Unsupervised ensembling of multiple software sensors with phase synchronization: a robust approach for electrocardiogram-derived respiration.

Objective.We aimed to fuse the outputs of different electrocardiogram-derived respiration (EDR) algorithms to create one higher quality EDR signal.Methods.We viewed each EDR algorithm as a software sensor that recorded breathing activity from a different vantage point, identified high-quality software sensors based on the respiratory signal quality index, aligned the highest-quality EDRs with a phase synchronization technique based on the graph connection Laplacian, and finally fused those aligned, high-quality EDRs. We refer to the output as the sync-ensembled EDR signal. The proposed algorithm was evaluated on two large-scale databases of whole-night polysomnograms. We evaluated the performance of the proposed algorithm using three respiratory signals recorded from different hardware sensors, and compared it with other existing EDR algorithms. A sensitivity analysis was carried out for a total of five cases: fusion by taking the mean of EDR signals, and the four cases of EDR signal alignment without and with synchronization and without and with signal quality selection.Results.The sync-ensembled EDR algorithm outperforms existing EDR algorithms when evaluated by the synchronized correlation (γ-score), optimal transport (OT) distance, and estimated average respiratory rate score, all with statistical significance. The sensitivity analysis shows that the signal quality selection and EDR signal alignment are both critical for the performance, both with statistical significance.Conclusion.The sync-ensembled EDR provides robust respiratory information from electrocardiogram.Significance.Phase synchronization is not only theoretically rigorous but also practical to design a robust EDR.

Parent-child couples display shared neural fingerprints while listening to stories.

Neural fingerprinting is a method to identify individuals from a group of people. Here, we established a new connectome-based identification model and used diffusion maps to show that biological parent-child couples share functional connectivity patterns while listening to stories. These shared fingerprints enabled the identification of children and their biological parents from a group of parents and children. Functional patterns were evident in both cognitive and sensory brain networks. Defining "typical" shared biological parent-child brain patterns may enable predicting or even preventing impaired parent-child connections that develop due to genetic or environmental causes. Finally, we argue that the proposed framework opens new opportunities to link similarities in connectivity patterns to behavioral, psychological, and medical phenomena among other populations. To our knowledge, this is the first study to reveal the neural fingerprint that represents distinct biological parent-child couples.

SORBET: Automated cell-neighborhood analysis of spatial transcriptomics or proteomics for interpretable sample classification via GNN.

Spatially resolved transcriptomics or proteomics data have the potential to contribute fundamental insights into the mechanisms underlying physiologic and pathological processes. However, analysis of these data capable of relating spatial information, multiplexed markers, and their observed phenotypes remains technically challenging. To analyze these relationships, we developed SORBET, a deep learning framework that leverages recent advances in graph neural networks (GNN). We apply SORBET to predict tissue phenotypes, such as response to immunotherapy, across different disease processes and different technologies including both spatial proteomics and transcriptomics methods. Our results show that SORBET accurately learns biologically meaningful relationships across distinct tissue structures and data acquisition methods. Furthermore, we demonstrate that SORBET facilitates understanding of the spatially-resolved biological mechanisms underlying the inferred phenotypes. In sum, our method facilitates mapping between the rich spatial and marker information acquired from spatial 'omics technologies to emergent biological phenotypes. Moreover, we provide novel techniques for identifying the biological processes that comprise the predicted phenotypes.

Enhancing the detection capabilities of nano-avalanches via data-driven classification of acoustic emission signals.

Acoustic emission (AE) is a powerful experimental method for studying discrete and impulsive events termed avalanches that occur in a wide variety of materials and physical phenomena. A particular challenge is the detection of small-scale avalanches, whose associated acoustic signals are at the noise level of the experimental setup. The conventional detection approach is based on setting a threshold significantly larger than this level, ignoring "false" events with low AE amplitudes that originate from noise. At the same time, this approach overlooks small-scale events that might be true and impedes the investigation of avalanches occurring at the nanoscale, constituting the natural response of many nanoparticles and nanostructured materials. In this work, we develop a data-driven method that allows the detection of small-scale AE events, which is based on two propositions. The first includes a modification of the experimental conditions by setting a lower threshold compared to the conventional threshold, such that an abundance of small-scale events with low amplitudes are considered. Second, instead of analyzing several conventional scalar features (e.g., amplitude, duration, energy), we consider the entire waveform of each AE event and obtain an informative representation using dynamic mode decomposition. We apply the developed method to AE signals measured during the compression of platinum nanoparticles and demonstrate a significant enhancement of the detection range toward small-scale events that are below the conventional threshold.

