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Found 30 papers, 11 papers with code
Diffusion Nets
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.
Hierarchical Coupled Geometry Analysis for Neuronal Structure and Activity Pattern Discovery
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.
The Geometry of Nodal Sets and Outlier Detection
Let $(M, g)$ be a compact manifold and let $-\Delta \phi_k = \lambda_k \phi_k$ be the sequence of Laplacian eigenfunctions.
Data-Driven Tree Transforms and Metrics
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.
Randomized Near Neighbor Graphs, Giant Components, and Applications in Data Science
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.
Co-manifold learning with missing data
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.
Spectral Embedding Norm: Looking Deep into the Spectrum of the Graph Laplacian
The extraction of clusters from a dataset which includes multiple clusters and a significant background component is a non-trivial task of practical importance.
Visualizing the PHATE of Neural Networks
We demonstrate M-PHATE with two vignettes: continual learning and generalization.
Multi-way Graph Signal Processing on Tensors: Integrative analysis of irregular geometries
Graph signal processing (GSP) is an important methodology for studying data residing on irregular structures.
Kernel-based parameter estimation of dynamical systems with unknown observation functions
A low-dimensional dynamical system is observed in an experiment as a high-dimensional signal; for example, a video of a chaotic pendulums system.
Provable Robustness by Geometric Regularization of ReLU Networks
Recent work has demonstrated that neural networks are vulnerable to small, adversarial perturbations of their input.
Online Adversarial Purification based on Self-supervised Learning
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.
Online Adversarial Purification based on Self-Supervision
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.
LDLE: Low Distortion Local Eigenmaps
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.
Learning Sample Reweighting for Adversarial Robustness
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.
Learning Disentangled Behavior Embeddings
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.
Data Processing of Functional Optical Microscopy for Neuroscience
Functional optical imaging in neuroscience is rapidly growing with the development of new optical systems and fluorescence indicators.
Evaluating Disentanglement in Generative Models Without Knowledge of Latent Factors
Probabilistic generative models provide a flexible and systematic framework for learning the underlying geometry of data.
Learning Sample Reweighting for Accuracy and Adversarial Robustness
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.
The Numerical Stability of Hyperbolic Representation Learning
Given the exponential growth of the volume of the ball w. r. t.
Implicit Graphon Neural Representation
We also show that our model is suitable for graph representation learning and graph generation.
DiSC: Differential Spectral Clustering of Features
Selecting subsets of features that differentiate between two conditions is a key task in a broad range of scientific domains.
Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learning
Finding meaningful representations and distances of hierarchical data is important in many fields.
SiBBlInGS: Similarity-driven Building-Block Inference using Graphs across States
Time series data across scientific domains are often collected under distinct states (e. g., tasks), wherein latent processes (e. g., biological factors) create complex inter- and intra-state variability.
Graph Laplacian Learning with Exponential Family Noise
A common challenge in applying graph machine learning methods is that the underlying graph of a system is often unknown.
Semi-Supervised Laplacian Learning on Stiefel Manifolds
Motivated by the need to address the degeneracy of canonical Laplace learning algorithms in low label rates, we propose to reformulate graph-based semi-supervised learning as a nonconvex generalization of a \emph{Trust-Region Subproblem} (TRS).
Contextual Feature Selection with Conditional Stochastic Gates
We study the problem of contextual feature selection, where the goal is to learn a predictive function while identifying subsets of informative features conditioned on specific contexts.
Learning Cartesian Product Graphs with Laplacian Constraints
We establish statistical consistency for the penalized maximum likelihood estimation (MLE) of a Cartesian product Laplacian, and propose an efficient algorithm to solve the problem.
Deep and shallow data science for multi-scale optical neuroscience
Optical imaging of the brain has expanded dramatically in the past two decades.
Comparing Graph Transformers via Positional Encodings
The distinguishing power of graph transformers is closely tied to the choice of positional encoding: features used to augment the base transformer with information about the graph.
