New kernels from neural networks show better performance than traditional methods.
problem Improving neural network performance on small datasets.
method Developed algebraic operations to create compositional kernels from neural network architectures.
result Compositional kernels achieve higher accuracy than neural tangent kernels and neural networks on small datasets.
Deep Local-Global network improves lung nodule malignancy prediction.
problem Challenging task of classifying lung nodules as benign or malignant.
method Proposes a novel method combining local and global feature extraction.
result Achieved state-of-the-art results with AUC=95.62%.
Deep-learning improves 6x6-mm OCTA angiograms by reducing noise and artifacts.
problem Reduced scan quality in 6x6-mm OCTA angiograms due to undersampling.
method Deep-learning-based high-resolution angiogram reconstruction network (HARNet) trained on 3x3-mm and 6x6-mm angiogram data.
result Reconstructed 6x6-mm angiograms have lower noise and better vascular connectivity.
In this paper we study geometric, algebraic, and computational aspects of flexibility and infinitesimal flexibility of Kokotsakis meshes. A Kokotsakis mesh is a mesh that consists of a face in the middle and a certain band of faces attached to the middle face by its perimeter. In particular any 3x3-mesh made of quadran…
The paper presents a generalized Weierstrass representation for pseudospherical surfaces in terms of 3x3 matrices, using moving frames and loop group decompositions. The construction of all such surfaces, starting from a given representation, constitutes the subject of a separate, ulterior report. The appendix of the p…
After recalling the notion of caustics of plane curves and basic equations, we first show the birationality of the caustic map for a general source point S in the plane. Then we prove more generally a theorem for curves D in the projective space of 3x3 symmetric matrices B. For a general 3x1 vector S the projection to …
Inspired by the paper on quantum knots and knot mosaics [23] and grid diagrams (or arc presentations), used extensively in the computations of Heegaard-Floer knot homology [2,3,7,24], we construct the more concise representation of knot mosaics and grid diagrams via mirror-curves. Tame knot theory is equivalent to knot…
Let G be the Heisenberg group of real lower triangular 3x3 matrices with unit diagonal. A locally free smooth action of G on a manifold M^4 is given by linearly independent vector fields X_1, X_2, X_3 such that X_3 = [X_1,X_2] and [X_1,X_3] = [X_2, X_3] = 0. The C^1 topology for vector fields induces a topology in the …
In this paper an alternative theory about space-time is given. First some preliminaries about 3-dimensional time and the reasons for its introduction are presented. Alongside the 3-dimensional space (S) the 3-dimensional space of spatial rotations (SR) is considered independently from the 3-dimensional space. Then it i…
This paper optimizes object tracking on edge devices with small matrices.
problem Efficiently tracking objects in video sequences on edge devices with small matrices.
method Parallelized a Simple Online and Real-time Tracking (SORT) application on shared-memory multicores.
result Throughput-based parallelization technique outperforms multi-threading for small matrices.
SparseRT accelerates sparse computations on GPUs for deep learning inference.
problem Efficiently handling unstructured sparsity patterns on GPUs for deep learning.
method SparseRT, a code generator that leverages unstructured sparsity for accelerating sparse linear algebra operations.
result Geometric mean speedups of 3.4x at 90% sparsity and 5.4x at 95% sparsity for 1x1 convolutions and fully connected layers.
By formulating N = 1, 2, 4, 8, D = 3, Yang-Mills with a single Lagrangian and single set of transformation rules, but with fields valued respectively in R,C,H,O, it was recently shown that tensoring left and right multiplets yields a Freudenthal-Rosenfeld-Tits magic square of D = 3 supergravities. This was subsequently…
New method detects inconsistencies in AHP matrices using triadic preference reversals.
problem Challenges in assessing consistency in AHP pairwise comparison matrices.
method Triadic preference reversals to detect inconsistencies between pairs of elements.
result 97% accuracy in detecting inconsistencies, significantly surpassing traditional methods.
Paper connects Painlevé VI equation to irregular systems, solving monodromy data.
problem Solving monodromy data for irregular systems related to Painlevé VI.
method Expressed Frobenius integrability in terms of PVI, computed monodromy data for coalescing eigenvalues.
result Computed monodromy data for transcendentals holomorphic at critical points of PVI.
Many unsupervised kernel methods rely on the estimation of the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). Both kernel CO and kernel CCO are sensitive to contaminated data, even when bounded positive definite kernels are used. To the best of our knowledge, there are few well…
Survey of kernels, RKHS, and their applications in machine learning.
problem Understanding kernels and their applications in machine learning.
method Review of historical context, mathematical definitions, and practical applications of kernels.
result Comprehensive overview of kernels, RKHS, and their applications.
