TL;DR
This paper proposes a novel active manifold learning method based on a unified framework of manifold landmarking that combines geometric manifold landmarking methods with algebraic ones and demonstrates its superiority compared to existing methods.
Feature selection is indispensable for mitigating overfitting and reducing feature redundancy in high-dimensional scenarios. However, most existing approaches rely on unstable overall separability and sample-wise geometry, thereby neglecting the stable class-specific discriminative structures and leading to poor perfor...
The manifold hypothesis suggests a natural criterion for clustering: partition data according to the manifold component from which each point is drawn. Whether two components are separable depends on a geometric tradeoff: the ambient separation between components versus the largest gap in sampling. In practice, this tr...
This work develops a bootstrap algorithm on Riemannian manifolds that is both computationally efficient and accurate for hypothesis testing and confidence region construction, and establishes high-order asymptotics under an appropriate coordinate representation induced by a second-order retraction.
This work introduces a Nested Inductive Bias framework that utilizes a two-stage diffeomorphic composition to formally pull back non-Euclidean target geometries onto the SPD manifold, and proposes the Rational Conformal Metric (RCM), designed to establish state-of-the-art geometric robustness against outliers by boundi...
Row-sparse projection provides a useful tool in machine learning (ML) when it comes to, for example, feature selection, aiming to choose most relevant features for various ML objectives. One way to seek a high quality row-sparse projection is to combine an ML objective, such as the ones for PCA, LDA, and OCCA, with the...
In this paper, we propose SHOPCA (Shape Operator-based Principal Component Analysis), a novel method for unsupervised metric learning and dimensionality reduction that incorporates differential geometric information into the covariance structure of classical PCA. SHOPCA regularizes the global covariance matrix using th...
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