Related papers: Deep Diffusion Maps
Deep neural networks are widely used in various domains. However, the nature of computations at each layer of the deep networks is far from being well understood. Increasing the interpretability of deep neural networks is thus important.…
Dimensionality reduction (DR) of image features plays an important role in image retrieval and classification tasks. Recently, two types of methods have been proposed to improve the both the accuracy and efficiency for the dimensionality…
State-of-the-art fully intrinsic networks for non-rigid shape matching often struggle to disambiguate the symmetries of the shapes leading to unstable correspondence predictions. Meanwhile, recent advances in the functional map framework…
Map matching for sparse trajectories is a fundamental problem for many trajectory-based applications, e.g., traffic scheduling and traffic flow analysis. Existing methods for map matching are generally based on Hidden Markov Model (HMM) or…
Real-world data usually have high dimensionality and it is important to mitigate the curse of dimensionality. High-dimensional data are usually in a coherent structure and make the data in relatively small true degrees of freedom. There are…
Diffusion models (DMs) have achieved state-of-the-art results for image synthesis tasks as well as density estimation. Applied in the latent space of a powerful pretrained autoencoder (LDM), their immense computational requirements can be…
Diffusion MRI tractography technique enables non-invasive visualization of the white matter pathways in the brain. It plays a crucial role in neuroscience and clinical fields by facilitating the study of brain connectivity and neurological…
Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in recent years to the analysis of large and complex data sets. However, such algorithms still encounter challenges when faced with real data. One…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…
Diffusion, a fundamental internal mechanism emerging in many physical processes, describes the interaction among different objects. In many learning tasks with limited training samples, the diffusion connects the labeled and unlabeled data…
Estimating correspondences between pairs of deformable shapes remains a challenging problem. Despite substantial progress, existing methods lack broad generalization capabilities and require category-specific training data. To address these…
We consider the problem of computing dense correspondences between non-rigid shapes with potentially significant partiality. Existing formulations tackle this problem through heavy manifold optimization in the spectral domain, given…
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…
Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…
Objective functions that optimize deep neural networks play a vital role in creating an enhanced feature representation of the input data. Although cross-entropy-based loss formulations have been extensively used in a variety of supervised…
In this work, we propose a simple kernel ridge regression (KRR) framework with a dynamic-aware validation strategy for long-term prediction of complex dynamical systems. By employing a data-driven kernel derived from diffusion maps, the…
Convolutional networks are successful, but they have recently been outperformed by new neural networks that are equivariant under rotations and translations. These new networks work better because they do not struggle with learning each…
Modern successes of diffusion models in learning complex, high-dimensional data distributions are attributed, in part, to their capability to construct diffusion processes with analytic transition kernels and score functions. The…
The process of decomposing target images into their internal properties is a difficult task due to the inherent ill-posed nature of the problem. The lack of data required to train a network is a one of the reasons why the decomposing…
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…