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We propose a novel node embedding of directed graphs to statistical manifolds, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way. Each node is encoded with a probability density…
Let $(X,\left\Vert \cdot \right\Vert )$ be a real normed space of dimension $N\in \mathbb{N}$ with a basis $(e_{i})_{1}^{N}$ such that the norm is invariant under coordinate permutations. Assume for simplicity that the basis constant is at…
Spectral Embedding (SE) has often been used to map data points from non-linear manifolds to linear subspaces for the purpose of classification and clustering. Despite significant advantages, the subspace structure of data in the original…
Node embedding refers to techniques that generate low-dimensional vector representations of nodes in a graph while preserving specific properties of the nodes. A key challenge in the field is developing scalable methods that can preserve…
Deep Metric Learning algorithms aim to learn an efficient embedding space to preserve the similarity relationships among the input data. Whilst these algorithms have achieved significant performance gains across a wide plethora of tasks,…
Nontrivial isometric embeddings for flat metrics (i.e., those which are not just planes in the ambient space) can serve as useful tools in the description of gravity in the embedding gravity approach. Such embeddings can additionally be…
Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…
Compressed sensing can increase resolution, and decrease electron dose and scan time of electron microscope point-scan systems with minimal information loss. Building on a history of successful deep learning applications in compressed…
We extend our work for compression of currents and varifolds to a compression algorithm for the embedded normal cycles representation of shape, restricted to the constant normal kernel case, using the Nystrom approximation in Reproducing…
The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…
Majority of the current dimensionality reduction or retrieval techniques rely on embedding the learned feature representations onto a computable metric space. Once the learned features are mapped, a distance metric aids the bridging of gaps…
Deep-embedding methods aim to discover representations of a domain that make explicit the domain's class structure and thereby support few-shot learning. Disentangling methods aim to make explicit compositional or factorial structure. We…
Incremental improvements in accuracy of Convolutional Neural Networks are usually achieved through use of deeper and more complex models trained on larger datasets. However, enlarging dataset and models increases the computation and storage…
Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
Neural population activity in sensory cortex is organized on low-dimensional manifolds, but why such manifolds arise and what determines their geometry remain unclear. We model cortical populations as recurrent circuits driven by…
We demonstrate an equivalence between reproducing kernel Hilbert space (RKHS) embeddings of conditional distributions and vector-valued regressors. This connection introduces a natural regularized loss function which the RKHS embeddings…
We propose a method for learning embeddings for few-shot learning that is suitable for use with any number of ways and any number of shots (shot-free). Rather than fixing the class prototypes to be the Euclidean average of sample…
In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…
Recently there is a line of research work proposing to employ Spectral Clustering (SC) to segment (group){Throughout the paper, we use segmentation, clustering, and grouping, and their verb forms, interchangeably.} high-dimensional…