Functional optical imaging in neuroscience is rapidly growing with the development of new optical systems and fluorescence indicators.
To understand the relationship between behavior and neural activity, experiments in neuroscience often include an animal performing a repeated behavior such as a motor task.
There has been great interest in enhancing the robustness of neural network classifiers to defend against adversarial perturbations through adversarial training, while balancing the trade-off between robust accuracy and standard accuracy.
We present Low Distortion Local Eigenmaps (LDLE), a manifold learning technique which constructs a set of low distortion local views of a dataset in lower dimension and registers them to obtain a global embedding.
To the best of our knowledge, our paper is the first that generalizes the idea of using self-supervised signals to perform online test-time purification.
Deep neural networks are known to be vulnerable to adversarial examples, where a perturbation in the input space leads to an amplified shift in the latent network representation.
A low-dimensional dynamical system is observed in an experiment as a high-dimensional signal; for example, a video of a chaotic pendulums system.
The extraction of clusters from a dataset which includes multiple clusters and a significant background component is a non-trivial task of practical importance.
We propose utilizing this coupled structure to perform co-manifold learning: uncovering the underlying geometry of both the rows and the columns of a given matrix, where we focus on a missing data setting.
If we pick $n$ random points uniformly in $[0, 1]^d$ and connect each point to its $k-$nearest neighbors, then it is well known that there exists a giant connected component with high probability.
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.
In the wake of recent advances in experimental methods in neuroscience, the ability to record in-vivo neuronal activity from awake animals has become feasible.
In this paper, we propose a manifold learning algorithm based on deep learning to create an encoder, which maps a high-dimensional dataset and its low-dimensional embedding, and a decoder, which takes the embedded data back to the high-dimensional space.