systems. Numerical simulations further demonstrate the performance of the proposed resonance-tracking scheme.

Sliding Modes in a Class of Complex-Valued Nonlinear Systems

A number of physical systems allow a complex-valued representation. This article extends the theory of sliding modes to a class of nonlinear systems described by complex-valued variables. Hence, states, parameters, control actions, and sliding manifolds belong, in general, to the complex field. In this article, it is also shown that the proposed design in the complex-valued framework provides shorter reaching times to the sliding manifold than the standard sliding-mode design at equal initial condition and control effort. Different implementation approaches are also evaluated, and numerical examples illustrate the proposal.

Quantifying intralimb coordination of terrestrial ungulates with Fourier coefficient affine superimposition

AbstractMany phenomena related to motor behaviour in animals are spatially and temporally periodic, making them accessible for transformation to the frequency domain via Fourier Series. Although this has been applied previously, it had not been noticed that the characteristic arrangement of Fourier coefficients in their complex-valued representation resembles landmarks in geometric morphometrics. We define a superimposition procedure in the frequency domain, which removes affine differences (mean, amplitude, phase) to reveal and compare the shape of periodic kinematic measures. This procedure is conceptually linked to dynamic similarity, which can thereby be assessed on the level of individual limb elements. We demonstrate how to make intralimb coordination accessible for large-scale, quantitative analyses. By applying this to a dataset from terrestrial ungulates, dominant patterns in forelimb coordination during walking are identified. This analysis shows that typical strides of these animals differ mostly in how much the limbs are lifted in the presence or absence of obstructive substrate features. This is shown to be independent of morphological features. Besides revealing fundamental characteristics of ungulate locomotion, we argue that the suggested method is generally suitable for the large-scale quantitative assessment of coordination and dynamics in periodic locomotor phenomena.

Indoor object recognition in RGBD images with complex-valued neural networks for visually-impaired people

We present a new multi-modal technique for assisting visually-impaired people in recognizing objects in public indoor environment. Unlike common methods which aim to solve the problem of multi-class object recognition in a traditional single-label strategy, a comprehensive approach is developed here allowing samples to take more than one label at a time. We jointly use appearance and depth cues, specifically RGBD images, to overcome issues of traditional vision systems using a new complex-valued representation. Inspired by complex-valued neural networks (CVNNs) and multi-label learning techniques, we propose two methods in order to associate each input RGBD image to a set of labels corresponding to the object categories recognized at once. The first one, ML-CVNN, is formalized as a ranking strategy where we make use of a fully complex-valued RBF network and extend it to be able to solve multi-label problems using an adaptive clustering method. The second method, L-CVNNs, deals with problem transformation strategy where instead of using a single network to formalize the classification problem as a ranking solution for the whole label set, we propose to construct one CVNN for each label where the predicted labels will be later aggregated to construct the resulting multi-label vector. Extensive experiments have been carried on two newly collected multi-labeled RGBD datasets prove the efficiency of the proposed techniques.

Complex-Valued Restricted Boltzmann Machine for Speaker-Dependent Speech Parameterization From Complex Spectra

This paper describes a novel energy-based probabilistic distribution that represents complex-valued data and explains how to apply it to direct feature extraction from complex-valued spectra. The proposed model, the complex-valued restricted Boltzmann machine (CRBM), is designed to deal with complex-valued visible units as an extension of the well-known restricted Boltzmann machine (RBM). Like the RBM, the CRBM learns the relationships between visible and hidden units without having connections between units in the same layer, which dramatically improves training efficiency by using Gibbs sampling or contrastive divergence. Another important characteristic is that the CRBM also has connections between real and imaginary parts of each of the complex-valued visible units that help represent the data distribution in the complex domain. In speech signal processing, classification and generation features are often based on amplitude spectra (e.g., MFCC, cepstra, and mel-cepstra) even if they are calculated from complex spectra, and they ignore phase information. In contrast, the proposed feature extractor using the CRBM directly encodes the complex spectra (or another complex-valued representation of the complex spectra) into binary-valued latent features (hidden units). Since the visible-hidden connections are undirected, we can also recover (decode) the complex spectra from the latent features directly. Our speech representation experiments demonstrated that the CRBM outperformed other speech representation methods, such as methods using a conventional RBM, a mel-log spectrum approximate decoder, etc.

A Sinusoidal Image Model Derived from the Circular Harmonic Vector

We introduce a sinusoidal image model consisting of an oriented sinusoid plus a residual component. The model parameters are derived from the circular harmonic vector, a representation of local image structure consisting of the responses to the higher-order Riesz transforms of an isotropic wavelet. The vector is split into sinusoidal and residual components. The sinusoidal component gives a phase-based description of the dominant local linear symmetry, with improved orientation estimation compared to previous sinusoidal models. The residual component describes the remaining parts of the local structure, from which a complex-valued representation of intrinsic dimension is derived. The usefulness of the model is demonstrated for corner and junction detection and parameter-driven image reconstruction.

Reassignment and synchrosqueezing for general time–frequency filter banks, subsampling and processing

In this contribution, we extend the reassignment method (RM) and synchrosqueezing transform (SST) to arbitrary time–frequency localized filters and, in the first case, arbitrary decimation factors. A sufficient condition for the invertibility of the SST is provided. RM and SST are techniques for deconvolution of short-time Fourier and wavelet representations. In both methods, the partial phase derivatives of a complex-valued time–frequency representation are used to determine the instantaneous frequency and group delay associated to the individual representation coefficients. Subsequently, the coefficient energy is reassigned to the determined position. Combining RM and frame theory, we propose a processing scheme that benefits both from the improved localization of the reassigned representation and the frame properties of the underlying complex-valued representation. This scheme is particularly interesting for applications that require low redundancy not achievable by an invertible SST.

