Developing Software for Graphing Neural Manifolds Visible in a Three-Dimensional Space Without Using Nonlinear Dimensionality Reduction
School Name
Spring Valley High School
Grade Level
10th Grade
Presentation Topic
Mathematics
Presentation Type
Non-Mentored
Abstract
The current method for dimensionality reduction in neural manifolds requires the use of dubiously accurate manifold data analysis algorithms due to differing perspectives on the efficacy of each technique. As such, this research was done in order to create a method to graph neural data without the need for nonlinear dimensionality reduction (NDR) while still having a representation of neural manifolds that keeps all data visible. Data were plotted on a graph with 3 physical dimensions and varying represented dimensions. Vectors were then sent from the position of the camera out to each graphed neuron, and intersections of data points before that neuron had opacity reduced by a metric scaled to their distance from the endpoint. The opacities of each point were then collected and compared to check for any values of 100%, as this indicates that some data would not be visible on the graph and result in a failure. Results showed that while every data point could be viewed independently, faults in manifold calculation mean that such results are not definitive; however the research does provide an alternative method for reducing the dimensionality of neural data while keeping structural uniformity. Future research should be done on alternative methods of dimensionality reduction to further develop this finding.
Recommended Citation
O'Connor, Fionn, "Developing Software for Graphing Neural Manifolds Visible in a Three-Dimensional Space Without Using Nonlinear Dimensionality Reduction" (2023). South Carolina Junior Academy of Science. 97.
https://scholarexchange.furman.edu/scjas/2023/all/97
Location
ECL 116
Start Date
3-25-2023 11:15 AM
Presentation Format
Oral and Written
Group Project
No
Developing Software for Graphing Neural Manifolds Visible in a Three-Dimensional Space Without Using Nonlinear Dimensionality Reduction
ECL 116
The current method for dimensionality reduction in neural manifolds requires the use of dubiously accurate manifold data analysis algorithms due to differing perspectives on the efficacy of each technique. As such, this research was done in order to create a method to graph neural data without the need for nonlinear dimensionality reduction (NDR) while still having a representation of neural manifolds that keeps all data visible. Data were plotted on a graph with 3 physical dimensions and varying represented dimensions. Vectors were then sent from the position of the camera out to each graphed neuron, and intersections of data points before that neuron had opacity reduced by a metric scaled to their distance from the endpoint. The opacities of each point were then collected and compared to check for any values of 100%, as this indicates that some data would not be visible on the graph and result in a failure. Results showed that while every data point could be viewed independently, faults in manifold calculation mean that such results are not definitive; however the research does provide an alternative method for reducing the dimensionality of neural data while keeping structural uniformity. Future research should be done on alternative methods of dimensionality reduction to further develop this finding.