To the best of our knowledge, there are no general well-founded robust methods for statistical unsupervised learning. Most of the unsupervised methods explicitly or implicitly depend on the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). They are sensitive to contaminated data, …
Deep neural kernels and Laplace kernel have equivalent RKHS on spheres.
problem Comparing RKHS of deep neural tangent and Laplace kernels.
method Proof of RKHS equivalence using sphere restrictions and kernel properties.
result RKHS of deep neural tangent kernel and Laplace kernel are the same on Sd−1. Kernel methods linked to feature subspaces and maximal correlation kernels.
problem Understanding kernel methods and their relationship to feature extraction.
method Established a correspondence between feature subspaces and kernels, introduced maximal correlation kernels, and demonstrated their optimality.
result Kernel SVM on maximal correlation kernel achieves minimum prediction error.
Adapts manifold structure for better clustering performance.
problem Lack of consideration for local manifold structure in existing multiple kernel k-means methods.
method Adopts manifold adaptive kernel to integrate local manifold structure of kernels.
result Proposed method outperforms state-of-the-art methods.
PGF kernels analyze spherical data using generalized RBF kernels.
problem Analysis of spherical data.
method Introduced PGF kernels and a semi-parametric learning algorithm.
result PGF kernels generalize RBF kernels for spherical data.
Optimal kernel in KR can be data-dependent, improving model performance.
problem Fixed kernel in KR limits model performance.
method Considered data-dependent kernels for KR, using posterior covariance.
result Data-dependent kernel choice leads to optimal performance.
Quantum kernels can be efficiently embedded into classical feature spaces.
problem Can all quantum kernels be efficiently embedded into classical feature spaces?
method Invoking computational universality and using techniques like random Fourier features, the authors show that certain classes of quantum kernels can be efficiently embedded.
result For shift-invariant and composition kernels, embedding quantum kernels are universal and efficient.
New random feature maps for Laplacian and related kernels.
problem Challenges in approximating the Laplacian kernel and its generalizations.
method Developed random feature maps for Laplacian and related kernels, providing efficient sampling schemes.
result Demonstrated the efficacy of these random feature maps on real datasets.
New method for learning with non-Euclidean data using decomposable kernels.
problem Difficulty in using classical kernels for non-Euclidean data.
method Reproducing kernel Krein space (RKKS) methods for kernels that admit a positive decomposition.
result Invariant kernels can be used for learning in non-Euclidean spaces.
New estimator reduces kernel mean estimation error.
problem Kernel mean estimation in reproducing kernel Hilbert spaces.
method Corrupt data with known distributions and estimate kernel mean under the corrupted distribution.
result The marginalized kernel mean estimator achieves lower estimation error.
Estimates kernel eigenvalues for compositional dot-product kernels.
problem Improving estimates for kernel eigenvalues.
method Eigenvalue decay estimates of integral operators associated with dot-product kernels.
result Improved estimates for kernel volumes in reproducing kernel Hilbert spaces.
A new kernel, Isolation Kernel, simplifies large scale online kernel learning without sacrificing accuracy.
problem Building efficient and scalable kernel-based models from large datasets with high accuracy.
method Introducing Isolation Kernel, which creates an exact, sparse, and finite-dimensional feature map of a kernel, allowing for efficient large scale online kernel learning without accuracy loss.
result Large scale online kernel learning can be achieved efficiently and accurately using Isolation Kernel.
Optimal Biweight kernel and computationally efficient Epanechnikov kernel for modal linear regression.
problem Finding the best kernel for modal linear regression.
method Refined analysis of asymptotic statistical behavior and IRLS algorithm convergence.
result Biweight kernel minimizes asymptotic mean squared error, Epanechnikov kernel guarantees IRLS convergence.
We present Random Partition Kernels, a new class of kernels derived by demonstrating a natural connection between random partitions of objects and kernels between those objects. We show how the construction can be used to create kernels from methods that would not normally be viewed as random partitions, such as Random…
The NNGP kernel's predictions closely match those of the Matern kernel under certain conditions.
problem Comparing NNGP kernels to Matern kernels in practical applications.
method Demonstrated the necessity of normalization for NNGP kernels, explored numerical challenges, and compared predictions and performance.
result NNGP kernel predictions closely match Matern kernel predictions under specific circumstances.