Time-averaged and time-dependent energy-related quantities of harmonic waves in inhomogeneous viscoelastic anisotropic media

SUMMARY The energy‐flux vector and other energy-related quantities play an important role in various wave propagation problems. In acoustics and seismology, the main attention has been devoted to the time-averaged energy flux of time-harmonic wavefields propagating in nondissipative, isotropic and anisotropic media. In this paper, we investigate the energy‐flux vector and other energy-related quantities of wavefields propagating in inhomogeneous anisotropic viscoelastic media. These quantities satisfy energy-balance equations, which have, as we show, formally different forms for real-valued wavefields with arbitrary time dependence and for timeharmonic wavefields. In case of time-harmonic wavefields, we study both time-averaged and time-dependent constituents of the energy-related quantities. We show that the energy-balance equations for time-harmonic wavefields can be obtained in two different ways. First, using real-valued wavefields satisfying the real-valued equation of motion and stress‐strain relation. Second, using complex-valued wavefields satisfying the complex-valued equation of motion and stress‐strain relation. The former approach yields simple results only for particularly simple viscoelastic models, such as the Kelvin‐Voigt model. The latter approach is considerably more general and can be applied to viscoelastic models of unrestricted anisotropy and viscoelasticity. Both approaches, when applied to the Kelvin‐Voigt viscoelastic model, yield the same expressions for the time-averaged and time-dependent constituents of all energy-related quantities and the same energy-balance equations. This indicates that the approach based on complex-valued representation of the wavefield may be used for time harmonic waves quite universally. This study also shows importance of joint consideration of time-averaged and time-dependent constituents of the energy-related quantities in some applications.

On the solution of plane boundary-value problems of elasticity in a rectangle

An algorithm for solving plane boundary-value problems of elasticity for a rectangular domain is expounded. The algorithm is based on a complex-valued representation of the general solution to the differential equations of the plane problem and on the use of Lagrange polynomials to satisfy the boundary conditions. The algorithm can quite easily be implemented in a computer program. This is probably the simplest way of solving boundary-value problems of this class

The minimum-phase demodulate and its application to autoregressive analysis of bandpass signal

The subject of our investigation is a minimum-phase demodulate (MPD) as a discrete-time baseband complex-valued representation of a bandpass signal whose instantaneous phase waveform is originally missed. In theoretical preliminaries a system of definitions for bandpass signal complete and incomplete representation is outlined and MPD choice as a supplemented complex-valued signal is argued. Next, MPD properties are specified and MPD as well as optional minimum-phase envelope-based bandpass signal estimators in time and frequency domains are proposed. Later on, MPD is treated as autoregressive process realization whose parameters and maximum entropy spectrum estimated by the use of a batch processing method are considered. Finally, MPD against envelope predictability improvement due to decrease of spectrum flatness measure is reported and visualized by numerical experiments with underwater echo-envelope data. Der Gegenstand unserer Untersuchung ist die minimalphasige Demodulation (MPD) eines Bandpaßsignals, dessen Augenblicksphasensignal ursprünglich fehlt, zu einer zeitdiskreten komplexwertigen Darstellung im Basisband. In theoretischen Voruntersuchungen wird ein System von Definitionen für die vollständige und unvollständige Darstellung von Bandpaßsignalen dargelegt und die MPD-Wahl als ein komplexwertig ergänztes Signal begründet. Als nächstes werden Eigenschaften der MPD spezifiziert und es werden die MPD sowie optionale minimalphasige, auf der Einhüllenden beruhende Schätzer von Bandpaßsignalen im Zeit- und Frequezbereich vorgeschlagen. Danach wird die MPD als Realisierung eines autoregressives Prozesses behandelt, für den die Schätzung der Parameter und des Spektrums maximaler Entropie mit Hilfe von Stapelverarbeitunsmethoden betrachtet wird. Schließlich wird die MPD der Verbesserung der Einhüllenden-Vorhersagbarkeit zufolge der Abnahme des spektralen Flachheitsmaßes gegenübergestellt und durch numerische Experimente mit Daten für Einhüllende von Unterwasserechos veranschaulicht. Le sujet de notre investigation est le signal démodulé à phase minimale (SDPM) comme représentation complexe discrète en bande de base de signaux à spectre passe-bande dont la phase instantanée est originellement manquante. Dans les préliminaires théoriques, un système de définitions pour la représentation complète et incomplète des signaux à spectre passebande est esquissé et le choix du SDPM comme nouveau signal complexe est justifié. Ensuite, les propriétés des SDPM sont décrites et des SDPM ainsi que des estimateurs à phase minimale basés sur l'enveloppe des signaux à spectre passe-bande sont proposés pour les domaines temporel et fréquentiel. Puis les SDPM sont traités comme réalisation de processus autorégressifs dont on considère les paramètres et l'estimation spectrale basée sur le maximum d'entropie. Finalement, l'amélioration de la prédictibilité des SDPM par rapport aux signaux d'enveloppe, qui est due à la diminution de l'uniformité spectrale, est démonstrée et visualisée sur des données expérimentales avec l'enveloppe d'échos en milieu aqueux.

Transformation of Operators

A method is given for the transformation of operators from one representation to another. Explicit expressions are derived. The transformation to complex valued representation is also considered.