scholarly journals Evaluating State Space Discovery by Persistent Cohomology in the Spatial Representation System

2021 ◽  
Vol 15 ◽  
Author(s):  
Louis Kang ◽  
Boyan Xu ◽  
Dmitriy Morozov
Keyword(s):  
Topological Structure ◽  
Spatial Representation ◽  
Persistent Homology ◽  
High Dimensional ◽  
Head Direction ◽  
Representation System ◽  
Topological Structures ◽  
Neural Recordings ◽  
Persistent Cohomology ◽  
Low Dimensional

Persistent cohomology is a powerful technique for discovering topological structure in data. Strategies for its use in neuroscience are still undergoing development. We comprehensively and rigorously assess its performance in simulated neural recordings of the brain's spatial representation system. Grid, head direction, and conjunctive cell populations each span low-dimensional topological structures embedded in high-dimensional neural activity space. We evaluate the ability for persistent cohomology to discover these structures for different dataset dimensions, variations in spatial tuning, and forms of noise. We quantify its ability to decode simulated animal trajectories contained within these topological structures. We also identify regimes under which mixtures of populations form product topologies that can be detected. Our results reveal how dataset parameters affect the success of topological discovery and suggest principles for applying persistent cohomology, as well as persistent homology, to experimental neural recordings.

scholarly journals State space discovery in spatial representation circuits with persistent cohomology

2020 ◽  
Author(s):  
Louis Kang ◽  
Boyan Xu ◽  
Dmitriy Morozov
Keyword(s):  
Neural Activity ◽  
Topological Structure ◽  
Spatial Representation ◽  
Persistent Homology ◽  
High Dimensional ◽  
Head Direction ◽  
Representation System ◽  
Neural Recordings ◽  
Persistent Cohomology ◽  
Low Dimensional

AbstractPersistent cohomology is a powerful technique for discovering topological structure in data. Strategies for its use in neuroscience are still undergoing development. We explore the application of persistent cohomology to the brain’s spatial representation system. We simulate populations of grid cells, head direction cells, and conjunctive cells, each of which span low-dimensional topological structures embedded in high-dimensional neural activity space. We evaluate the ability for persistent cohomology to discover these structures and demonstrate its robustness to various forms of noise. We identify regimes under which mixtures of populations form product topologies can be detected. Our results suggest guidelines for applying persistent cohomology, as well as persistent homology, to experimental neural recordings.

scholarly journals Generalized penalty for circular coordinate representation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hengrui Luo ◽  
Alice Patania ◽  
Jisu Kim ◽  
Mikael Vejdemo-Johansson
Keyword(s):  
Dimension Reduction ◽  
Real Data ◽  
Topological Data Analysis ◽  
High Dimensional ◽  
Topological Structures ◽  
Sampling Schemes ◽  
Coordinate Representation ◽  
Geometrical Shapes ◽  
Persistent Cohomology ◽  
High Dimensional Datasets

<p style='text-indent:20px;'>Topological Data Analysis (TDA) provides novel approaches that allow us to analyze the geometrical shapes and topological structures of a dataset. As one important application, TDA can be used for data visualization and dimension reduction. We follow the framework of circular coordinate representation, which allows us to perform dimension reduction and visualization for high-dimensional datasets on a torus using persistent cohomology. In this paper, we propose a method to adapt the circular coordinate framework to take into account the roughness of circular coordinates in change-point and high-dimensional applications. To do that, we use a generalized penalty function instead of an <inline-formula><tex-math id="M1">\begin{document}$ L_{2} $\end{document}</tex-math></inline-formula> penalty in the traditional circular coordinate algorithm. We provide simulation experiments and real data analyses to support our claim that circular coordinates with generalized penalty will detect the change in high-dimensional datasets under different sampling schemes while preserving the topological structures.</p>

scholarly journals Unsupervised discovery of temporal sequences in high-dimensional datasets, with applications to neuroscience

2018 ◽  
Author(s):  
Emily L. Mackevicius ◽  
Andrew H. Bahle ◽  
Alex H. Williams ◽  
Shijie Gu ◽  
Natalia I. Denissenko ◽  
...  
Keyword(s):  
Large Scale ◽  
Temporal Structure ◽  
Simulated Data ◽  
Salient Feature ◽  
High Dimensional ◽  
Neural Data ◽  
Neural Recordings ◽  
Reduction Techniques ◽  
Low Dimensional ◽  
Neural Sequences

