Robust Group Subspace Recovery: A New Approach for Multi-Modality Data Fusion

• URL: http://arxiv.org/abs/2006.10657v1
• Date: Thu, 18 Jun 2020 16:31:31 GMT
• Title: Robust Group Subspace Recovery: A New Approach for Multi-Modality Data Fusion
• Authors: Sally Ghanem, Ashkan Panahi, Hamid Krim, and Ryan A. Kerekes
• Abstract summary: We propose a novel multi-modal data fusion approach based on group sparsity. The proposed approach exploits the structural dependencies between the different modalities data to cluster the associated target objects. The resulting UoS structure is employed to classify newly observed data points, highlighting the abstraction capacity of the proposed method.
• Score: 18.202825916298437
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Robust Subspace Recovery (RoSuRe) algorithm was recently introduced as a principled and numerically efficient algorithm that unfolds underlying Unions of Subspaces (UoS) structure, present in the data. The union of Subspaces (UoS) is capable of identifying more complex trends in data sets than simple linear models. We build on and extend RoSuRe to prospect the structure of different data modalities individually. We propose a novel multi-modal data fusion approach based on group sparsity which we refer to as Robust Group Subspace Recovery (RoGSuRe). Relying on a bi-sparsity pursuit paradigm and non-smooth optimization techniques, the introduced framework learns a new joint representation of the time series from different data modalities, respecting an underlying UoS model. We subsequently integrate the obtained structures to form a unified subspace structure. The proposed approach exploits the structural dependencies between the different modalities data to cluster the associated target objects. The resulting fusion of the unlabeled sensors' data from experiments on audio and magnetic data has shown that our method is competitive with other state of the art subspace clustering methods. The resulting UoS structure is employed to classify newly observed data points, highlighting the abstraction capacity of the proposed method.

Related papers

• ComboStoc: Combinatorial Stochasticity for Diffusion Generative Models [65.82630283336051]
  We show that the space spanned by the combination of dimensions and attributes is insufficiently sampled by existing training scheme of diffusion generative models. We present a simple fix to this problem by constructing processes that fully exploit the structures, hence the name ComboStoc.
  arXiv  Detail & Related papers  (2024-05-22T15:23:10Z)
• Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein [56.62376364594194]
  Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. In this work, we revisit these approaches under the lens of optimal transport and exhibit relationships with the Gromov-Wasserstein problem. This unveils a new general framework, called distributional reduction, that recovers DR and clustering as special cases and allows addressing them jointly within a single optimization problem.
  arXiv  Detail & Related papers  (2024-02-03T19:00:19Z)
• Exploiting Data Hierarchy as a New Modality for Contrastive Learning [0.0]
  This work investigates how hierarchically structured data can help neural networks learn conceptual representations of cathedrals. The underlying WikiScenes dataset provides a spatially organized hierarchical structure of cathedral components. We propose a novel hierarchical contrastive training approach that leverages a triplet margin loss to represent the data's spatial hierarchy in the encoder's latent space.
  arXiv  Detail & Related papers  (2024-01-06T21:47:49Z)
• Joint Distributional Learning via Cramer-Wold Distance [0.7614628596146602]
  We introduce the Cramer-Wold distance regularization, which can be computed in a closed-form, to facilitate joint distributional learning for high-dimensional datasets. We also introduce a two-step learning method to enable flexible prior modeling and improve the alignment between the aggregated posterior and the prior distribution.
  arXiv  Detail & Related papers  (2023-10-25T05:24:23Z)
• Hierarchical clustering with dot products recovers hidden tree structure [53.68551192799585]
  In this paper we offer a new perspective on the well established agglomerative clustering algorithm, focusing on recovery of hierarchical structure. We recommend a simple variant of the standard algorithm, in which clusters are merged by maximum average dot product and not, for example, by minimum distance or within-cluster variance. We demonstrate that the tree output by this algorithm provides a bona fide estimate of generative hierarchical structure in data, under a generic probabilistic graphical model.
  arXiv  Detail & Related papers  (2023-05-24T11:05:12Z)
• Unified Multi-View Orthonormal Non-Negative Graph Based Clustering Framework [74.25493157757943]
  We formulate a novel clustering model, which exploits the non-negative feature property and incorporates the multi-view information into a unified joint learning framework. We also explore, for the first time, the multi-model non-negative graph-based approach to clustering data based on deep features.
  arXiv  Detail & Related papers  (2022-11-03T08:18:27Z)
• Fusion Subspace Clustering for Incomplete Data [0.0]
  This paper introduces em fusion subspace clustering, a novel method to learn low-dimensional structures that approximate large scale yet highly incomplete data. Our method allows low, high, and even full-rank data; it directly accounts for noise, and its sample complexity approaches the information-theoretic limit. We show through extensive experiments on real and synthetic data that our approach performs comparably to the state-of-the-art with complete data, and dramatically better if data is missing.
  arXiv  Detail & Related papers  (2022-05-22T17:23:41Z)
• Information Fusion: Scaling Subspace-Driven Approaches [16.85310886805588]
  We seek to exploit the deep structure of multi-modal data to robustly exploit the group subspace distribution of the information using the Convolutional Neural Network (CNN) formalism. Referred to as deep Multimodal Robust Group Subspace Clustering (DRoGSuRe), this approach is compared against the independently developed state-of-the-art approach named Deep Multimodal Subspace Clustering (DMSC)
  arXiv  Detail & Related papers  (2022-04-26T02:16:01Z)
• Joint Geometric and Topological Analysis of Hierarchical Datasets [7.098759778181621]
  In this paper, we focus on high-dimensional data that are organized into several hierarchical datasets. The main novelty in this work lies in the combination of two powerful data-analytic approaches: topological data analysis and geometric manifold learning. We show that our new method gives rise to superior classification results compared to state-of-the-art methods.
  arXiv  Detail & Related papers  (2021-04-03T13:02:00Z)
• Model Fusion with Kullback--Leibler Divergence [58.20269014662046]
  We propose a method to fuse posterior distributions learned from heterogeneous datasets. Our algorithm relies on a mean field assumption for both the fused model and the individual dataset posteriors.
  arXiv  Detail & Related papers  (2020-07-13T03:27:45Z)
• Two-Dimensional Semi-Nonnegative Matrix Factorization for Clustering [50.43424130281065]
  We propose a new Semi-Nonnegative Matrix Factorization method for 2-dimensional (2D) data, named TS-NMF. It overcomes the drawback of existing methods that seriously damage the spatial information of the data by converting 2D data to vectors in a preprocessing step.
  arXiv  Detail & Related papers  (2020-05-19T05:54:14Z)

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

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.