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Found 19 papers, 7 papers with code
Sample-Efficient Geometry Reconstruction from Euclidean Distances using Non-Convex Optimization
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications.
Riemannian Optimization for Non-convex Euclidean Distance Geometry with Global Recovery Guarantees
For the first algorithm, under a uniform sampling with replacement model for the observed distance entries, we demonstrate that, with high probability, a Riemannian gradient-like algorithm on the manifold of rank-$r$ matrices converges linearly to the true solution, given initialization via a one-step hard thresholding.
Locality Regularized Reconstruction: Structured Sparsity and Delaunay Triangulations
We prove that, for all levels of regularization and under a mild condition that the columns of $\mathbf{X}$ have a unique Delaunay triangulation, the optimal coefficients' number of non-zero entries is upper bounded by $d+1$, thereby providing local sparse solutions when $d \ll n$.
Clustering Inductive Biases with Unrolled Networks
We propose an autoencoder architecture (WLSC) whose latent representations are implicitly, locally organized for spectral clustering through a Laplacian quadratic form of a bipartite graph, which generates a diverse set of artificial receptive fields that match primate data in V1 as faithfully as recent contrastive frameworks like Local Low Dimensionality, or LLD \citep{lld} that discard sparse dictionary learning.
Localization from structured distance matrices via low-rank matrix recovery
One sampling scheme is Nystrom sampling, which assumes known distances between the anchors and between the anchors and the $n$ points, while the distances among the $n$ points are unknown.
RACH-Space: Reconstructing Adaptive Convex Hull Space with Applications in Weak Supervision
We introduce RACH-Space, an algorithm for labelling unlabelled data in weakly supervised learning, given incomplete, noisy information about the labels.
A dual basis approach to multidimensional scaling
Classical multidimensional scaling (CMDS) is a technique that embeds a set of objects in a Euclidean space given their pairwise Euclidean distances.
Sparse, Geometric Autoencoder Models of V1
The classical sparse coding model represents visual stimuli as a linear combination of a handful of learned basis functions that are Gabor-like when trained on natural image data.
Alternating minimization algorithm with initialization analysis for r-local and k-sparse unlabeled sensing
The unlabeled sensing problem is to recover an unknown signal from permuted linear measurements.
Geometric Sparse Coding in Wasserstein Space
We show this approach leads to sparse representations in Wasserstein space and addresses the problem of non-uniqueness of barycentric representation.
Measure Estimation in the Barycentric Coding Model
Our first main result leverages the Riemannian geometry of Wasserstein-2 space to provide a procedure for recovering the barycentric coordinates as the solution to a quadratic optimization problem assuming access to the true reference measures.
r-local sensing: Improved algorithm and applications
The unlabeled sensing problem is to solve a noisy linear system of equations under unknown permutation of the measurements.
Weighed l1 on the simplex: Compressive sensing meets locality
Sparse manifold learning algorithms combine techniques in manifold learning and sparse optimization to learn features that could be utilized for downstream tasks.
On the convergence of group-sparse autoencoders
Recent approaches in the theoretical analysis of model-based deep learning architectures have studied the convergence of gradient descent in shallow ReLU networks that arise from generative models whose hidden layers are sparse.
Deep Diffusion Processes for Active Learning of Hyperspectral Images
A method for active learning of hyperspectral images (HSI) is proposed, which combines deep learning with diffusion processes on graphs.
K-Deep Simplex: Deep Manifold Learning via Local Dictionaries
We theoretically analyze the proposed program by relating the weighted $\ell_1$ penalty in KDS to a weighted $\ell_0$ program.
Towards improving discriminative reconstruction via simultaneous dense and sparse coding
We propose a novel dense and sparse coding model that integrates both representation capability and discriminative features.
R-local unlabeled sensing: A novel graph matching approach for multiview unlabeled sensing under local permutations
Unlabeled sensing is a linear inverse problem where the measurements are scrambled under an unknown permutation leading to loss of correspondence between the measurements and the rows of the sensing matrix.
Exact Reconstruction of Euclidean Distance Geometry Problem Using Low-rank Matrix Completion
In this paper, this minimization program is recast as a matrix completion problem of a low-rank $r$ Gram matrix with respect to a suitable basis.
