An evaluation framework for dimensionality reduction through sectional curvature

• URL: http://arxiv.org/abs/2303.09909v1
• Date: Fri, 17 Mar 2023 11:59:33 GMT
• Title: An evaluation framework for dimensionality reduction through sectional curvature
• Authors: Ra\'ul Lara-Cabrera, \'Angel Gonz\'alez-Prieto, Diego P\'erez-L\'opez, Diego Trujillo, Fernando Ortega
• Abstract summary: In this work, we aim to introduce the first highly non-supervised dimensionality reduction performance metric. To test its feasibility, this metric has been used to evaluate the performance of the most commonly used dimension reduction algorithms. A new parameterized problem instance generator has been constructed in the form of a function generator.
• Score: 59.40521061783166
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Unsupervised machine learning lacks ground truth by definition. This poses a major difficulty when designing metrics to evaluate the performance of such algorithms. In sharp contrast with supervised learning, for which plenty of quality metrics have been studied in the literature, in the field of dimensionality reduction only a few over-simplistic metrics has been proposed. In this work, we aim to introduce the first highly non-trivial dimensionality reduction performance metric. This metric is based on the sectional curvature behaviour arising from Riemannian geometry. To test its feasibility, this metric has been used to evaluate the performance of the most commonly used dimension reduction algorithms in the state of the art. Furthermore, to make the evaluation of the algorithms robust and representative, using curvature properties of planar curves, a new parameterized problem instance generator has been constructed in the form of a function generator. Experimental results are consistent with what could be expected based on the design and characteristics of the evaluated algorithms and the features of the data instances used to feed the method.

Related papers

• Eliminating Ratio Bias for Gradient-based Simulated Parameter Estimation [0.7673339435080445]
  This article addresses the challenge of parameter calibration in models where the likelihood function is not analytically available. We propose a gradient-based simulated parameter estimation framework, leveraging a multi-time scale that tackles the issue of ratio bias in both maximum likelihood estimation and posterior density estimation problems.
  arXiv  Detail & Related papers  (2024-11-20T02:46:15Z)
• Dimension reduction via score ratio matching [0.9012198585960441]
  We propose a framework, derived from score-matching, to extend gradient-based dimension reduction to problems where gradients are unavailable. We show that our approach outperforms standard score-matching for problems with low-dimensional structure.
  arXiv  Detail & Related papers  (2024-10-25T22:21:03Z)
• A Universal Class of Sharpness-Aware Minimization Algorithms [57.29207151446387]
  We introduce a new class of sharpness measures, leading to new sharpness-aware objective functions. We prove that these measures are textitly expressive, allowing any function of the training loss Hessian matrix to be represented by appropriate hyper and determinants.
  arXiv  Detail & Related papers  (2024-06-06T01:52:09Z)
• Interpretable Linear Dimensionality Reduction based on Bias-Variance Analysis [45.3190496371625]
  We propose a principled dimensionality reduction approach that maintains the interpretability of the resulting features. In this way, all features are considered, the dimensionality is reduced and the interpretability is preserved.
  arXiv  Detail & Related papers  (2023-03-26T14:30:38Z)
• Robust online joint state/input/parameter estimation of linear systems [0.0]
  This paper presents a method for jointly estimating the state, input, and parameters of linear systems in an online fashion. The method is specially designed for measurements that are corrupted with non-Gaussian noise or outliers.
  arXiv  Detail & Related papers  (2022-04-12T09:41:28Z)
• Gradient-Based Learning of Discrete Structured Measurement Operators for Signal Recovery [16.740247586153085]
  We show how to leverage gradient-based learning to solve discrete optimization problems. Our approach is formalized by GLODISMO (Gradient-based Learning of DIscrete Structured Measurement Operators) We empirically demonstrate the performance and flexibility of GLODISMO in several signal recovery applications.
  arXiv  Detail & Related papers  (2022-02-07T18:27:08Z)
• An AI-Assisted Design Method for Topology Optimization Without Pre-Optimized Training Data [68.8204255655161]
  An AI-assisted design method based on topology optimization is presented, which is able to obtain optimized designs in a direct way. Designs are provided by an artificial neural network, the predictor, on the basis of boundary conditions and degree of filling as input data.
  arXiv  Detail & Related papers  (2020-12-11T14:33:27Z)
• Precise expressions for random projections: Low-rank approximation and randomized Newton [63.68433510953756]
  Matrix sketching has emerged as a powerful technique for performing such dimensionality reduction very efficiently. We develop techniques that provide provably accurate expressions for the expected value of random projection matrices obtained via sketching. These expressions can be used to characterize the performance of dimensionality reduction in a variety of common machine learning tasks.
  arXiv  Detail & Related papers  (2020-06-18T16:23:00Z)
• Deep Dimension Reduction for Supervised Representation Learning [51.10448064423656]
  We propose a deep dimension reduction approach to learning representations with essential characteristics. The proposed approach is a nonparametric generalization of the sufficient dimension reduction method. We show that the estimated deep nonparametric representation is consistent in the sense that its excess risk converges to zero.
  arXiv  Detail & Related papers  (2020-06-10T14:47:43Z)
• Semiparametric Nonlinear Bipartite Graph Representation Learning with Provable Guarantees [106.91654068632882]
  We consider the bipartite graph and formalize its representation learning problem as a statistical estimation problem of parameters in a semiparametric exponential family distribution. We show that the proposed objective is strongly convex in a neighborhood around the ground truth, so that a gradient descent-based method achieves linear convergence rate. Our estimator is robust to any model misspecification within the exponential family, which is validated in extensive experiments.
  arXiv  Detail & Related papers  (2020-03-02T16:40:36Z)

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.