Unsupervised Detection of Sub-Territories of the Subthalamic Nucleus During DBS Surgery With Manifold Learning.

During Deep Brain Stimulation (DBS) surgery for treating Parkinson's disease, detecting the Subthalamic Nucleus (STN) and its sub-territory called the Dorsolateral Oscillatory Region (DLOR) is crucial for adequate clinical outcomes. Currently, the detection is based on human experts, often guided by supervised machine learning detection algorithms. This procedure depends on the knowledge and experience of particular experts and on the amount and quality of the labeled data used for training the machine learning algorithms. In this paper, to circumvent such dependence and the inevitable bias introduced by the training data, we present a data-driven unsupervised algorithm for detecting the STN and the DLOR during DBS surgery based on an agnostic modeling approach. Given measurements, we extract new features and compute a variant of the Mahalanobis distance between these features. We show theoretically that this distance enhances the differences between measurements with different intrinsic characteristics. Incorporating the new features and distance into a manifold learning method, called Diffusion Maps, gives rise to a representation that is consistent with the underlying factors that govern the measurements. Since this representation does not rely on rigid modeling assumptions and is obtained solely from the measurements, it facilitates a broad range of detection tasks; here, we propose a specification for STN and DLOR detection during DBS surgery. We present detection results on 25 sets of measurements recorded from 16 patients during surgery. Compared to a supervised algorithm, our unsupervised method demonstrates similar results in detecting the STN and superior results in detecting the DLOR.

Time-series forecasting using manifold learning, radial basis function interpolation, and geometric harmonics.

We address a three-tier numerical framework based on nonlinear manifold learning for the forecasting of high-dimensional time series, relaxing the "curse of dimensionality" related to the training phase of surrogate/machine learning models. At the first step, we embed the high-dimensional time series into a reduced low-dimensional space using nonlinear manifold learning (local linear embedding and parsimonious diffusion maps). Then, we construct reduced-order surrogate models on the manifold (here, for our illustrations, we used multivariate autoregressive and Gaussian process regression models) to forecast the embedded dynamics. Finally, we solve the pre-image problem, thus lifting the embedded time series back to the original high-dimensional space using radial basis function interpolation and geometric harmonics. The proposed numerical data-driven scheme can also be applied as a reduced-order model procedure for the numerical solution/propagation of the (transient) dynamics of partial differential equations (PDEs). We assess the performance of the proposed scheme via three different families of problems: (a) the forecasting of synthetic time series generated by three simplistic linear and weakly nonlinear stochastic models resembling electroencephalography signals, (b) the prediction/propagation of the solution profiles of a linear parabolic PDE and the Brusselator model (a set of two nonlinear parabolic PDEs), and (c) the forecasting of a real-world data set containing daily time series of ten key foreign exchange rates spanning the time period 3 September 2001-29 October 2020.

The spatiotemporal coupling in delay-coordinates dynamic mode decomposition.

Dynamic mode decomposition (DMD) is a leading tool for equation-free analysis of high-dimensional dynamical systems from observations. In this work, we focus on a combination of DMD and delay-coordinates embedding, which is termed delay-coordinates DMD and is based on augmenting observations from current and past time steps, accommodating the analysis of a broad family of observations. An important utility of DMD is the compact and reduced-order spectral representation of observations in terms of the DMD eigenvalues and modes, where the temporal information is separated from the spatial information. From a spatiotemporal viewpoint, we show that when DMD is applied to delay-coordinates embedding, temporal information is intertwined with spatial information, inducing a particular spectral structure on the DMD components. We formulate and analyze this structure, which we term the spatiotemporal coupling in delay-coordinates DMD. Based on this spatiotemporal coupling, we propose a new method for DMD components selection. When using delay-coordinates DMD that comprises redundant modes, this selection is an essential step for obtaining a compact and reduced-order representation of the observations. We demonstrate our method on noisy simulated signals and various dynamical systems and show superior component selection compared to a commonly used method that relies on the amplitudes of the modes.

