Semi-Supervised Laplace Learning on Stiefel Manifolds

• URL: http://arxiv.org/abs/2308.00142v2
• Date: Wed, 14 Aug 2024 17:57:05 GMT
• Title: Semi-Supervised Laplace Learning on Stiefel Manifolds
• Authors: Chester Holtz, Pengwen Chen, Alexander Cloninger, Chung-Kuan Cheng, Gal Mishne,
• Abstract summary: We develop the framework Sequential Subspace for graph-based, supervised samples at low-label rates. We achieves that our methods at extremely low rates, and high label rates.
• Score: 48.3427853588646
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Motivated by the need to address the degeneracy of canonical Laplace learning algorithms in low label rates, we propose to reformulate graph-based semi-supervised learning as a nonconvex generalization of a \emph{Trust-Region Subproblem} (TRS). This reformulation is motivated by the well-posedness of Laplacian eigenvectors in the limit of infinite unlabeled data. To solve this problem, we first show that a first-order condition implies the solution of a manifold alignment problem and that solutions to the classical \emph{Orthogonal Procrustes} problem can be used to efficiently find good classifiers that are amenable to further refinement. To tackle refinement, we develop the framework of Sequential Subspace Optimization for graph-based SSL. Next, we address the criticality of selecting supervised samples at low-label rates. We characterize informative samples with a novel measure of centrality derived from the principal eigenvectors of a certain submatrix of the graph Laplacian. We demonstrate that our framework achieves lower classification error compared to recent state-of-the-art and classical semi-supervised learning methods at extremely low, medium, and high label rates.

Related papers

• P$^2$OT: Progressive Partial Optimal Transport for Deep Imbalanced Clustering [16.723646401890495]
  We propose a novel pseudo-labeling-based learning framework for deep clustering. Our framework generates imbalance-aware pseudo-labels and learning from high-confident samples. Experiments on various datasets, including a human-curated long-tailed CIFAR100, demonstrate the superiority of our method.
  arXiv  Detail & Related papers  (2024-01-17T15:15:46Z)
• Graph Laplacian for Semi-Supervised Learning [8.477619837043214]
  We propose a new type of graph-Laplacian adapted for Semi-Supervised Learning (SSL) problems. It is based on both density and contrastive measures and allows the encoding of the labeled data directly in the operator.
  arXiv  Detail & Related papers  (2023-01-12T12:02:26Z)
• Projection-free Constrained Stochastic Nonconvex Optimization with State-dependent Markov Data [0.0]
  We show a projection-free gradient-type algorithm for constrained non- Markovian case chain problems with Markovian data. We also empirically demonstrate the performance of our algorithm on the problem of strategic classification with neural networks.
  arXiv  Detail & Related papers  (2022-06-22T19:43:15Z)
• Semi-Supervised Subspace Clustering via Tensor Low-Rank Representation [64.49871502193477]
  We propose a novel semi-supervised subspace clustering method, which is able to simultaneously augment the initial supervisory information and construct a discriminative affinity matrix. Comprehensive experimental results on six commonly-used benchmark datasets demonstrate the superiority of our method over state-of-the-art methods.
  arXiv  Detail & Related papers  (2022-05-21T01:47:17Z)
• Towards the Semantic Weak Generalization Problem in Generative Zero-Shot Learning: Ante-hoc and Post-hoc [89.68803484284408]
  We present a simple and effective strategy lowering the previously unexplored factors that limit the performance ceiling of generative Zero-Shot Learning (ZSL) We begin by formally defining semantic generalization, then look into approaches for reducing the semantic weak generalization problem. In the ante-hoc phase, we augment the generator's semantic input, as well as relax the fitting target of the generator.
  arXiv  Detail & Related papers  (2022-04-24T13:54:42Z)
• Semi-Supervised Learning with Meta-Gradient [123.26748223837802]
  We propose a simple yet effective meta-learning algorithm in semi-supervised learning. We find that the proposed algorithm performs favorably against state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-07-08T08:48:56Z)
• Gradient Descent in RKHS with Importance Labeling [58.79085525115987]
  We study importance labeling problem, in which we are given many unlabeled data. We propose a new importance labeling scheme that can effectively select an informative subset of unlabeled data.
  arXiv  Detail & Related papers  (2020-06-19T01:55:00Z)
• Progressive Identification of True Labels for Partial-Label Learning [112.94467491335611]
  Partial-label learning (PLL) is a typical weakly supervised learning problem, where each training instance is equipped with a set of candidate labels among which only one is the true label. Most existing methods elaborately designed as constrained optimizations that must be solved in specific manners, making their computational complexity a bottleneck for scaling up to big data. This paper proposes a novel framework of classifier with flexibility on the model and optimization algorithm.
  arXiv  Detail & Related papers  (2020-02-19T08:35:15Z)

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.