Paper proposes a new framework for learning discriminative similarity for clustering and semi-supervised learning.
problem The importance of pairwise similarity for clustering and semi-supervised learning performance.
method Proposes a novel discriminative similarity learning framework that learns from hypothetical labelings and minimizes generalization error.
result Discriminative similarity learned from hypothetical labelings can improve clustering and semi-supervised learning performance.
Proposes rpf-kernel for clustering via random projection forests.
problem Clustering similar data points while distinguishing them from dissimilar ones.
method Random projection forests to learn a similarity kernel.
result rpf-kernel effectively clusters data with competitive performance.
Meta-learning framework uses task similarity through nonparametric kernel regression.
problem Limited tasks and outliers/dissimilar tasks hinder meta-learning performance.
method Nonparametric kernel regression to quantify and use task similarity.
result Meta-learning algorithm outperforms existing methods in task-limited settings.
Graph kernels assess graph similarity for various applications.
problem Assessing similarity between graphs for predictions.
method Review and comparison of existing graph kernels.
result State-of-the-art graph kernels reviewed and compared.
Given only information in the form of similarity triplets "Object A is more similar to object B than to object C" about a data set, we propose two ways of defining a kernel function on the data set. While previous approaches construct a low-dimensional Euclidean embedding of the data set that reflects the given similar…
We propose a new method to model multi-way similarities into hypergraphs for clustering.
problem Clustering real-valued data using hypergraphs with multi-way similarities.
method Formulate multi-way similarities using kernel functions, establish connections to hypergraph cut, and develop a fast spectral clustering algorithm.
result Our method outperforms existing graph and heuristic modeling methods in clustering performance.
Neural network learns kernel functions for survival analysis and prediction intervals.
problem Predicting survival times for individuals based on similar training subjects.
method Develops a neural network framework to learn kernel functions for kernel survival analysis and uses these to construct valid prediction intervals.
result Neural network survival estimators are competitive with existing methods and provide valid prediction intervals.
New clustering method using point-set kernel measures similarity.
problem Measuring similarity between objects for clustering.
method Point-set kernel for similarity computation; clustering procedure uses this measure.
result Proposed method is more effective and faster than existing algorithms.
Extends Tanimoto kernel to real-valued functions.
problem Measuring similarity between real-valued functions.
method Unified representation of real-valued functions via sets, derived general form of the kernel, explicit feature representation, and smooth approximation.
result General Tanimoto kernel for real-valued functions.
Many similarity-based clustering methods work in two separate steps including similarity matrix computation and subsequent spectral clustering. However, similarity measurement is challenging because it is usually impacted by many factors, e.g., the choice of similarity metric, neighborhood size, scale of data, noise an…
Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector machine compared to other competing similarity measures. Specifically, the idea of usi…
A new kernel measures brain network similarities, improving disease classification.
problem Lack of edge weight information in existing graph kernels for brain connectivity networks.
method Ordinal pattern kernel for weighted brain connectivity networks.
result The ordinal pattern kernel achieves better classification performance than state-of-the-art graph kernels.
Kernelized Taylor diagram visualizes data populations with fewer assumptions.
problem Limitations of Taylor diagram in capturing non-linear relationships and sensitivity to outliers.
method Proposes a kernelized version of the Taylor diagram that uses maximum mean discrepancy and kernel mean embedding.
result Kernelized Taylor diagram visualizes data populations with minimal assumptions of data distributions.
Despite the success of the popular kernelized support vector machines, they have two major limitations: they are restricted to Positive Semi-Definite (PSD) kernels, and their training complexity scales at least quadratically with the size of the data. Many natural measures of similarity between pairs of samples are not…
Graph kernels improve graph similarity and learning tasks.
problem Tackling graph similarity and learning tasks.
method Proposes a message passing scheme framework for designing graph kernels.
result Kernels derived from the framework are competitive with state-of-the-art methods.
Proposes a method to preserve graph similarities for better clustering accuracy.
problem Sub-optimal performance due to non-similarity-preserving kernels in graph-based clustering.
method Adaptive graph learning method that preserves pairwise similarities and unifies clustering and graph learning.
result Improves clustering accuracy by preserving pairwise similarities in the graph.
