Related papers: Geometric Matrix Completion: A Functional View

Geometric Matrix Completion: A Functional View

URL: http://arxiv.org/abs/2009.14343v1
Date: Tue, 29 Sep 2020 23:23:04 GMT
Title: Geometric Matrix Completion: A Functional View
Abstract summary: We propose a novel regularization inspired from the functional map literature that is more interpretable and theoretically sound. On synthetic tasks with strong underlying geometric structure, our framework outperforms state of the art by a huge margin. On real datasets, we achieve state-of-the-art results at a fraction of the computational effort of previous methods.
Score: 35.58521417084282
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We propose a totally functional view of geometric matrix completion problem. Differently from existing work, we propose a novel regularization inspired from the functional map literature that is more interpretable and theoretically sound. On synthetic tasks with strong underlying geometric structure, our framework outperforms state of the art by a huge margin (two order of magnitude) demonstrating the potential of our approach. On real datasets, we achieve state-of-the-art results at a fraction of the computational effort of previous methods. Our code is publicly available at https://github.com/Not-IITian/functional-matrix-completion

Related papers

Polyatomic Complexes: A topologically-informed learning representation for atomistic systems [0.5461938536945723]
We present a representation of atomistic systems. We provide a general algorithm to encode any atomistic system. We report performance comparable to state-of-the-art methods on numerous tasks.
arXiv Detail & Related papers (2024-09-23T23:09:23Z)
Functional-Edged Network Modeling [5.858447612884839]
We transform the adjacency matrix into a functional adjacency tensor, introducing an additional dimension dedicated to function representation. To deal with irregular observations of the functional edges, we conduct model inference to solve a tensor completion problem. We also derive several theorems to show the desirable properties of the functional edged network model.
arXiv Detail & Related papers (2024-03-30T02:23:01Z)
Data-driven abstractions via adaptive refinements and a Kantorovich metric [extended version] [56.94699829208978]
We introduce an adaptive refinement procedure for smart, and scalable abstraction of dynamical systems. In order to learn the optimal structure, we define a Kantorovich-inspired metric between Markov chains. We show that our method yields a much better computational complexity than using classical linear programming techniques.
arXiv Detail & Related papers (2023-03-30T11:26:40Z)
Marching-Primitives: Shape Abstraction from Signed Distance Function [29.7543198254021]
We present a novel method, named Marching-Primitives, to obtain a primitive-based abstraction directly from an SDF. Our method grows geometric primitives iteratively by analyzing the connectivity of voxels. We evaluate the performance of our method on both synthetic and real-world datasets.
arXiv Detail & Related papers (2023-03-23T11:42:35Z)
Matrix Completion with Hierarchical Graph Side Information [39.00971122472004]
We consider a matrix completion problem that exploits social or item similarity graphs as side information. We develop a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering. We conduct extensive experiments on synthetic and real-world datasets to corroborate our theoretical results.
arXiv Detail & Related papers (2022-01-02T03:47:41Z)
How Fine-Tuning Allows for Effective Meta-Learning [50.17896588738377]
We present a theoretical framework for analyzing representations derived from a MAML-like algorithm. We provide risk bounds on the best predictor found by fine-tuning via gradient descent, demonstrating that the algorithm can provably leverage the shared structure. This separation result underscores the benefit of fine-tuning-based methods, such as MAML, over methods with "frozen representation" objectives in few-shot learning.
arXiv Detail & Related papers (2021-05-05T17:56:00Z)
Matrix Decomposition on Graphs: A Functional View [36.85782408336389]
We propose a functional view of matrix decomposition problems on graphs. Our framework is based on the key idea that using a reduced basis to represent functions on the product space is sufficient to recover a low rank matrix approximation.
arXiv Detail & Related papers (2021-02-05T15:28:11Z)
Geometrically Principled Connections in Graph Neural Networks [66.51286736506658]
We argue geometry should remain the primary driving force behind innovation in the emerging field of geometric deep learning. We relate graph neural networks to widely successful computer graphics and data approximation models: radial basis functions (RBFs) We introduce affine skip connections, a novel building block formed by combining a fully connected layer with any graph convolution operator.
arXiv Detail & Related papers (2020-04-06T13:25:46Z)
Spatial Pyramid Based Graph Reasoning for Semantic Segmentation [67.47159595239798]
We apply graph convolution into the semantic segmentation task and propose an improved Laplacian. The graph reasoning is directly performed in the original feature space organized as a spatial pyramid. We achieve comparable performance with advantages in computational and memory overhead.
arXiv Detail & Related papers (2020-03-23T12:28:07Z)
Image Matching across Wide Baselines: From Paper to Practice [80.9424750998559]
We introduce a comprehensive benchmark for local features and robust estimation algorithms. Our pipeline's modular structure allows easy integration, configuration, and combination of different methods. We show that with proper settings, classical solutions may still outperform the perceived state of the art.
arXiv Detail & Related papers (2020-03-03T15:20:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.