Kernel-based parameter estimation of dynamical systems with unknown observation functions.

A low-dimensional dynamical system is observed in an experiment as a high-dimensional signal, for example, a video of a chaotic pendulums system. Assuming that we know the dynamical model up to some unknown parameters, can we estimate the underlying system's parameters by measuring its time-evolution only once? The key information for performing this estimation lies in the temporal inter-dependencies between the signal and the model. We propose a kernel-based score to compare these dependencies. Our score generalizes a maximum likelihood estimator for a linear model to a general nonlinear setting in an unknown feature space. We estimate the system's underlying parameters by maximizing the proposed score. We demonstrate the accuracy and efficiency of the method using two chaotic dynamical systems-the double pendulum and the Lorenz '63 model.

Graph of graphs analysis for multiplexed data with application to imaging mass cytometry.

Imaging Mass Cytometry (IMC) combines laser ablation and mass spectrometry to quantitate metal-conjugated primary antibodies incubated in intact tumor tissue slides. This strategy allows spatially-resolved multiplexing of dozens of simultaneous protein targets with 1µm resolution. Each slide is a spatial assay consisting of high-dimensional multivariate observations (m-dimensional feature space) collected at different spatial positions and capturing data from a single biological sample or even representative spots from multiple samples when using tissue microarrays. Often, each of these spatial assays could be characterized by several regions of interest (ROIs). To extract meaningful information from the multi-dimensional observations recorded at different ROIs across different assays, we propose to analyze such datasets using a two-step graph-based approach. We first construct for each ROI a graph representing the interactions between the m covariates and compute an m dimensional vector characterizing the steady state distribution among features. We then use all these m-dimensional vectors to construct a graph between the ROIs from all assays. This second graph is subjected to a nonlinear dimension reduction analysis, retrieving the intrinsic geometric representation of the ROIs. Such a representation provides the foundation for efficient and accurate organization of the different ROIs that correlates with their phenotypes. Theoretically, we show that when the ROIs have a particular bi-modal distribution, the new representation gives rise to a better distinction between the two modalities compared to the maximum a posteriori (MAP) estimator. We applied our method to predict the sensitivity to PD-1 axis blockers treatment of lung cancer subjects based on IMC data, achieving 97.3% average accuracy on two IMC datasets. This serves as empirical evidence that the graph of graphs approach enables us to integrate multiple ROIs and the intra-relationships between the features at each ROI, giving rise to an informative representation that is strongly associated with the phenotypic state of the entire image.

Identifying Topological Phase Transitions in Experiments Using Manifold Learning.

We demonstrate the identification of topological phase transitions from experimental data using diffusion maps: a nonlocal unsupervised machine learning method. We analyze experimental data from an optical system undergoing a topological phase transition and demonstrate the ability of this approach to identify topological phase transitions even when the data originates from a small part of the system, and does not even include edge states.

Cell-Type-Specific Outcome Representation in the Primary Motor Cortex.

Adaptive movements are critical for animal survival. To guide future actions, the brain monitors various outcomes, including achievement of movement and appetitive goals. The nature of these outcome signals and their neuronal and network realization in the motor cortex (M1), which directs skilled movements, is largely unknown. Using a dexterity task, calcium imaging, optogenetic perturbations, and behavioral manipulations, we studied outcome signals in the murine forelimb M1. We found two populations of layer 2-3 neurons, termed success- and failure-related neurons, that develop with training, and report end results of trials. In these neurons, prolonged responses were recorded after success or failure trials independent of reward and kinematics. In addition, the initial state of layer 5 pyramidal tract neurons contained a memory trace of the previous trial's outcome. Intertrial cortical activity was needed to learn new task requirements. These M1 layer-specific performance outcome signals may support reinforcement motor learning of skilled behavior.

Layer- and Cell-Specific Recruitment Dynamics during Epileptic Seizures In Vivo.

