New measure quantifies function similarity for optimization.
problem Measuring similarity between functions for optimization.
method Quantifies sub-optimality gaps and operation rules.
result Unified measure for various functional similarities.
Improved CNN for HCCR with new loss function and ranking method.
problem Loss of inter-class information in traditional CNN models for HCCR.
method Combining cross entropy with a new similarity ranking function (Average variance similarity) as loss function.
result New loss function (SoftMax cross entropy with Average variance similarity) achieves highest accuracy in HCCR.
Study uses trajectory embedding to measure place function similarity at fine spatial granularity.
problem Measuring place function similarity at fine spatial granularity.
method Trajectory embedding to reduce dimensions and measure similarity of place functions.
result Embedding similarity can be a metric proxy for place functions at fine spatial granularity.
Introduces CHL, a new loss function for continuous similarity learning.
problem Binary similarity learning limitations.
method CHL is a novel loss function that generalizes histogram loss to continuous similarities.
result CHL solves a wider range of tasks including similarity learning, representation learning, and data visualization.
Exploits class similarity for better machine learning models with confidence labels and projective loss functions.
problem Poor model performance due to confusing similar classes.
method Exploits class similarity with confidence labels and projective loss functions.
result Improved model performance on noisy labels.
Quantum networks learn task-dependent asymmetric similarity measures.
problem Challenges of conventional distance functions in capturing meaningful similarity.
method GQSim: Quantum networks for learning task-dependent (a)symmetric similarity.
result Quantum similarity measures extract salient features and achieve theoretically guaranteed performance.
fMRI is a unique non-invasive approach for understanding the functional organization of the human brain, and task-based fMRI promotes identification of functionally relevant brain regions associated with a given task. Here, we use fMRI (using the Poffenberger Paradigm) data collected in mono- and dizygotic twin pairs t…
Study finds solutions to flows by negative curvature powers.
problem Curvature flows with negative powers.
method Closed self-similar solutions in warped product manifolds, proving non-strict convexity.
result Proves self-similar solutions are slices of warped product manifolds.
SBSS uses similarity to split data for better classifier training.
problem Training better classifiers with realistic performance estimation.
method SBSS uses both input and output space information to split data using similarity functions.
result SBSS outperformed ordinary stratified 10-fold cross-validation in 75% of scenarios.
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…
LSH methods extend to function spaces for efficient similarity search.
problem Efficient similarity search in function spaces.
method Locality-sensitive hashing (LSH) extended to Lp spaces using function approximation or Monte Carlo techniques. result An LSH family for Wasserstein distance over continuous probability distributions.
Measuring the similarity of two files is an important task in malware analysis, with fuzzy hash functions being a popular approach. Traditional fuzzy hash functions are data agnostic: they do not learn from a particular dataset how to determine similarity; their behavior is fixed across all datasets. In this paper, we …
In this paper, a similarity-driven cluster merging method is proposed for unsuper-vised fuzzy clustering. The cluster merging method is used to resolve the problem of cluster validation. Starting with an overspecified number of clusters in the data, pairs of similar clusters are merged based on the proposed similarity-…
This paper provides a theoretical and computational justification of the long held claim that of the similarity of the probit and logit link functions often used in binary classification. Despite this widespread recognition of the strong similarities between these two link functions, very few (if any) researchers have …
The study proves uniqueness and symmetry of self-similar solutions in warped product spaces.
problem Uniqueness and symmetry of self-similar solutions in warped product spaces.
method Analysis of curvature flows with homogeneous speed functions in warped product spaces.
result Compact star-shaped self-similar solutions in warped product spaces are slices.
Proposes a new neural network approach to credit assignment.
problem Credit assignment problem in deep neural networks.
method Contrastive similarity matching objective function.
result Deep networks learn to match similarity between layers.
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.
Task loss matching misrepresents similarity between neural network layers.
problem Measuring similarity between neural network layers using task loss matching.
method Task loss matching vs. direct matching; comparison with CCA and CKA.
result Direct matching provides a better similarity index than task loss matching.
Improved similarity search in embeddings using InfoNCE loss.
problem Improving similarity search in embedding models trained by contrastive learning.
method Introduced a new continuity bound for InfoNCE loss via Gâteaux differentiation, preserving the averaging effect of negative samples.
result Demonstrated that the averaging effect of k negative samples in InfoNCE loss carries over to stabilisation of generalisation error as k grows. 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.
The two main theorems of this paper provide a characterization of hyperbolic affine iterated function systems defined on Rm. Atsushi Kameyama (Distances on Topological Self-Similar Sets, Proceedings of Symposia in Pure Mathematics, Volume 72.1, 2004) asked the following fundamental question: given a topological self-si…
Framework learns item representations from text data for complementary and similar items.
problem Generating accurate complementary item recommendations from textual data.
method Quadruplet network learning framework for latent space representation of items.
result Items are placed closer together in latent space for similar and complementary items compared to non-complementary items.
We address the problem of general supervised learning when data can only be accessed through an (indefinite) similarity function between data points. Existing work on learning with indefinite kernels has concentrated solely on binary/multi-class classification problems. We propose a model that is generic enough to hand…
The paper develops a decision support system for hierarchical text classification of conference proceedings.
problem Classifying documents with a fixed hierarchical structure of topics.
method Developed a weighted hierarchical similarity function to calculate topic relevance, using entropy of words to estimate weights.
result The weighted hierarchical similarity function improves ranking accuracy compared to other methods.
