Calcium imaging is a popular tool among neuroscientists because of its capability to monitor
in vivo large neural populations across weeks with single neuron and single spike …

Highlights•Modern recording technologies are creating data at a scale and complexity that
demand rigorous data analytical approaches.•Neural data science is an essential bridge …

Graph-based subspace clustering methods have exhibited promising performance.
However, they still suffer some of these drawbacks: they encounter the expensive time …

Neural Collapse refers to the remarkable structural properties characterizing the geometry of
class embeddings and classifier weights, found by deep nets when trained beyond zero …

In this paper, we introduce the Layer-Peeled Model, a nonconvex, yet analytically tractable,
optimization program, in a quest to better understand deep neural networks that are trained …

Nonnegative matrix factorization (NMF) has become a widely used tool for the analysis of
high-dimensional data as it automatically extracts sparse and meaningful features from a set …

Identifying the underlying structure of a data set and extracting meaningful information is a
key problem in data analysis. Simple and powerful methods to achieve this goal are linear …

Algorithmic approaches endow deep learning systems with implicit bias that helps them
generalize even in over-parametrized settings. In this paper, we focus on understanding …

The quality of obtained features by representation learning determines the performance of a
learning algorithm and subsequent application tasks (eg, high-dimensional data clustering) …

A rank-r matrix X∈R^m*n can be written as a product UV^⊤, where U∈R^m*r and
V∈R^n*r. One could exploit this observation in optimization: eg, consider the minimization …