OBJECTIVE: To investigate the network dynamics mechanisms underlying differential initiation of epileptic interictal spikes and seizures. METHODS: We performed combined in vivo 2-photon calcium imaging from different targeted neuronal subpopulations and extracellular electrophysiological recordings during 4-aminopyridine-induced neocortical spikes and seizures. RESULTS: Both spikes and seizures were associated with intense synchronized activation of excitatory layer 2/3 pyramidal neurons (PNs) and to a lesser degree layer 4 neurons, as well as inhibitory parvalbumin-expressing interneurons (INs). In sharp contrast, layer 5 PNs and somatostatin-expressing INs were gradually and asynchronously recruited into the ictal activity during the course of seizures. Within layer 2/3, the main difference between onset of spikes and seizures lay in the relative recruitment dynamics of excitatory PNs compared to parvalbumin- and somatostatin-expressing inhibitory INs. Whereas spikes exhibited balanced recruitment of PNs and parvalbumin-expressing INs, during seizures IN responses were reduced and less synchronized than in layer 2/3 PNs. Similar imbalance was not observed in layers 4 or 5 of the neocortex. Machine learning-based algorithms we developed were able to distinguish spikes from seizures based solely on activation dynamics of layer 2/3 PNs at discharge onset. INTERPRETATION: During onset of seizures, the recruitment dynamics markedly differed between neuronal subpopulations, with rapid synchronous recruitment of layer 2/3 PNs, layer 4 neurons, and parvalbumin-expressing INs and gradual asynchronous recruitment of layer 5 PNs and somatostatin-expressing INs. Seizures initiated in layer 2/3 due to a dynamic mismatch between local PNs and inhibitory INs, and only later spread to layer 5 by gradually and asynchronously recruiting PNs in this layer. ANN NEUROL 2020;87:97-115.

Data-Driven Tree Transforms and Metrics.

We consider the analysis of high dimensional data given in the form of a matrix with columns consisting of observations and rows consisting of features. Often the data is such that the observations do not reside on a regular grid, and the given order of the features is arbitrary and does not convey a notion of locality. Therefore, traditional transforms and metrics cannot be used for data organization and analysis. In this paper, our goal is to organize the data by defining an appropriate representation and metric such that they respect the smoothness and structure underlying the data. We also aim to generalize the joint clustering of observations and features in the case the data does not fall into clear disjoint groups. For this purpose, we propose multiscale data-driven transforms and metrics based on trees. Their construction is implemented in an iterative refinement procedure that exploits the co-dependencies between features and observations. Beyond the organization of a single dataset, our approach enables us to transfer the organization learned from one dataset to another and to integrate several datasets together. We present an application to breast cancer gene expression analysis: learning metrics on the genes to cluster the tumor samples into cancer sub-types and validating the joint organization of both the genes and the samples. We demonstrate that using our approach to combine information from multiple gene expression cohorts, acquired by different profiling technologies, improves the clustering of tumor samples.

An Emergent Space for Distributed Data with Hidden Internal Order through Manifold Learning.

Manifold-learning techniques are routinely used in mining complex spatiotemporal data to extract useful, parsimonious data representations/parametrizations; these are, in turn, useful in nonlinear model identification tasks. We focus here on the case of time series data that can ultimately be modelled as a spatially distributed system (e.g. a partial differential equation, PDE), but where we do not know the space in which this PDE should be formulated. Hence, even the spatial coordinates for the distributed system themselves need to be identified - to "emerge from"-the data mining process. We will first validate this "emergent space" reconstruction for time series sampled without space labels in known PDEs; this brings up the issue of observability of physical space from temporal observation data, and the transition from spatially resolved to lumped (order-parameter-based) representations by tuning the scale of the data mining kernels. We will then present actual emergent space "discovery" illustrations. Our illustrative examples include chimera states (states of coexisting coherent and incoherent dynamics), and chaotic as well as quasiperiodic spatiotemporal dynamics, arising in partial differential equations and/or in heterogeneous networks. We also discuss how data-driven "spatial" coordinates can be extracted in ways invariant to the nature of the measuring instrument. Such gauge-invariant data mining can go beyond the fusion of heterogeneous observations of the same system, to the possible matching of apparently different systems. For an older version of this article, including other examples, see https://arxiv.org/abs/1708.05406.

Data-driven Evolution Equation Reconstruction for Parameter-Dependent Nonlinear Dynamical Systems.

