Using state space differential geometry for nonlinear blind source separation

Given a time series of multicomponent measurements of an evolving stimulus, nonlinear blind source separation (BSS) seeks to find a "source" time series, comprised of statistically independent combinations of the measured components. In this paper, we seek a source time series with local velocity cross correlations that vanish everywhere in stimulus state space. However, in an earlier paper the local velocity correlation matrix was shown to constitute a metric on state space. Therefore, nonlinear BSS maps onto a problem of differential geometry: given the metric observed in the measurement coordinate system, find another coordinate system in which the metric is diagonal everywhere. We show how to determine if the observed data are separable in this way, and, if they are, we show how to construct the required transformation to the source coordinate system, which is essentially unique except for an unknown rotation that can be found by applying the methods of linear BSS. Thus, the proposed technique solves nonlinear BSS in many situations or, at least, reduces it to linear BSS, without the use of probabilistic, parametric, or iterative procedures. This paper also describes a generalization of this methodology that performs nonlinear independent subspace separation. In every case, the resulting decomposition of the observed data is an intrinsic property of the stimulus' evolution in the sense that it does not depend on the way the observer chooses to view it (e.g., the choice of the observing machine's sensors). In other words, the decomposition is a property of the evolution of the "real" stimulus that is "out there" broadcasting energy to the observer. The technique is illustrated with analytic and numerical examples.Comment: Contains 14 pages and 3 figures. For related papers, see http://www.geocities.com/dlevin2001/ . New version is identical to original version except for URL in the bylin

Non-Redundant Spectral Dimensionality Reduction

Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known as the "repeated Eigen-directions" phenomenon. That is, many of the embedding coordinates they produce typically capture the same direction along the data manifold. This leads to redundant and inefficient representations that do not reveal the true intrinsic dimensionality of the data. In this paper, we propose a general method for avoiding redundancy in spectral algorithms. Our approach relies on replacing the orthogonality constraints underlying those methods by unpredictability constraints. Specifically, we require that each embedding coordinate be unpredictable (in the statistical sense) from all previous ones. We prove that these constraints necessarily prevent redundancy, and provide a simple technique to incorporate them into existing methods. As we illustrate on challenging high-dimensional scenarios, our approach produces significantly more informative and compact representations, which improve visualization and classification tasks

What's in a score:A longitudinal investigation of scores based on item response theory and classical test theory for the Amsterdam Instrumental Activities of Daily Living Questionnaire in cognitively normal and impaired older adults

OBJECTIVE:We aimed to investigate whether item response theory (IRT)-based scoring allows for a more accurate, responsive, and less biased assessment of everyday functioning than traditional classical test theory (CTT)-based scoring, as measured with the Amsterdam Instrumental Activities of Daily Living Questionnaire. METHOD: In this longitudinal multicenter study including cognitively normal and impaired individuals, we examined IRT-based and CTT-based score distributions and differences between diagnostic groups using linear regressions, and investigated scale attenuation. We compared change over time between scoring methods using linear mixed models with random intercepts and slopes for time.RESULTS: Two thousand two hundred ninety-four participants were included (66.6 ± 7.7 years, 54% female): n = 2,032 (89%) with normal cognition, n = 93 (4%) with subjective cognitive decline, n = 79 (3%) with mild cognitive impairment, and n = 91 (4%) with dementia. At baseline, IRT-based and CTT-based scores were highly correlated (r = -0.92). IRT-based scores showed less scale attenuation than CTT-based scores. In a subsample of n = 1,145 (62%) who were followed for a mean of 1.3 (SD = 0.6) years, IRT-based scores declined significantly among cognitively normal individuals (unstandardized coefficient [B] = -0.15, 95% confidence interval, 95% CI [-0.28, -0.03], effect size = -0.02), whereas CTT-based scores did not (B = 0.20, 95% CI [-0.02, 0.41], effect size = 0.02). In the other diagnostic groups, effect sizes of change over time were similar. CONCLUSIONS: IRT-based scores were less affected by scale attenuation than CTT-based scores. With regard to responsiveness, IRT-based scores showed more signal than CTT-based scores in early disease stages, highlighting the IRT-based scores' superior suitability for use in preclinical populations. (PsycInfo Database Record (c) 2023 APA, all rights reserved).</p

An Introduction to EEG Source Analysis with an illustration of a study on Error-Related Potentials