AbstractIdentifying low-dimensional features that describe large-scale neural recordings is a major challenge in neuroscience. Repeated temporal patterns (sequences) are thought to be a salient feature of neural dynamics, but are not succinctly captured by traditional dimensionality reduction techniques. Here we describe a software toolbox—called seqNMF—with new methods for extracting informative, non-redundant, sequences from high-dimensional neural data, testing the significance of these extracted patterns, and assessing the prevalence of sequential structure in data. We test these methods on simulated data under multiple noise conditions, and on several real neural and behavioral data sets. In hippocampal data, seqNMF identifies neural sequences that match those calculated manually by reference to behavioral events. In songbird data, seqNMF discovers neural sequences in untutored birds that lack stereotyped songs. Thus, by identifying temporal structure directly from neural data, seqNMF enables dissection of complex neural circuits without relying on temporal references from stimuli or behavioral outputs.

scholarly journals Decoding of neural data using cohomological learning

2018 ◽  
Author(s):  
Erik Rybakken ◽  
Nils Baas ◽  
Benjamin Dunn
Keyword(s):  
Spatial Organization ◽  
Large Population ◽  
Dimensional Structure ◽  
Neural Population ◽  
Head Direction ◽  
Population Activity ◽  
Neural Data ◽  
Neural Recordings ◽  
Data Driven Approach ◽  
Low Dimensional

AbstractWe introduce a novel data-driven approach to discover and decode features in the neural code coming from large population neural recordings with minimal assumptions, using cohomological learning. We apply our approach to neural recordings of mice moving freely in a box, where we find a circular feature. We then observe that the decoded value corresponds well to the head direction of the mouse. Thus we capture head direction cells and decode the head direction from the neural population activity without having to process the behaviour of the mouse. Interestingly, the decoded values convey more information about the neural activity than the tracked head direction does, with differences that have some spatial organization. Finally, we note that the residual population activity, after the head direction has been accounted for, retains some low-dimensional structure which is correlated with the speed of the mouse.

scholarly journals Unsupervised discovery of temporal sequences in high-dimensional datasets, with applications to neuroscience

eLife ◽  
2019 ◽  
Vol 8 ◽  
Author(s):  
Emily L Mackevicius ◽  
Andrew H Bahle ◽  
Alex H Williams ◽  
Shijie Gu ◽  
Natalia I Denisenko ◽  
...  
Keyword(s):  
Large Scale ◽  
Temporal Structure ◽  
Simulated Data ◽  
Salient Feature ◽  
High Dimensional ◽  
Neural Data ◽  
Neural Recordings ◽  
Reduction Techniques ◽  
Low Dimensional ◽  
Neural Sequences

Identifying low-dimensional features that describe large-scale neural recordings is a major challenge in neuroscience. Repeated temporal patterns (sequences) are thought to be a salient feature of neural dynamics, but are not succinctly captured by traditional dimensionality reduction techniques. Here, we describe a software toolbox—called seqNMF—with new methods for extracting informative, non-redundant, sequences from high-dimensional neural data, testing the significance of these extracted patterns, and assessing the prevalence of sequential structure in data. We test these methods on simulated data under multiple noise conditions, and on several real neural and behavioral data sets. In hippocampal data, seqNMF identifies neural sequences that match those calculated manually by reference to behavioral events. In songbird data, seqNMF discovers neural sequences in untutored birds that lack stereotyped songs. Thus, by identifying temporal structure directly from neural data, seqNMF enables dissection of complex neural circuits without relying on temporal references from stimuli or behavioral outputs.

scholarly journals Decoding of Neural Data Using Cohomological Feature Extraction

2019 ◽  
Vol 31 (1) ◽  
pp. 68-93 ◽  
Author(s):  
Erik Rybakken ◽  
Nils Baas ◽  
Benjamin Dunn
Keyword(s):  
Feature Extraction ◽  
Spatial Organization ◽  
Large Population ◽  
Dimensional Structure ◽  
Neural Population ◽  
Head Direction ◽  
Population Activity ◽  
Neural Recordings ◽  
Data Driven Approach ◽  
Low Dimensional

We introduce a novel data-driven approach to discover and decode features in the neural code coming from large population neural recordings with minimal assumptions, using cohomological feature extraction. We apply our approach to neural recordings of mice moving freely in a box, where we find a circular feature. We then observe that the decoded value corresponds well to the head direction of the mouse. Thus, we capture head direction cells and decode the head direction from the neural population activity without having to process the mouse's behavior. Interestingly, the decoded values convey more information about the neural activity than the tracked head direction does, with differences that have some spatial organization. Finally, we note that the residual population activity, after the head direction has been accounted for, retains some low-dimensional structure that is correlated with the speed of the mouse.

