Correlated Signal Components Research Articles

Stimulus-Informed Generalized Canonical Correlation Analysis for Group Analysis of Neural Responses to Natural Stimuli.

Various new brain-computer interface technologies or neuroscience applications require decoding stimulus-following neural responses to natural stimuli such as speech and video from, e.g., electroencephalography (EEG) signals. In this context, generalized canonical correlation analysis (GCCA) is often used as a group analysis technique, which allows the extraction of correlated signal components from the neural activity of multiple subjects attending to the same stimulus. GCCA can be used to improve the signal-to-noise ratio of the stimulus-following neural responses relative to all other irrelevant ( non-)neural activity, or to quantify the correlated neural activity across multiple subjects in a group- wise coherence metric. However, the traditional GCCA technique is stimulus-unaware: no information about the stimulus is used to estimate the correlated components from the neural data of several subjects. Therefore, the GCCA technique might fail to extract relevant correlated signal components in practical situations where the amount of information is limited, for example, because of a limited amount of training data or group size. This motivates a new stimulus-informed GCCA (SI-GCCA) framework that allows taking the stimulus into account to extract the correlated components. We show that SI-GCCA outperforms GCCA in various practical settings, for both auditory and visual stimuli. Moreover, we showcase how SI-GCCA can be used to steer the estimation of the components towards the stimulus. As such, SI-GCCA substantially improves upon GCCA for various purposes, ranging from preprocessing to quantifying attention.

MAXVAR-Based Distributed Correlation Estimation in a Wireless Sensor Network

The performance of most array signal processing tasks relies on the presence of correlation between sensor signals. In a wireless sensor network, where sensor nodes are spread out over a relatively large area, it is useful to identify nodes observing similar sensor signals and hence common phenomenons, for example to partition the network according to the observed latent signals and corresponding correlation structure. This can be achieved via the so-called MAXVAR formulation of generalized canonical correlation analysis, which finds a low-dimensional subspace that highlights correlated signal components between multiple nodes' observed signal subspaces. The classical procedure for computing the solutions of MAXVAR consists in performing a generalized eigenvalue decomposition after collecting all the sensors' signals at a fusion center. However, this typically incurs high communication and computational costs. In this paper, we describe a low communication and computational cost distributed algorithm that computes the solutions of MAXVAR without aggregating the nodes' observations at a central location. We show how a subset of those solutions can be used locally by each node to estimate the global correlation structure across all nodes in the network, thereby allowing any node to evaluate the presence of correlated signals at any other node, even if no direct link is shared. We prove the convergence of the algorithm and validate our method for estimating the correlation structure via simulations.

Encoding- and decision-related brain activity during a motion judgment task

We have previously used steady-state VEPs to show that responses in visual cortex are strongly suppressed when motion stimuli produce inter-ocular velocity differences (Kohler et al., 2018), regardless of whether these differences give rise to movement in depth (MID). Here we used an event-related VEP design to explore how activity evoked by lateral movement and MID unfolds over time. Participants (n=20) viewed stereoscopically presented random-dot patterns in which a central region moved in one of four directions. Dots underwent single-shot apparent motion on every trial: in-phase motion between the two eyes produced lateral movement (left/right), while anti-phase motion gave rise to MID (towards/away). Participants indicated movement direction as quickly and accurately as possible using the keyboard arrow keys. For lateral movement, accuracy was at ceiling and reaction time (RT) was ~800ms, while MID produced lower accuracies (~80%) and longer RTs (~1000ms). We used reliable components analysis to extract maximally correlated signal components from the EEG data (Dmochowski et al., 2012). A medio-frontal component appeared to capture decision-related activity, exhibiting a ramp-like shape that was shallower for MID, consistent with a longer integration period leading to slower RTs. An additional component, centered over occipital cortex, appeared to primarily capture encoding-related activity. Lateral movement and MID produced indistinguishable positive peaks at ~70ms, but diverged at later negative (~180ms) and positive (~350ms) peaks. MID responses were enhanced (more negative) around the negative peak (100–200ms) and suppressed (less positive) leading up to the second positive peak (250–350ms). This late-onset suppression is consistent with the finding that suppression depends on second-order processes, including extraction of relative motion and relative disparity (Kohler et al., 2018). The current results provide a time-resolved electrophysiological analogue to psychophysical data showing that temporal integration underlying decision making is near-perfect for lateral motion, but sub-optimal for MID (Katz et al., 2015).

