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We propose a simple yet novel data augmentation method for general data modalities based on energy-based modeling and principles from information geometry. Unlike most existing learning-based data augmentation methods, which rely on…
Distance metric learning can be viewed as one of the fundamental interests in pattern recognition and machine learning, which plays a pivotal role in the performance of many learning methods. One of the effective methods in learning such a…
This survey is written in summer, 2016. The purpose of this survey is to briefly introduce nonlinear dimensionality reduction (NLDR) in data reduction. The first two NLDR were respectively published in Science in 2000 in which they solve…
Manifold learning aims to discover and represent low-dimensional structures underlying high-dimensional data while preserving critical topological and geometric properties. Existing methods often fail to capture local details with global…
Conformal Autoencoders are a neural network architecture that imposes orthogonality conditions between the gradients of latent variables to obtain disentangled representations of data. In this work we show that orthogonality relations…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
The rapid progress in machine learning methods has been empowered by i) huge datasets that have been collected and annotated, ii) improved engineering (e.g. data pre-processing/normalization). The existing datasets typically include several…
We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on…
Although Structure-from-Motion (SfM) as a maturing technique has been widely used in many applications, state-of-the-art SfM algorithms are still not robust enough in certain situations. For example, images for inspection purposes are often…
Deep latent variable models learn condensed representations of data that, hopefully, reflect the inner workings of the studied phenomena. Unfortunately, these latent representations are not statistically identifiable, meaning they cannot be…
Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning. To better classify the manifold-valued features, researchers have started extending Euclidean…
Machine learning models with both good predictability and high interpretability are crucial for decision support systems. Linear regression is one of the most interpretable prediction models. However, the linearity in a simple linear…
Manifold learning seeks a low dimensional representation that faithfully captures the essence of data. Current methods can successfully learn such representations, but do not provide a meaningful set of operations that are associated with…
Retrieval Augmented Generation (RAG) systems often struggle with domain-specific knowledge due to performance deterioration of pre-trained embeddings and prohibitive computational costs of large language model (LLM)-based retrievers. While…
Estimating the state of an environment from high-dimensional, multimodal, and noisy observations is a fundamental challenge in reinforcement learning (RL). Traditional approaches rely on probabilistic models to account for the uncertainty,…
By incorporating physical consistency as inductive bias, deep neural networks display increased generalization capabilities and data efficiency in learning nonlinear dynamic models. However, the complexity of these models generally…
Meta-learning, or "learning to learn," aims to enable models to quickly adapt to new tasks with minimal data. While traditional methods like Model-Agnostic Meta-Learning (MAML) optimize parameters in Euclidean space, they often struggle to…
LiDAR (short for "Light Detection And Ranging" or "Laser Imaging, Detection, And Ranging") technology can be used to provide detailed three-dimensional elevation maps of urban and rural landscapes. To date, airborne LiDAR imaging has been…
How do the neural networks distinguish two images? It is of critical importance to understand the matching mechanism of deep models for developing reliable intelligent systems for many risky visual applications such as surveillance and…
Safe motion planning in robotics requires planning into space which has been verified to be free of obstacles. However, obtaining such environment representations using lidars is challenging by virtue of the sparsity of their depth…