Tree++ graph kernel captures similarities at multiple granularities.
problem Lack of scale-adaptivity in existing graph kernels.
method Tree++ uses truncated BFS trees and super paths to represent graphs at different granularities.
result Tree++ achieves best classification accuracy on real-world graphs.
The paper proves recurrence relations for heat kernels on hyperbolic and spherical spaces.
problem Understanding recurrence relations of heat kernels on different space forms.
method Direct proof and computation of recurrence relations for heat kernels on hyperbolic and spherical spaces.
result Computed diagonal of heat kernels for odd dimensional hyperbolic spaces and heat trace asymptotic expansions for odd dimensional spheres.
GraKeL combines multiple graph kernels for graph similarity measurement.
problem Accurately measuring graph similarity across various applications.
method Unified graph kernel library in Python with scikit-learn interface.
result Facilitates graph classification and clustering tasks.
Enhances graph neural networks by considering feature similarities in node aggregation.
problem Ignoring node feature similarities in traditional graph aggregation schemes.
method Interprets node aggregation as kernel weighting, proposing a framework that considers feature similarities.
result Proposed framework outperforms traditional GCNs in real-world applications.
Paper proposes a new method to learn similarity from data.
problem Learning similarity from data without losing manifold structure.
method Minimizing reconstruction error of kernel matrices.
result Significant improvements in clustering tasks compared to state-of-the-art methods.
This research calculates node similarity on graphs using path-based kernels.
problem Computing similarity between nodes on graphs.
method Derives closed-form expressions for co-presence and co-occurrence of nodes on paths.
result Introduced kernels provide competitive results in semi-supervised classification.
Kernel alignment measures the degree of similarity between two kernels. In this paper, inspired from kernel alignment, we propose a new Linear Discriminant Analysis (LDA) formulation, kernel alignment LDA (kaLDA). We first define two kernels, data kernel and class indicator kernel. The problem is to find a subspace to …
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 review introduces graph kernels for chemoinformatics.
problem Quantifying similarity between molecular graphs.
method Graph kernels as a method for quantifying molecular graph similarity.
result Graph kernels have direct applications in chemoinformatics.
Deep kernels learn from embeddings to capture data similarity efficiently.
problem Capturing similarity between high-dimensional data points with small labeled data.
method Probabilistic neural network to learn deep kernels on probabilistic embeddings.
result Our approach outperforms state-of-the-art GP kernel learning in various settings.
New framework for node classification on graphs using kernel methods.
problem Graph kernel methods for node classification are ill-posed and rely on heuristics.
method Theoretical kernel-based framework for node classification, combining graph kernel methodology with node feature aggregation and data-driven similarity metrics.
result Our framework sets a new state of the art in node classification benchmarks.
Fuzzy hashes learn from data to improve file similarity detection.
problem Measuring similarity between files, especially malware.
method Learned fuzzy hashes using a minimax training framework.
result Learned fuzzy hashes outperform traditional methods for file similarity.
Study improves material similarity measures considering distinctiveness.
problem Improving similarity measures for materials science applications.
method Used machine learning techniques with specific descriptors and kernels.
result Minimizing loss of distinctiveness improves prediction accuracy.
The paper studies how neural networks evolve representations, finding a unique fixed point for nonlinear activations.
problem Understanding how neural networks transform input data across layers.
method Theoretical framework for the evolution of the kernel sequence, using mean-field regime and Hermite polynomials.
result For nonlinear activations, the kernel sequence converges globally to a unique fixed point.
Producing overlapping schemes is a major issue in clustering. Recent proposed overlapping methods relies on the search of an optimal covering and are based on different metrics, such as Euclidean distance and I-Divergence, used to measure closeness between observations. In this paper, we propose the use of another meas…
Kernel methods summarize and integrate posterior similarity matrices from Bayesian clustering.
problem Summarizing and integrating posterior similarity matrices from Bayesian clustering.
method Positive semi-definite PSMs, kernel matrices, kernel methods, combining kernels.
result Kernel methods effectively summarize and integrate posterior similarity matrices.