Multiplicative Complementary Binary Signal-Code Constructions

There are proposed signal-code constructions consisting of two or more components shaped on a basis of binary sequences with a property of multiplicative complementariness of their matched filtering results. There are considered systematically the rules of synthesis of such binary sequences containing signal-code constructions; there are described analytically their correlation properties, their processing specificities and the structure of obtained resulting signal. On a basis of statistical model of correlated signal components and their clusterization there is shown theoretical continuity of proposed signal-code constructions and Barker’s binary sequences. There are represented the examples of shaping, processing and parameters of researched signal-code constructions. It is carried out comparative analysis of structural specificities and noise immunity of multiplicative complementary signal-code constructions with complementary sequences (Golay’s codes), i.e. signal-code constructions with property of additive complementariness, there are exposed their advantages and drawbacks regarding spectral characteristics and signal detection characteristics (errors of the first and second genus).

Canonical correlation analysis of high-dimensional data with very small sample support

This paper is concerned with the analysis of correlation between two high-dimensional data sets when there are only few correlated signal components but the number of samples is very small, possibly much smaller than the dimensions of the data. In such a scenario, a principal component analysis (PCA) rank-reduction preprocessing step is commonly performed before applying canonical correlation analysis (CCA). We present simple, yet very effective, approaches to the joint model-order selection of the number of dimensions that should be retained through the PCA step and the number of correlated signals. These approaches are based on reduced-rank versions of the Bartlett–Lawley hypothesis test and the minimum description length information-theoretic criterion. Simulation results show that the techniques perform well for very small sample sizes even in colored noise.

Subspace Methods for Joint Sparse Recovery

We propose robust and efficient algorithms for the joint sparse recovery problem in compressed sensing, which simultaneously recover the supports of jointly sparse signals from their multiple measurement vectors obtained through a common sensing matrix. In a favorable situation, the unknown matrix, which consists of the jointly sparse signals, has linearly independent nonzero rows. In this case, the MUSIC (MUltiple SIgnal Classification) algorithm, originally proposed by Schmidt for the direction of arrival problem in sensor array processing and later proposed and analyzed for joint sparse recovery by Feng and Bresler, provides a guarantee with the minimum number of measurements. We focus instead on the unfavorable but practically significant case of rank-defect or ill-conditioning. This situation arises with limited number of measurement vectors, or with highly correlated signal components. In this case MUSIC fails, and in practice none of the existing methods can consistently approach the fundamental limit. We propose subspace-augmented MUSIC (SA-MUSIC), which improves on MUSIC so that the support is reliably recovered under such unfavorable conditions. Combined with subspace-based greedy algorithms also proposed and analyzed in this paper, SA-MUSIC provides a computationally efficient algorithm with a performance guarantee. The performance guarantees are given in terms of a version of restricted isometry property. In particular, we also present a non-asymptotic perturbation analysis of the signal subspace estimation that has been missing in the previous study of MUSIC.

Correlated Components of Ongoing EEG Point to Emotionally Laden Attention – A Possible Marker of Engagement?

Recent evidence from functional magnetic resonance imaging suggests that cortical hemodynamic responses coincide in different subjects experiencing a common naturalistic stimulus. Here we utilize neural responses in the electroencephalogram (EEG) evoked by multiple presentations of short film clips to index brain states marked by high levels of correlation within and across subjects. We formulate a novel signal decomposition method which extracts maximally correlated signal components from multiple EEG records. The resulting components capture correlations down to a one-second time resolution, thus revealing that peak correlations of neural activity across viewings can occur in remarkable correspondence with arousing moments of the film. Moreover, a significant reduction in neural correlation occurs upon a second viewing of the film or when the narrative is disrupted by presenting its scenes scrambled in time. We also probe oscillatory brain activity during periods of heightened correlation, and observe during such times a significant increase in the theta band for a frontal component and reductions in the alpha and beta frequency bands for parietal and occipital components. Low-resolution EEG tomography of these components suggests that the correlated neural activity is consistent with sources in the cingulate and orbitofrontal cortices. Put together, these results suggest that the observed synchrony reflects attention- and emotion-modulated cortical processing which may be decoded with high temporal resolution by extracting maximally correlated components of neural activity.