scholarly journals Classification of Brainwaves for Sleep Stages by High-Dimensional FFT Features from EEG Signals

2020 ◽  
Vol 10 (5) ◽  
pp. 1797 ◽  
Author(s):  
Mera Kartika Delimayanti ◽  
Bedy Purnama ◽  
Ngoc Giang Nguyen ◽  
Mohammad Reza Faisal ◽  
Kunti Robiatul Mahmudah ◽  
...  
Keyword(s):  
Machine Learning ◽  
Sleep Stage ◽  
Machine Learning Algorithms ◽  
High Dimensional ◽  
Sleep Stages ◽  
Eeg Signals ◽  
Stage Classification ◽  
Sleep Stage Classification ◽  
Low Dimensional

Manual classification of sleep stage is a time-consuming but necessary step in the diagnosis and treatment of sleep disorders, and its automation has been an area of active study. The previous works have shown that low dimensional fast Fourier transform (FFT) features and many machine learning algorithms have been applied. In this paper, we demonstrate utilization of features extracted from EEG signals via FFT to improve the performance of automated sleep stage classification through machine learning methods. Unlike previous works using FFT, we incorporated thousands of FFT features in order to classify the sleep stages into 2–6 classes. Using the expanded version of Sleep-EDF dataset with 61 recordings, our method outperformed other state-of-the art methods. This result indicates that high dimensional FFT features in combination with a simple feature selection is effective for the improvement of automated sleep stage classification.

scholarly journals A Nonlinear Maximum Correntropy Information Filter for High-Dimensional Neural Decoding

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 743
Author(s):  
Xi Liu ◽  
Shuhang Chen ◽  
Xiang Shen ◽  
Xiang Zhang ◽  
Yiwen Wang
Keyword(s):  
State Estimation ◽  
Measurement Model ◽  
High Dimensional ◽  
Neural Firing ◽  
The Neural Network ◽  
Information Filter ◽  
Critical Technology ◽  
Dimensional Measurements ◽  
Non Gaussian ◽  
Low Dimensional

Neural signal decoding is a critical technology in brain machine interface (BMI) to interpret movement intention from multi-neural activity collected from paralyzed patients. As a commonly-used decoding algorithm, the Kalman filter is often applied to derive the movement states from high-dimensional neural firing observation. However, its performance is limited and less effective for noisy nonlinear neural systems with high-dimensional measurements. In this paper, we propose a nonlinear maximum correntropy information filter, aiming at better state estimation in the filtering process for a noisy high-dimensional measurement system. We reconstruct the measurement model between the high-dimensional measurements and low-dimensional states using the neural network, and derive the state estimation using the correntropy criterion to cope with the non-Gaussian noise and eliminate large initial uncertainty. Moreover, analyses of convergence and robustness are given. The effectiveness of the proposed algorithm is evaluated by applying it on multiple segments of neural spiking data from two rats to interpret the movement states when the subjects perform a two-lever discrimination task. Our results demonstrate better and more robust state estimation performance when compared with other filters.

PSS Business Case Map: Supporting Idea Generation in PSS Design

2012 ◽  
Author(s):  
Fumiya Akasaka ◽  
Kazuki Fujita ◽  
Yoshiki Shimomura
Keyword(s):  
Idea Generation ◽  
Business Case ◽  
Literature Survey ◽  
The Self ◽  
High Dimensional ◽  
Self Organizing Map ◽  
Two Dimensional ◽  
Service Type ◽  
Business Cases ◽  
Low Dimensional

This paper proposes the PSS Business Case Map as a tool to support designers’ idea generation in PSS design. The map visualizes the similarities among PSS business cases in a two-dimensional diagram. To make the map, PSS business cases are first collected by conducting, for example, a literature survey. The collected business cases are then classified from multiple aspects that characterize each case such as its product type, service type, target customer, and so on. Based on the results of this classification, the similarities among the cases are calculated and visualized by using the Self-Organizing Map (SOM) technique. A SOM is a type of artificial neural network that is trained using unsupervised learning to produce a low-dimensional (typically two-dimensional) view from high-dimensional data. The visualization result is offered to designers in a form of a two-dimensional map, which is called the PSS Business Case Map. By using the map, designers can figure out the position of their current business and can acquire ideas for the servitization of their business.

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