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Deep learning methods have played a more and more important role in hyperspectral image classification. However, the general deep learning methods mainly take advantage of the information of sample itself or the pairwise information between…
This paper presents a fundamental algorithm, called VDB-EDT, for Euclidean distance transform (EDT) based on the VDB data structure. The algorithm executes on grid maps and generates the corresponding distance field for recording distance…
In recent years, Denoising Diffusion Models have demonstrated remarkable success in generating semantically valuable pixel-wise representations for image generative modeling. In this study, we propose a novel end-to-end framework, called…
The embedded topic model (ETM) is a widely used approach that assumes the sampled document-topic distribution conforms to the logistic normal distribution for easier optimization. However, this assumption oversimplifies the real…
We introduce the diffusion and superposition distances as two metrics to compare signals supported in the nodes of a network. Both metrics consider the given vectors as initial temperature distributions and diffuse heat trough the edges of…
A graph embedding is a representation of graph vertices in a low-dimensional space, which approximately preserves properties such as distances between nodes. Vertex sequence-based embedding procedures use features extracted from linear…
The Diffusion Probabilistic Model (DPM) has recently gained popularity in the field of computer vision, thanks to its image generation applications, such as Imagen, Latent Diffusion Models, and Stable Diffusion, which have demonstrated…
The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…
Neuron segmentation in electron microscopy (EM) aims to reconstruct the complete neuronal connectome; however, current deep learning-based methods are limited by their reliance on large-scale training data and extensive, time-consuming…
Limited by the encoder-decoder architecture, learning-based edge detectors usually have difficulty predicting edge maps that satisfy both correctness and crispness. With the recent success of the diffusion probabilistic model (DPM), we…
We introduce the Linearized Diffusion Map (LDM), a novel linear dimensionality reduction method constructed via a linear approximation of the diffusion-map kernel. LDM integrates the geometric intuition of diffusion-based nonlinear methods…
Diffusion geometry is a manifold learning framework that uses random walks defined by Markov transition matrices to characterize the geometry of a dataset at multiple scales. We use diffusion geometry for neural representations,…
Under a set of assumptions on a family of submanifolds $\subset {\mathbb R}^D$, we derive a series of geometric properties that remain valid after finite-dimensional and almost isometric Diffusion Maps (DM), including almost uniform…
Although ubiquitous in the sciences, histogram data have not received much attention by the Deep Learning community. Whilst regression and classification tasks for scalar and vector data are routinely solved by neural networks, a principled…
In this paper, we address the challenging task of achieving multi-view dimensionality reduction. The goal is to effectively use the availability of multiple views for extracting a coherent low-dimensional representation of the data. The…
Diffusion models (DMs) have emerged as a powerful class of generative AI models, showing remarkable potential in anomaly detection (AD) tasks across various domains, such as cybersecurity, fraud detection, healthcare, and manufacturing. The…
We introduce multi-frequency vector diffusion maps (MFVDM), a new framework for organizing and analyzing high dimensional datasets. The new method is a mathematical and algorithmic generalization of vector diffusion maps (VDM) and other…
Diffusion-based manifold learning methods have proven useful in representation learning and dimensionality reduction of modern high dimensional, high throughput, noisy datasets. Such datasets are especially present in fields like biology…
Denoising Diffusion Models (DDMs) have become a popular tool for generating high-quality samples from complex data distributions. These models are able to capture sophisticated patterns and structures in the data, and can generate samples…
Stable Diffusion Models (SDMs) have shown remarkable proficiency in image synthesis. However, their broad application is impeded by their large model sizes and intensive computational requirements, which typically require expensive cloud…