When studying observations of chemical reaction dynamics, closed form equations based on a putative mechanism may not be available. Yet when sufficient data from experimental observations can be obtained, even without knowing what exactly the physical meaning of the parameter settings or recorded variables are, data-driven methods can be used to construct minimal (and in a sense, robust) realizations of the system. The approach attempts, in a sense, to circumvent physical understanding, by building intrinsic "information geometries" of the observed data, and thus enabling prediction without physical/chemical knowledge. Here we use such an approach to obtain evolution equations for a data-driven realization of the original system - in effect, allowing prediction based on the informed interrogation of the agnostically organized observation database. We illustrate the approach on observations of (a) the normal form for the cusp singularity, (b) a cusp singularity for the nonisothermal CSTR, and (c) a random invertible transformation of the nonisothermal CSTR, showing that one can predict even when the observables are not "simply explainable" physical quantities. We discuss current limitations and possible extensions of the procedure.

Reconstruction of normal forms by learning informed observation geometries from data.

The discovery of physical laws consistent with empirical observations is at the heart of (applied) science and engineering. These laws typically take the form of nonlinear differential equations depending on parameters; dynamical systems theory provides, through the appropriate normal forms, an "intrinsic" prototypical characterization of the types of dynamical regimes accessible to a given model. Using an implementation of data-informed geometry learning, we directly reconstruct the relevant "normal forms": a quantitative mapping from empirical observations to prototypical realizations of the underlying dynamics. Interestingly, the state variables and the parameters of these realizations are inferred from the empirical observations; without prior knowledge or understanding, they parametrize the dynamics intrinsically without explicit reference to fundamental physical quantities.

Assess sleep stage by modern signal processing techniques.

In this paper, two modern adaptive signal processing techniques, empirical intrinsic geometry and synchrosqueezing transform, are applied to quantify different dynamical features of the respiratory and electroencephalographic signals. We show that the proposed features are theoretically rigorously supported, as well as capture the sleep information hidden inside the signals. The features are used as input to multiclass support vector machines with the radial basis function to automatically classify sleep stages. The effectiveness of the classification based on the proposed features is shown to be comparable to human expert classification-the proposed classification of awake, REM, N1, N2, and N3 sleeping stages based on the respiratory signal (resp. respiratory and EEG signals) has the overall accuracy 81.7% (resp. 89.3%) in the relatively normal subject group. In addition, by examining the combination of the respiratory signal with the electroencephalographic signal, we conclude that the respiratory signal consists of ample sleep information, which supplements to the information stored in the electroencephalographic signal.

Nonlinear intrinsic variables and state reconstruction in multiscale simulations.

Finding informative low-dimensional descriptions of high-dimensional simulation data (like the ones arising in molecular dynamics or kinetic Monte Carlo simulations of physical and chemical processes) is crucial to understanding physical phenomena, and can also dramatically assist in accelerating the simulations themselves. In this paper, we discuss and illustrate the use of nonlinear intrinsic variables (NIV) in the mining of high-dimensional multiscale simulation data. In particular, we focus on the way NIV allows us to functionally merge different simulation ensembles, and different partial observations of these ensembles, as well as to infer variables not explicitly measured. The approach relies on certain simple features of the underlying process variability to filter out measurement noise and systematically recover a unique reference coordinate frame. We illustrate the approach through two distinct sets of atomistic simulations: a stochastic simulation of an enzyme reaction network exhibiting both fast and slow time scales, and a molecular dynamics simulation of alanine dipeptide in explicit water.

Identifying preseizure state in intracranial EEG data using diffusion kernels.

The goal of this study is to identify preseizure changes in intracranial EEG (icEEG). A novel approach based on the recently developed diffusion map framework, which is considered to be one of the leading manifold learning methods, is proposed. Diffusion mapping provides dimensionality reduction of the data as well as pattern recognition that can be used to distinguish different states of the patient, for example, interictal and preseizure. A new algorithm, which is an extension of diffusion maps, is developed to construct coordinates that generate efficient geometric representations of the complex structures in the icEEG data. In addition, this method is adapted to the icEEG data and enables the extraction of the underlying brain activity. The algorithm is tested on icEEG data recorded from several electrode contacts from a patient being evaluated for possible epilepsy surgery at the Yale-New Haven Hospital. Numerical results show that the proposed approach provides a distinction between interictal and preseizure states.

Empirical intrinsic geometry for nonlinear modeling and time series filtering.

In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization.