Tensorial Independent Component Analysis Research Articles

Tensorial independent component analysis reveals social and reward networks associated with major depressive disorder.

Major depressive disorder (MDD) has been associated with changes in functional brain connectivity. Yet, typical analyses of functional connectivity, such as spatial independent components analysis (ICA) for resting-state data, often ignore sources of between-subject variability, which may be crucial for identifying functional connectivity patterns associated with MDD. Typically, methods like spatial ICA will identify a single component to represent a network like the default mode network (DMN), even if groups within the data show differential DMN coactivation. To address this gap, this project applies a tensorial extension of ICA (tensorial ICA)-which explicitly incorporates between-subject variability-to identify functionally connected networks using functional MRI data from the Human Connectome Project (HCP). Data from the HCP included individuals with a diagnosis of MDD, a family history of MDD, and healthy controls performing a gambling and social cognition task. Based on evidence associating MDD with blunted neural activation to rewards and social stimuli, we predicted that tensorial ICA would identify networks associated with reduced spatiotemporal coherence and blunted social and reward-based network activity in MDD. Across both tasks, tensorial ICA identified three networks showing decreased coherence in MDD. All three networks included ventromedial prefrontal cortex, striatum, and cerebellum and showed different activation across the conditions of their respective tasks. However, MDD was only associated with differences in task-based activation in one network from the social task. Additionally, these results suggest that tensorial ICA could be a valuable tool for understanding clinical differences in relation to network activation and connectivity.

The Artificial Microscope

Optical microscopy demonstrated an incredible power and ability in producing large data set originated from biological samples by light interrogation and tunable in terms of spatial at temporal resolution down to the nano- and pico- scale, respectively. Such a data set is the core for developing an artificial microscope aiming to transform a label-free interrogation of the sample into a molecular-rich fluorescence-based image. The intelligent artificial microscope is AI-guided through a computational core based on three modules based on a convolutional neural network (CNN) and a tensor independent component analysis (tICA) un-supervised machine learning within a supervised deep learning strategy having the ambitious target to create a robust virtual environment "to see "what we could not perceive before". An interesting case study is related to understanding the visualisation of chromatin organisation.

Higher-Order Tensor Independent Component Analysis for MIMO Remote Sensing of Respiration and Heartbeat Signals

This paper proposes a novel method of independent component analysis (ICA), which we name higher-order tensor ICA (HOT-ICA). We newly develop a robust microwave multiple-input multiple-output (MIMO) radar system, in which HOT-ICA performs separation of multiple-target signals to detect respiration and heartbeat. In comparison with millimeter waves, microwaves spread wider with diffraction and propagate even in an environment with obstacles to reach targets. However, it often requires more powerful signal separation because of its lower resolution. HOT-ICA realizes high robustness in self-organization of a separation tensor by utilizing channel information, i.e., the information of physical-measurement circumstances concerning, e.g., which transmitting/receiving antennas are used. In numerical and living-human experiments, our HOT-ICA system effectively separates the bio-signals successfully even in an obstacle-affecting environment, which has been a difficult task. The results demonstrate the significance of HOT-ICA in remote sensing. It fully utilizes the high dimensionality of the separation tensor by keeping the tensor structure unchanged to take advantage of the measurement-circumstances information.

Coupled canonical polyadic decomposition of multi-group fMRI data with spatial reference and orthonormality constraints

Multi-group fMRI data may possess different types of subjects, tasks, scans, etc. Fortunately, coupled canonical polyadic decomposition (CCPD) requires multiple tensor datasets to share one or more factor matrices. Considering that spatial variability is generally smaller than temporal variability, we attempt CCPD to decompose multi-group fMRI data into shared spatial maps (SMs), group-specific time courses (TCs) and subject intensities. As spatial references of interested components are generally available and the spatial orthonormality can reduce crosstalk among components, we propose a novel CCPD by adding spatial reference and orthonormality constraints. Specifically, based on accelerated alternating least squares, we further update shared SMs twice: 1) we orthonormalize shared SM components by orthogonal Procrustes solution; 2) after identifying the interested components by maximizing Pearson correlation coefficients between shared SMs and spatial references, we update interested shared SMs by minimizing the square error between magnitude part of normalized shared SMs and corresponding normalized spatial references. The results of two-group simulated and experimental task-related fMRI data as well as resting-state fMRI data with 24 healthy controls (HCs) and 24 schizophrenia patients (SZs) all show outperformed performance for the proposed method compared with unconstrained CCPD, CCPD with a spatial orthonormality constraint, widely-used tensor independent component analysis (ICA) and semi-blind group information guide ICA in both magnitude-only analysis and complex-valued analysis. Moreover, by using AdaBoost, resting-state group-specific TCs estimated by the proposed method significantly exhibit larger group differences, especially for the sensorimotor network, and thus provide a potential biomarker for schizophrenia.

Modulation of cortical resting state functional connectivity during a visuospatial attention task in Parkinson's disease.

Visual dysfunction is a recognized early symptom of Parkinson's disease (PD) that partly scales motor symptoms, yet its background is heterogeneous. With additional deficits in visuospatial attention, the two systems are hard to disentangle and it is not known whether impaired functional connectivity in the visual cortex is translative in nature or disrupted attentional modulation also contributes. In this study, we investigate functional connectivity modulation during a visuospatial attention task in patients with PD. In total, 15 PD and 16 age-matched healthy controls performed a visuospatial attention task while undergoing fMRI, in addition to a resting-state fMRI scan. Tensorial independent component analysis was used to investigate task-related network activity patterns. Independently, an atlas-based connectivity modulation analysis was performed using the task potency method. Spearman's rank correlation was calculated between task-related network expression, connectivity modulation, and clinical characteristics. Task-related networks including mostly visual, parietal, and prefrontal cortices were expressed to a significantly lesser degree in patients with PD (p < 0.027). Resting-state functional connectivity did not differ between the healthy and diseased cohorts. Connectivity between the precuneus and ventromedial prefrontal cortex was modulated to a higher degree in patients with PD (p < 0.004), while connections between the posterior parietal cortex and primary visual cortex, and also the superior frontal gyrus and opercular cortex were modulated to a lesser degree (p < 0.001 and p < 0.011). Task-related network expression and superior frontal gyrus–opercular cortex connectivity modulation were significantly associated with UPDRSIII motor scores and the Hoehn–Yahr stages (R = −0.72, p < 0.006 and R = −0.90, p < 0.001; R = −0.68, p < 0.01 and R = −0.71, p < 0.007). Task-related networks function differently in patients with PD in association with motor symptoms, whereas impaired modulation of visual and default-mode network connectivity was not correlated with motor function.

Proposal of higher-order tensor independent component analysis for signal separation in multiple-input multiple-output respiration/heartbeat remote sensing.

This paper proposes higher-order tensor independent component analysis (HOT-ICA). HOT-ICA is a tensor ICA that makes effective use of the relationships among the axes of a separating tensor. We deal with multiple-target signal separation in a multiple-input multiple-output (MIMO) radar system to detect respiration and heartbeat. Numerical physical experiments demonstrate the significance of the HOT-ICA which keeps the tensor structure unchanged to fully utilizes the high-dimensionality of the separation tensor.

Altered brain network function during attention-modulated visual processing in multiple sclerosis

Background: Multiple sclerosis may damage cognitive performance in several domains, including attention. Although attention network deficits were described during rest, studies that investigate their function during task performance are scarce. Objective: To investigate connectivity within and between task-related networks in multiple sclerosis during a visual attention task as a function of cognitive performance. Methods: A total of 23 relapsing-remitting multiple sclerosis (RRMS) patients and 29 healthy controls underwent task-functional magnetic resonance imaging (fMRI) scans using a visual attention paradigm on a 3T scanner. Scans were analysed using tensor-independent component analysis (TICA). Functional connectivity was calculated within and between components. We assessed cognitive function with the Brief International Cognitive Assessment for MS (BICAMS) battery. Results: TICA extracted components related to visual processing, attention, executive function and the default-mode network. Subject scores of visual/attention-related and executive components were greater in healthy controls (p < 0.032, p < 0.023). Connectivity between visual/attention-related and default-mode components was higher in patients (p < 0.043), correlating with Brief Visuospatial Memory Test–Revised (BVMT-R) scores (R = −0.48, p < 0.036). Patients showed reduced connectivity between the right intraparietal sulcus (rIPS) and frontal eye field (rFEF), and bilateral frontal eye fields (p < 0.012, p < 0.003). Reduced rIPS-rFEF connectivity came with lower Symbol Digit Modalities Test (SDMT)/BVMT-R scores in patients (R = 0.53, p < 0.02, R = 0.46, p < 0.049). Conclusion: Attention-related networks show altered connectivity during task performance in RRMS patients, scaling with cognitive disability.

Fast tensorial JADE.

We propose a novel method for tensorial‐independent component analysis. Our approach is based on TJADE and k‐JADE, two recently proposed generalizations of the classical JADE algorithm. Our novel method achieves the consistency and the limiting distribution of TJADE under mild assumptions and at the same time offers notable improvement in computational speed. Detailed mathematical proofs of the statistical properties of our method are given and, as a special case, a conjecture on the properties of k‐JADE is resolved. Simulations and timing comparisons demonstrate remarkable gain in speed. Moreover, the desired efficiency is obtained approximately for finite samples. The method is applied successfully to large‐scale video data, for which neither TJADE nor k‐JADE is feasible. Finally, an experimental procedure is proposed to select the values of a set of tuning parameters. Supplementary material including the R‐code for running the examples and the proofs of the theoretical results is available online.

Data-driven tensor independent component analysis for model-based connectivity neurofeedback

Neurofeedback based on real-time functional MRI is an emerging technique to train voluntary control over brain activity in healthy and disease states. Recent developments even allow for training of brain networks using connectivity feedback based on dynamic causal modeling (DCM). DCM is an influential hypothesis-driven approach that requires prior knowledge about the target brain network dynamics and the modulatory influences. Data-driven approaches, such as tensor independent component analysis (ICA), can reveal spatiotemporal patterns of brain activity without prior assumptions. Tensor ICA allows flexible data decomposition and extraction of components consisting of spatial maps, time-series, and session/subject-specific weights, which can be used to characterize individual neurofeedback regulation per regulation trial, run, or session. In this study, we aimed to better understand the spatiotemporal brain patterns involved and affected by model-based feedback regulation using data-driven tensor ICA. We found that task-specific spatiotemporal brain patterns obtained using tensor ICA were highly consistent with model-based feedback estimates. However, we found that the DCM approach captured specific network interdependencies that went beyond what could be detected with either general linear model (GLM) or ICA approaches. We also found that neurofeedback-guided regulation resulted in activity changes that were characteristic of the mental strategies used to control the feedback signal, and that these activity changes were not limited to periods of active self-regulation, but were also evident in distinct gradual recovery processes during subsequent rest periods. Complementary data-driven and model-based approaches could aid in interpretation of the neurofeedback data when applied post-hoc, and in the definition of the target brain area/pattern/network/model prior to the neurofeedback training study when applied to the pilot data. Systematically investigating the triad of mental effort, spatiotemporal brain network changes, and activity and recovery processes might lead to a better understanding of how learning with neurofeedback is accomplished, and how such learning can cause plastic brain changes along with specific behavioral effects.

Tensorial blind source separation for improved analysis of multi-omic data

There is an increased need for integrative analyses of multi-omic data. We present and benchmark a novel tensorial independent component analysis (tICA) algorithm against current state-of-the-art methods. We find that tICA outperforms competing methods in identifying biological sources of data variation at a reduced computational cost. On epigenetic data, tICA can identify methylation quantitative trait loci at high sensitivity. In the cancer context, tICA identifies gene modules whose expression variation across tumours is driven by copy-number or DNA methylation changes, but whose deregulation relative to normal tissue is independent of such alterations, a result we validate by direct analysis of individual data types.

Olfactory fMRI: Implications of Stimulation Length and Repetition Time

Studying olfaction with functional magnetic resonance imaging (fMRI) poses various methodological challenges. This study aimed to investigate the effects of stimulation length and repetition time (TR) on the activation pattern of 4 olfactory brain regions: the anterior and the posterior piriform cortex, the orbitofrontal cortex, and the insula. Twenty-two healthy participants with normal olfaction were examined with fMRI, with 2 stimulation lengths (6 s and 15 s) and 2 TRs (0.901 s and 1.34 s). Data were analyzed using General Linear Model (GLM), Tensorial Independent Component Analysis (TICA), and by plotting the event-related time course of brain activation in the 4 olfactory regions of interest. The statistical analysis of the time courses revealed that short TR was associated with more pronounced signal increase and short stimulation was associated with shorter time to peak signal. Additionally, both long stimulation and short TR were associated with oscillatory time courses, whereas both short stimulation and short TR resulted in more typical time courses. GLM analysis showed that the combination of short stimulation and short TR could result in visually larger activation within these olfactory areas. TICA validated that the tested paradigm was spatially and temporally associated with a functionally connected network that included all 4 olfactory regions. In conclusion, the combination of short stimulation and short TR is associated with higher signal increase and shorter time to peak, making it more amenable to standard GLM-type analyses than long stimulation and long TR, and it should, thus, be preferable for olfactory fMRI.

Caffeine impact on working memory-related network activation patterns in early stages of cognitive decline

Recent evidence indicates that caffeine may have a beneficial effect on cognitive decline and dementia. The current investigation assessed the effect of acute caffeine administration on working memory during the earliest stage of cognitive decline in elderly participants. The study includes consecutive 45 elderly controls and 18 individuals with mild cognitive impairment (MCI, 71.6±4.7years, 7 females). During neuropsychological follow-up at 18months, 24 controls remained stable (sCON, 70.0±4.3years, 11 women), while the remaining 21 showed subtle cognitive deterioration (dCON, 73.4±5.9years, 14 women). All participants underwent an established 2-back working task in a crossover design of 200mg caffeine versus placebo. Data analysis included task-related general linear model and functional connectivity tensorial independent component analysis. Working memory behavioral performances did not differ between sCON and dCON, while MCI was slower and less accurate than both control groups (p<0.05). The dCON group had a less pronounced effect of acute caffeine administration essentially restricted to the right hemisphere (p<0.05 corrected) and reduced default mode network (DMN) deactivation compared to sCON (p<0.01 corrected). dCON cases are characterized by decreased sensitivity to caffeine effects on brain activation and DMN deactivation. These complex fMRI patterns possibly reflect the instable status of these cases with intact behavioral performances despite already existing functional alterations in neocortical circuits.

Motor Recovery After Subcortical Stroke Depends on Modulation of Extant Motor Networks.

Stroke is the leading cause of long-term disability. Functional imaging studies report widespread changes in movement-related cortical networks after stroke. Whether these are a result of stroke-specific cognitive processes or reflect modulation of existing movement-related networks is unknown. Understanding this distinction is critical in establishing more effective restorative therapies after stroke. Using multivariate analysis (tensor-independent component analysis - TICA), we map the neural networks involved during motor imagery (MI) and executed movement (EM) in subcortical stroke patients and age-matched controls. Twenty subcortical stroke patients and 17 age-matched controls were recruited. They were screened for their ability to carry out MI (Chaotic MI Assessment). The fMRI task was a right-hand finger-thumb opposition sequence (auditory-paced 1 Hz; 2, 3, 4, 5, 2…). Two separate runs were acquired (MI and rest and EM and rest; block design). There was no distinction between groups or tasks until the last stage of analysis, which allowed TICA to identify independent components (ICs) that were common or distinct to each group or task with no prior assumptions. TICA defined 28 ICs. ICs representing artifacts were excluded. ICs were only included if the subject scores were significant (for either EM or MI). Seven ICs remained that involved the primary and secondary motor networks. All ICs were shared between the stroke and age-matched controls. Five ICs were common to both tasks and three were exclusive to EM. Two ICs were related to motor recovery and one with time since stroke onset, but all were shared with age-matched controls. No IC was exclusive to stroke patients. We report that the cortical networks in stroke patients that relate to recovery of motor function represent modulation of existing cortical networks present in age-matched controls. The absence of cortical networks specific to stroke patients suggests that motor adaptation and other potential confounders (e.g., effort and additional muscle use) are not responsible for the changes in the cortical networks reported after stroke. This highlights that recovery of motor function after subcortical stroke involves preexisting cortical networks that could help identify more effective restorative therapies.

White Matter Connectivity of the Thalamus Delineates the Functional Architecture of Competing Thalamocortical Systems.

There is an increasing awareness of the involvement of thalamic connectivity on higher level cortical functioning in the human brain. This is reflected by the influence of thalamic stimulation on cortical activity and behavior as well as apparently cortical lesion syndromes occurring as a function of small thalamic insults. Here, we attempt to noninvasively test the correspondence of structural and functional connectivity of the human thalamus using diffusion-weighted and resting-state functional MRI. Using a large sample of 102 adults, we apply tensor independent component analysis to diffusion MRI tractography data to blindly parcellate bilateral thalamus according to diffusion tractography-defined structural connectivity. Using resting-state functional MRI collected in the same subjects, we show that the resulting structurally defined thalamic regions map to spatially distinct, and anatomically predictable, whole-brain functional networks in the same subjects. Although there was significant variability in the functional connectivity patterns, the resulting 51 structural and functional patterns could broadly be reduced to a subset of 7 similar core network types. These networks were distinct from typical cortical resting-state networks. Importantly, these networks were distributed across the brain and, in a subset, map extremely well to known thalamocortico-basal-ganglial loops.

