Search Results for author:
Found 12 papers, 4 papers with code
Gappy local conformal auto-encoders for heterogeneous data fusion: in praise of rigidity
Fusing measurements from multiple, heterogeneous, partial sources, observing a common object or process, poses challenges due to the increasing availability of numbers and types of sensors.
Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learning
Finding meaningful representations and distances of hierarchical data is important in many fields.
A common variable minimax theorem for graphs
Let $\mathcal{G} = \{G_1 = (V, E_1), \dots, G_m = (V, E_m)\}$ be a collection of $m$ graphs defined on a common set of vertices $V$ but with different edge sets $E_1, \dots, E_m$.
Doubly-Stochastic Normalization of the Gaussian Kernel is Robust to Heteroskedastic Noise
When the data points reside in Euclidean space, a widespread approach is to from an affinity matrix by the Gaussian kernel with pairwise distances, and to follow with a certain normalization (e. g. the row-stochastic normalization or its symmetric variant).
LOCA: LOcal Conformal Autoencoder for standardized data coordinates
We propose a deep-learning based method for obtaining standardized data coordinates from scientific measurements. Data observations are modeled as samples from an unknown, non-linear deformation of an underlying Riemannian manifold, which is parametrized by a few normalized latent variables.
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.
Manifold learning with bi-stochastic kernels
In this paper we answer the following question: what is the infinitesimal generator of the diffusion process defined by a kernel that is normalized such that it is bi-stochastic with respect to a specified measure?
Two-sample Statistics Based on Anisotropic Kernels
The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples.
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.
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.
Provable approximation properties for deep neural networks
We discuss approximation of functions using deep neural nets.
Bigeometric Organization of Deep Nets
In this paper, we build an organization of high-dimensional datasets that cannot be cleanly embedded into a low-dimensional representation due to missing entries and a subset of the features being irrelevant to modeling functions of interest.
