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Unsupervised learning is the most challenging problem in machine learning and especially in deep learning. Among many scenarios, we study an unsupervised learning problem of high economic value --- learning to predict without costly pairing…

Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…

In machine learning or statistics, it is often desirable to reduce the dimensionality of a sample of data points in a high dimensional space $\mathbb{R}^d$. This paper introduces a dimensionality reduction method where the embedding…

We present a general framework of semi-supervised dimensionality reduction for manifold learning which naturally generalizes existing supervised and unsupervised learning frameworks which apply the spectral decomposition. Algorithms derived…

Manifold learning flows are a class of generative modelling techniques that assume a low-dimensional manifold description of the data. The embedding of such a manifold into the high-dimensional space of the data is achieved via learnable…

A fundamental problem in supervised learning is to find a good set of features or distance measures. If the new set of features is of lower dimensionality and can be obtained by a simple transformation of the original data, they can make…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

Representation learning is typically applied to only one mode of a data matrix, either its rows or columns. Yet in many applications, there is an underlying geometry to both the rows and the columns. We propose utilizing this coupled…

Nonlinear embedding manifold learning methods provide invaluable visual insights into the structure of high-dimensional data. However, due to a complicated nonconvex objective function, these methods can easily get stuck in local minima and…

Fine-tuned pre-trained language models can suffer from severe miscalibration for both in-distribution and out-of-distribution (OOD) data due to over-parameterization. To mitigate this issue, we propose a regularized fine-tuning method. Our…

This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…

Manifold learning (ML) aims to seek low-dimensional embedding from high-dimensional data. The problem is challenging on real-world datasets, especially with under-sampling data, and we find that previous methods perform poorly in this case.…

Many approaches in the field of machine learning and data analysis rely on the assumption that the observed data lies on lower-dimensional manifolds. This assumption has been verified empirically for many real data sets. To make use of this…

Local discriminative representation is needed in many medical image analysis tasks such as identifying sub-types of lesion or segmenting detailed components of anatomical structures. However, the commonly applied supervised representation…

Statistically correcting measured cross sections for detector effects is an important step across many applications. In particle physics, this inverse problem is known as unfolding. In cases with complex instruments, the distortions they…

spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. The main aim is to learn a meaningful low dimensional embedding of the data. However, most subspace learning methods do not take into…

Uniform Manifold Approximation and Projection (UMAP) is a widely used manifold learning technique for dimensionality reduction. This paper studies UMAP, supervised UMAP, and several competing dimensionality reduction methods, including…

The inability of deep learning models to handle data drawn from unseen distributions has sparked much interest in unsupervised out-of-distribution (U-OOD) detection, as it is crucial for reliable deep learning models. Despite considerable…

In video surveillance, person re-identification is the task of searching person images in non-overlapping cameras. Though supervised methods for person re-identification have attained impressive performance, obtaining large scale cross-view…

In mesh-based numerical simulations, the interpolation of mesh-defined functions across different meshes is a critical task, and achieving high-precision interpolation is of great significance for improving the computational efficiency and…