Relationship between working‐memory network function and substance use: a 3‐year longitudinal fMRI study in heavy cannabis users and controls

Deficient executive functions play an important role in the development of addiction. Working-memory may therefore be a powerful predictor of the course of drug use, but chronic substance use may also impair working-memory. The aim of this 3-year longitudinal neuro-imaging study was to investigate the relationship between substance use (e.g. alcohol, cannabis, nicotine, illegal psychotropic drugs) and working-memory network function over time in heavy cannabis users and controls. Forty-nine participants performed an n-back working-memory task at baseline and at 3-year follow-up. At follow-up, there were 22 current heavy cannabis users, 4 abstinent heavy cannabis users and 23 non-cannabis-using controls. Tensor-independent component analysis (Tensor-ICA) was used to investigate individual differences in working-memory network functionality over time. Within the group of cannabis users, cannabis-related problems remained stable, whereas alcohol-related problems, nicotine dependence and illegal psychotropic substance use increased over time. At both measurements, behavioral performance and network functionality during the n-back task did not differ between heavy cannabis users and controls. Although n-back accuracy improved, working-memory network function remained stable over time. Within the group of cannabis users, working-memory network functionality was not associated with substance use. These results suggest that sustained moderate to heavy levels of cannabis, nicotine, alcohol and illegal psychotropic substance use do not change working-memory network functionality. Moreover, baseline network functionality did not predict cannabis use and related problems three years later, warranting longitudinal studies in more chronic or dependent cannabis users.

Shoulder Apprehension Impacts Large-Scale Functional Brain Networks

Shoulder apprehension is defined as anxiety and resistance in patients with a history of anterior glenohumeral instability. It remains unclear whether shoulder apprehension is the result of true recurrent instability or a memorized subjective sensation. We tested whether visual presentation of apprehension videos modifies functional brain networks associated with motor resistance and anxiety. This prospective study includes 15 consecutive right-handed male patients with shoulder apprehension (9 with right shoulder apprehension, 6 with left shoulder apprehension; 27.5 ± 6.4 years) and 10 healthy male right-handed age-matched control participants (29.0 ± 4.7 years). Multimodal MR imaging included 1) functional connectivity tensorial independent component analysis, 2) task-related general linear model analysis during visual stimulation of movies showing typical apprehension movements vs control videos, 3) voxel-based morphometry analysis of GM, and 4) tract-based spatial statistics analysis of WM. Patients with shoulder apprehension had significant (P < .05 corrected) increase in task-correlated functional connectivity, notably in the bilateral primary sensory-motor area and dorsolateral prefrontal cortex and, to a lesser degree, the bilateral dorsomedial prefrontal cortex, anterior insula, and dorsal anterior cingulate cortex (+148% right, +144% left). Anticorrelated functional connectivity decreased in the higher-level visual and parietal areas (-185%). There were no potentially confounding structural changes in GM or WM. Shoulder apprehension induces specific reorganization in apprehension-related functional connectivity of the primary sensory-motor areas (motor resistance), dorsolateral prefrontal cortex (cognitive control of motor behavior), and the dorsal anterior cingulate cortex/dorsomedial prefrontal cortex and anterior insula (anxiety and emotional regulation).

Effect of baseline cannabis use and working‐memory network function on changes in cannabis use in heavy cannabis users: A prospective fMRI study

Theoretical models of addiction suggest that a substance use disorder represents an imbalance between hypersensitive motivational processes and deficient regulatory executive functions. Working-memory (a central executive function) may be a powerful predictor of the course of drug use and drug-related problems. Goal of the current functional magnetic resonance imaging study was to assess the predictive power of working-memory network function for future cannabis use and cannabis-related problem severity in heavy cannabis users. Tensor independent component analysis was used to investigate differences in working-memory network function between 32 heavy cannabis users and 41 nonusing controls during an N-back working-memory task. In addition, associations were examined between working-memory network function and cannabis use and problem severity at baseline and at 6-month follow-up. Behavioral performance and working-memory network function did not significantly differ between heavy cannabis users and controls. However, among heavy cannabis users, individual differences in working-memory network response had an independent effect on change in weekly cannabis use 6 months later (ΔR(2) = 0.11, P = 0.006, f(2) = 0.37) beyond baseline cannabis use (ΔR(2) = 0.41) and a behavioral measure of approach bias (ΔR(2) = 0.18): a stronger network response during the N-back task was related to an increase in weekly cannabis use. These findings imply that heavy cannabis users requiring greater effort to accurately complete an N-back working-memory task have a higher probability of escalating cannabis use. Working-memory network function may be a biomarker for the prediction of course and treatment outcome in cannabis users.

Acute caffeine administration impact on working memory-related brain activation and functional connectivity in the elderly: A BOLD and perfusion MRI study

In young individuals, caffeine-mediated blockade of adenosine receptors and vasoconstriction has direct repercussions on task-related activations, changes in functional connectivity, as well as global vascular effects. To date, no study has explored the effect of caffeine on brain activation patterns during highly demanding cognitive tasks in the elderly.This prospective, placebo-controlled crossover design comprises 24 healthy elderly individuals (mean age 68.8±4.0years, 17 females) performing a 2-back working memory (WM) task in functional magnetic resonance imaging (fMRI). Analyses include complimentary assessment of task-related activations (general linear model, GLM), functional connectivity (tensorial independent component analysis, TICA), and baseline perfusion (arterial spin labeling).Despite a reduction in whole-brain global perfusion (−22.7%), caffeine-enhanced task-related GLM activation in a local and distributed network is most pronounced in the bilateral striatum and to a lesser degree in the right middle and inferior frontal gyrus, bilateral insula, left superior and inferior parietal lobule as well as in the cerebellum bilaterally. TICA was significantly enhanced (+8.2%) in caffeine versus placebo in a distributed and task-relevant network including the pre-frontal cortex, the supplementary motor area, the ventral premotor cortex and the parietal cortex as well as the occipital cortex (visual stimuli) and basal ganglia. The inverse comparison of placebo versus caffeine had no significant difference. Activation strength of the task-relevant-network component correlated with response accuracy for caffeine yet not for placebo, indicating a selective cognitive effect of caffeine.The present findings suggest that acute caffeine intake enhances WM-related brain activation as well as functional connectivity of blood oxygen level-dependent fMRI in elderly individuals.

Brain Effects of Cognitive Remediation Therapy in Schizophrenia: A Structural and Functional Neuroimaging Study

Cognitive remediation therapy positively affects cognition and daily functioning in patients with schizophrenia. However, studies on the underlying neurobiological mechanisms of this treatment are scarce. The aim of the current study was to investigate functional and structural connectivity brain changes in schizophrenia patients after cognitive remediation therapy using a whole-brain approach that combined functional magnetic resonance imaging and diffusion tensor imaging. A randomized controlled trial with 30 schizophrenia outpatients and 15 healthy volunteers. A strategy-learning-based treatment was used as a cognitive remediation therapy. A social skills training that provides useful information about illness management was used as an active control. We investigated changes in the pattern of functional connectivity assessed during an n-back task by tensorial independent component analysis as implemented in the multivariate exploratory linear decomposition into independent components and in the fractional anisotropy index of white matter integrity using tract-based spatial statistics. Brain networks activation pattern significantly changed in patients exposed to the cognitive treatment in the sense of normalizing toward the patterns observed in healthy control subjects. Additionally, in white matter, they showed an increase in fractional anisotropy index in the anterior part of the genu of the corpus callosum. Cognitive improvement, functional, and also structural changes showed statistically significant correlations. Improvement in brain functioning detected after cognitive remediation therapy in schizophrenia patients might be based on an increase of the interhemispheric information transfer between the bilateral prefrontal cortexes via the corpus callosum.

A combination of parallel factor and independent component analysis

Although CPA (canonical/parallel factor analysis) has a unique solution, the actual computation can be made more robust by incorporating extra constraints. In several applications, the factors in one mode are known to be statistically independent. On the other hand, in Independent Component Analysis (ICA), it often makes sense to impose a Khatri-Rao structure on the mixing vectors. In this paper, we propose a new algorithm to impose independence constraints in CPA. Our algorithm implements the algebraic CPA structure and the property of statistical independence simultaneously. Numerical experiments show that our method outperforms in several cases pure CPA, pure ICA, and tensor ICA, a previously proposed method for combining ICA and CPA. We also present a strategy for imposing full or partial symmetry in CPA.