Method and apparatus for processing noisy sound signals

A method for processing a sound signal y in which redundancy, consisting mainly of almost repetitions of signal profiles, is detected and correlations between the signal profiles are determined within segments of the sound signal. Correlated signal components are allocated to a power component and uncorrelated signal components to a noise component of the sound signal. The correlations between the signal profiles are determined by methods of nonlinear noise reduction in deterministic systems in reconstructed vector spaces based on the time domain.

Noise coherence in closely-spaced electrodes: the implications for spatial averaged ECG recordings.

Ensemble signal averaging is conventionally used to reduce the noise content of ECG recordings. One shortcoming of this technique is that it removes the possibility of registering transient signals. As a consequence the simultaneous averaging of spatially related leads has been used. This relies on the recording electrodes receiving correlated signal components for reinforcement together with uncorrelated noise. We have developed a methodology for studying EMG noise reduction by spatial averaging and present results for different electrode spacings which suggest minimum separations for noise rejection.

Fetal Electrocardiogram Enhancement by Time-Sequenced Adaptive Filtering

An adaptive method for performing optimal time-varying filtering of nonstationary signals having a recurring statistical character, e.g., recurring pulses in noise, has been proposed. This method, called time-sequenced adaptive filtering, is applied to the enhancement of abdominally derived fetal electrocardiograms against background muscle noise. It is shown that substantial improvement in terms of signal distortion is obtained when time-sequenced filtering, rather than conventional time-invariant filtering, is employed. The method requires two or more abdominal channels containing correlated signal components, but uncorrelated muscle noise components. The location of the fetal pulses in time must be estimated in order to synchronize the filter's time-varying impulse response to the fetal cardiac cycle.

Multichannel adaptive filtering for signal enhancement

An adaptive technique for enhancing a signal against additive noise is described. It makes use of two or more input channels containing correlated signal components but uncorrelated noise components. The various input signals need not be of the same waveshape, since the adaptive enhancer filters the inputs before summing them. The output is a best least squares estimate of the underlying signal in a chosen input channel. Adaptivity allows optimal performance even though the signal and noise characteristics differ from channel to channel and are unknown a priori. Formulas for signal distortion and output noise power are developed. The more input channels available containing correlated signal components, the better will be the system performance. Excellent performance is obtained when the sum of the filter input signal-to-noise ratios (SNR's), defined as functions of frequency, is large compared to unity at all frequencies of interest. In this case the output noise is small, the output signal distortion is small, and the output SNR is approximately equal to the sum of the filter input SNR's. As such, the multichannel adaptive signal enhancer is a generalization of the classic time-delay-and-sum beamforming antenna.

Multichannel adaptive filtering for signal enhancement

An adaptive technique for enhancing a signal against additive noise is described. It makes use of two or more input channels containing correlated signal components but uncorrelated noise components. The various input signals need not be of the same waveshape, since the adaptive enhancer filters the inputs before summing them. The output is a best least squares estimate of the underlying signal in a chosen input channel. Adaptivity allows optimal performance even though the signal and noise characteristics differ from channel to channel and are unknown a priori. Formulas for signal distortion and output noise power are developed. The more input channels available containing correlated signal components, the better will be the system performance. Excellent performance is obtained when the sum of the filter input signal-to-noise ratios (SNR's), defined as functions of frequency, is large compared to unity at all frequencies of interest. In this case the output noise is small, the output signal distortion is small, and the output SNR is approximately equal to the sum of the filter input SNR's. As such, the multichannel adaptive signal enhancer is a generalization of the classic time-delay-and-sum beamforming antenna.