International audienceOver the last twenty years blind source separation (BSS) has become a fundamental signal processing tool in the study of human electroencephalography (EEG), other biological data, as well as in many other signal processing domains such as speech, images, geophysics and wireless communication (Comon and Jutten, 2010). Without relying on head modeling BSS aims at estimating both the waveform and the scalp spatial pattern of the intracranial dipolar current responsible of the observed EEG, increasing the sensitivity and specificity of the signal received from the electrodes on the scalp. This chapter begins with a short review of brain volume conduction theory, demonstrating that BSS modeling is grounded on current physiological knowledge. We then illustrate a general BSS scheme requiring the estimation of second-order statistics (SOS) only. A simple and efficient implementation based on the approximate joint diagonalization of covariance matrices (AJDC) is described. The method operates in the same way in the time or frequency domain (or both at the same time) and is capable of modeling explicitly physiological and experimental source of variations with remarkable flexibility. Finally, we provide a specific example illustrating the analysis of a new experimental study on error-related potentials

Selection and characterisation of a phage-displayed human antibody (Fab) reactive to the lung resistance-related major vault protein

The major vault protein is the main component on multimeric vault particles, that are likely to play an essential role in normal cell physiology and to be associated with multidrug resistance of tumour cells. In order to unravel the function of vaults and their putative contribution to multidrug resistance, specific antibodies are invaluable tools. Until now, only conventional major vault protein-reactive murine monoclonal antibodies have been generated, that are most suitable for immunohistochemical analyses. The phage display method allows for selection of human antibody fragments with potential use in clinical applications. Furthermore, cDNA sequences encoding selected antibody fragments are readily identified, facilitating various molecular targeting approaches. In order to obtain such human Fab fragments recognising major vault protein we used a large non-immunized human Fab fragment phage library. Phages displaying major vault protein-reactive Fabs were obtained through several rounds of selection on major vault protein-coated immunotubes and subsequent amplification in TG1 E coli bacteria. Eventually, one major vault protein-reactive clone was selected and further examined. The anti-major vault protein Fab was found suitable for immunohistochemical and Western blot analysis of tumour cell lines and human tissues. BIAcore analysis showed that the binding affinity of the major vault protein-reactive clone almost equalled that of the murine anti-major vault protein Mabs. The cDNA sequence of this human Fab may be exploited to generate an intrabody for major vault protein-knock out studies. Thus, this human Fab fragment should provide a valuable tool in elucidating the contribution(s) of major vault protein/vaults to normal physiology and cellular drug resistance mechanisms

Prevalence of abnormal Alzheimer’s disease biomarkers in patients with subjective cognitive decline: cross-sectional comparison of three European memory clinic samples

Introduction: Subjective cognitive decline (SCD) in cognitively unimpaired older individuals has been recognized as an early clinical at-risk state for Alzheimer's disease (AD) dementia and as a target population for future dementia prevention trials. Currently, however, SCD is heterogeneously defined across studies, potentially leading to variations in the prevalence of AD pathology. Here, we compared the prevalence and identified common determinants of abnormal AD biomarkers in SCD across three European memory clinics participating in the European initiative on harmonization of SCD in preclinical AD (Euro-SCD). Methods: We included three memory clinic SCD samples with available cerebrospinal fluid (CSF) biomaterial (IDIBAPS, Barcelona, Spain, n = 44; Amsterdam Dementia Cohort (ADC), The Netherlands, n = 50; DELCODE multicenter study, Germany, n = 42). CSF biomarkers (amyloid beta (Aβ)42, tau, and phosphorylated tau (ptau181)) were centrally analyzed in Amsterdam using prespecified cutoffs to define prevalence of pathological biomarker concentrations. We used logistic regression analysis in the combined sample across the three centers to investigate center effects with regard to likelihood of biomarker abnormality while taking potential common predictors (e.g., age, sex, apolipoprotein E (APOE) status, subtle cognitive deficits, depressive symptoms) into account. Results: The prevalence of abnormal Aβ42, but not tau or ptau181, levels was different across centers (64% DELCODE, 57% IDIBAPS, 22% ADC; p < 0.001). Logistic regression analysis revealed that the likelihood of abnormal Aβ42 (and also abnormal tau or ptau181) levels was predicted by age and APOE status. For Aβ42 abnormality, we additionally observed a center effect, indicating between-center heterogeneity not explained by age, APOE, or the other included covariates. Conclusions: While heterogeneous frequency of abnormal Aβ42 was partly explained by between-sample differences in age range and APOE status, the additional observation of center effects indicates between-center heterogeneity that may be attributed to different recruitment procedures. These findings highlight the need for the development of harmonized recruitment protocols for SCD case definition in multinational studies to achieve similar enrichment rates of preclinical AD