The method of "random Fourier features (RFF)" has become a popular tool for approximating the "radial basis function (RBF)" kernel. The variance of RFF is actually large. Interestingly, the variance can be substantially reduced by a simple normalization step as we theoretically demonstrate. We name the improved scheme …
This work analyzes when contrastive models are close to PCA or kernel methods.
problem Understanding when contrastive models are equivalent to kernel methods or PCA.
method Analyzing the training dynamics of two-layer contrastive models with non-linear activation.
result Wide contrastive models with cosine similarity based losses are close to PCA.
Optimizes graph spectral density learning for large networks.
problem Ad-hoc kernel function and bandwidth selection in graph spectral techniques.
method Maximum Entropy approach to learn a smooth graph spectral density.
result Outperforms comparable iterative spectral approaches on synthetic and real graphs.
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.
We propose a simple kernel based nearest neighbor approach for handwritten digit classification. The "distance" here is actually a kernel defining the similarity between two images. We carefully study the effects of different number of neighbors and weight schemes and report the results. With only a few nearest neighbo…
Unified spectral clustering improves on traditional methods by optimizing similarity graph and reducing information loss.
problem Traditional spectral clustering steps lead to information loss and performance degradation.
method Automatically learns optimal similarity graph and integrates continuous and discrete label learning.
result Unified framework optimizes clustering performance and reduces information loss.
Enhances autoencoders with kernel alignment for better data representation.
problem Lack of clear properties for autoencoders to capture in data representations.
method Aligns inner products between codes with a kernel matrix to capture topological properties.
result Effective data representations learned, preserving input data similarities.
New methods predict drug interactions using drug co-medication patterns and graph matching.
problem Predicting adverse drug reactions from drug combinations.
method Developed novel kernels over drug combinations using support vector machines and graph matching to measure similarities.
result Achieved an AUC of 0.912 on a real-world dataset.
New similarity index avoids limitations of CCA in neural networks.
problem Limitations of existing methods in measuring neural network representation similarity.
method Introducing a similarity index based on centered kernel alignment (CKA) to measure representational similarity matrices.
result CKA reliably identifies correspondences between representations in networks trained from different initializations.
Method predicts PAF episodes up to 15 minutes in advance from ECGs.
problem Predicting Paroxysmal Atrial Fibrillation (PAF) from ECGs.
method Feature extraction of ECGs as multi-variate time series, kernel similarity-based classification.
result Comparable classification accuracy with state-of-the-art methods, predictive up to 15 minutes.
Improves Bayesian optimization efficiency for mixed variable spaces.
problem Boosting sample efficiency in Bayesian optimization for mixed variable spaces.
method Proposes frequency modulated (FM) kernels to model complex dependencies across different types of variables.
result BO-FM outperforms competitors in various optimization problems.
Proposes neural similarity for CNNs to enhance flexibility and performance.
problem Limited flexibility of inner product-based convolution in CNNs.
method Introduces neural similarity as a learnable parametric similarity measure, and proposes NSL for adaptive learning from data.
result Dynamic neural similarity improves flexibility and performance in visual recognition and few-shot learning.
Improved forecasting of suicide attempts using LSGPs for patients with little data.
problem Challenges in predicting suicide attempts due to their rarity and patient heterogeneity.
method Introduced Latent Similarity Gaussian Processes (LSGPs) to capture patient heterogeneity.
result LSGPs outperform baseline models, even without kernel-design, and offer new insights into patient similarity.
New algorithms optimize multiple tasks with shared similarities, reducing regret.
problem Optimizing multiple objectives with shared similarities in non-parametric Bayesian optimization.
method Developed two novel BO algorithms using multi-task kernels and random scalarizations.
result Derived worst-case regret bounds capturing inter-task similarities.
Machine learning predicts graph layouts and metrics.
problem Selecting a good graph layout method is subjective and computationally expensive.
method Uses graph kernels to compute topological similarity and estimate layout aesthetics.
result Estimation is faster and more accurate than actual layout calculations.
We investigate iterated compositions of weighted sums of Gaussian kernels and provide an interpretation of the construction that shows some similarities with the architectures of deep neural networks. On the theoretical side, we show that these kernels are universal and that SVMs using these kernels are universally con…