We propose a new approach for analyzing price fluctuations in their strongly correlated regime ranging from minutes to months. This is done by employing a self-similarity assumption for the magnitude of coarse-grained price fluctuation or volatility. The existence of a Cramer function, the characteristic function for s…
Extends graph similarity theory to improve MPNNs' generalization abilities.
problem Understanding MPNNs' generalization beyond training data.
method Extends graph similarity theory, assesses graph structure, aggregation, and loss functions.
result Improves understanding of MPNNs' generalization properties.
Study on self-similar sets on Riemannian manifolds with new separation conditions.
problem Analyzing self-similar sets on Riemannian manifolds with new separation conditions.
method Formulated weak separation and finite type conditions for conformal iterated function systems on Riemannian manifolds.
result Obtained formulas for Hausdorff dimensions of self-similar and graph self-similar sets.
The development of algorithms for hierarchical clustering has been hampered by a shortage of precise objective functions. To help address this situation, we introduce a simple cost function on hierarchies over a set of points, given pairwise similarities between those points. We show that this criterion behaves sensibl…
Graph Matching Networks learn graph similarity using GNN embeddings.
problem Learning similarity between graph structured objects.
method Graph Matching Network model using cross-graph attention mechanism.
result Models outperform baseline systems in function similarity search.
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.
Paper improves image retrieval quality using nonlinear rank approximations.
problem Improving image retrieval quality in high-dimensional feature spaces.
method Computes normalized approximated ranks, converts to similarities, and uses them in a new loss function.
result Significant improvement in image retrieval quality on multiple datasets.
New measure assesses neural network models' functional similarity.
problem Measuring functional similarity between similar-performing neural networks.
method Robust nonparametric hypothesis testing framework.
result Proposed measure assesses neural networks' functional similarity.
Enzyme sequences and structures are routinely used in the biological sciences as queries to search for functionally related enzymes in online databases. To this end, one usually departs from some notion of similarity, comparing two enzymes by looking for correspondences in their sequences, structures or surfaces. For a…
Defines a similarity measure for classification distributions.
problem Measuring similarity between classification distributions.
method Proposes task similarity, a novel measure quantifying performance of source distributions on target distributions.
result Empirical task similarity correlates with transfer efficiency and semantic similarity of source distributions.
We consider the representation power of siamese-style similarity functions used in neural network-based graph embedding. The inner product similarity (IPS) with feature vectors computed via neural networks is commonly used for representing the strength of association between two nodes. However, only a little work has b…
As a highlighting research topic in the multimedia area, cross-media retrieval aims to capture the complex correlations among multiple media types. Learning better shared representation and distance metric for multimedia data is important to boost the cross-media retrieval. Motivated by the strong ability of deep neura…
We propose shifted inner-product similarity (SIPS), which is a novel yet very simple extension of the ordinary inner-product similarity (IPS) for neural-network based graph embedding (GE). In contrast to IPS, that is limited to approximating positive-definite (PD) similarities, SIPS goes beyond the limitation by introd…
The paper analyzes the generalization of deep neural networks for metric and similarity learning.
problem Lack of rigorous understanding of generalization performance in metric and similarity learning.
method Derive explicit form of true metric, construct structured deep ReLU neural network, establish excess risk bounds.
result Explicit excess risk bounds for metric and similarity learning are derived.
This paper tackles efficient optimization for nonlinear embeddings in similarity learning.
problem Learning similarity with nonlinear embeddings is challenging due to the large number of pairs.
method Detailed derivations and efficient optimization methods for nonlinear embeddings are developed.
result Efficient optimization methods for nonlinear embeddings are shown to be highly effective.
Proposes a revenue function to evaluate dendrograms from comparisons.
problem Evaluate dendrograms from comparisons without ground-truth.
method Introduces a new revenue function related to Dasgupta's cost.
result Revenue function allows meaningful evaluation of dendrograms.
Similarity measure for Gaussian process predictive distributions.
problem Comparing predictive distributions of Gaussian processes for correlated functions.
method Developed a similarity metric to compare predictive distributions of Gaussian processes.
result Gaussian process predictive distributions can be compared and one is enough to model two correlated functions.
Inverse depth scaling found in LLMs due to similar layers averaging error.
problem Understanding how depth affects loss in large language models.
method Analysis of LLMs and toy residual networks.
result Loss scales inversely proportional to depth in LLMs.
This paper improves nearest neighbor search by learning optimal routing functions.
problem Local minima issues in greedy routing on similarity graphs.
method Learn routing function that considers global graph structure.
result Significant improvement in search performance via learning.
SimLoss improves classification by considering class similarities.
problem Equal punishment of all misclassifications in CCE.
method Integrates class similarities into Categorical Cross Entropy using matrices constructed from task-specific knowledge.
result Significant improvements over CCE on Age Estimation and Image Classification.
We consider the setting of Reeb graphs of piecewise linear functions and study distances between them that are stable, meaning that functions which are similar in the supremum norm ought to have similar Reeb graphs. We define an edit distance for Reeb graphs and prove that it is stable and universal, meaning that it pr…
This paper studies quasar-convex functions to improve optimization methods.
problem Improving optimization methods for non-convex functions.
method Study of first order methods for quasar-convex functions.
result Proves complexity upper bounds similar to convex functions.
Local regularization improves geometric estimates from noisy data.
problem Improving geometric understanding from noisy, perturbed data.
method Local regularization of noisy point clouds to define similarity.
result Locally regularized similarity leads to better geometric recovery.
Financial market dynamics is rigorously studied via the exact generalized Langevin equation. Assuming market Brownian self-similarity, the market return rate memory and autocorrelation functions are derived, which exhibit an oscillatory-decaying behavior with a long-time tail, similar to empirical observations. Individ…