In this paper, we compare 5 different nonlinear kernels: min-max, RBF, fRBF (folded RBF), acos, and acos-χ2, on a wide range of publicly available datasets. The proposed fRBF kernel performs very similarly to the RBF kernel. Both RBF and fRBF kernels require an important tuning parameter (γ). Interestingly, for a …
New kernels allow learning from non-separable data.
problem Learning from non-separable data.
method Introducing entangled kernels and a two-step algorithm.
result Efficient algorithm for learning entangled kernels.
Laplace kernel and Neural Tangent Kernels are shown to be nearly identical for normalized data.
problem Understanding the similarity between Laplace and Neural Tangent Kernels.
method Theoretical analysis and experiments on normalized data.
result Laplace kernel and Neural Tangent Kernels have nearly identical eigenfunctions and RKHS for normalized data.
Kernel smoothing on unknown manifolds with bounds and asymptotic normality.
problem Data on unknown manifolds without boundaries.
method Finite sample bounds and asymptotic normality for kernel smoothing and its derivatives.
result Established finite sample bounds and asymptotic normality for kernel smoothing.
In this paper we propose a family of tractable kernels that is dense in the family of bounded positive semi-definite functions (i.e. can approximate any bounded kernel with arbitrary precision). We start by discussing the case of stationary kernels, and propose a family of spectral kernels that extends existing approac…
The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce a new algorithm for kernel learning that combines a {\em continuous set of base …
Quantum kernel machines need to use more complex kernels to fully exploit their potential.
problem Current quantum kernels struggle with complex learning tasks due to limited degrees of freedom.
method Propose using operator-valued kernels and C∗-algebraic representations to enhance quantum kernels. result Quantum operator-valued kernels can reveal structural dependencies that scalar-valued kernels miss.
New kernels capture both local and non-local interactions efficiently.
problem Designing kernels that capture both local and non-local interactions while remaining computationally tractable.
method Spectral truncation kernels based on C∗-algebra. result Spectral truncation kernels induce interactions across the data function domain and reduce computational cost.
Constructing the adjacency graph is fundamental to graph-based clustering. Graph learning in kernel space has shown impressive performance on a number of benchmark data sets. However, its performance is largely determined by the chosen kernel matrix. To address this issue, the previous multiple kernel learning algorith…
Optimal kernel improves estimation accuracy in modal statistical methods.
problem Estimation accuracy of kernel-based modal statistical methods depends on the kernel used.
method The study theoretically shows an optimal kernel that minimizes asymptotic error criterion.
result An optimal kernel minimizes the error criterion when using an optimal bandwidth.
Efficiently searches through Gaussian process kernels using symbolic representation and Bayesian optimization.
problem Manual selection of kernels in Gaussian processes is complex and computationally expensive.
method Proposes a novel method using symbolic representation and Bayesian optimization to search through a structured kernel space.
result Empirically shows a computationally more efficient way of searching through a discrete kernel space.
New kernel learns optimal bijection for graph classification.
problem Graph classification with optimal bijection.
method Multiple kernel learning for Weisfeiler-Lehman assignment kernels.
result Feasibility and effectiveness of the approach demonstrated.
This paper improves t-SNE using Isolation kernel for better data representation and efficiency.
problem Misrepresentation of data structures and high computational cost in t-SNE.
method Replacing Gaussian kernel with Isolation kernel in t-SNE.
result Isolation kernel improves t-SNE's accuracy and efficiency without sacrificing quality.
The term "CoRE kernel" stands for correlation-resemblance kernel. In many applications (e.g., vision), the data are often high-dimensional, sparse, and non-binary. We propose two types of (nonlinear) CoRE kernels for non-binary sparse data and demonstrate the effectiveness of the new kernels through a classification ex…
Sparse Kernel Flows learns dynamical systems from data.
problem Learning dynamical systems from limited data.
method Sparse Kernel Flows: trains optimal kernel from a dictionary of kernels.
result Sparse Kernel Flows can learn from 132 chaotic systems.
MKLpy simplifies Multiple Kernel Learning in Python.
problem Learning optimal kernel functions from data.
method Python-based framework for Multiple Kernel Learning algorithms.
result Maximizes usability and simplifies development of novel solutions.
The study investigates kernel-target alignment in tree ensemble kernels.
problem The degree of kernel-target alignment affects the performance of tree ensemble kernels in kernel learning.
method Eigenanalysis of the kernel matrix and sensitivity analysis via landmark learning.
result Good performance of tree ensemble kernels is associated with strong kernel-target alignment.