Affinity propagation is one of the most effective unsupervised pattern recognition algorithms for data clustering in high-dimensional feature space. However, the numerous attempts to test its performance for community detection in complex networks have been attaining results very far from the state of the art methods s…
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48 results for “affinity propagation”
Affinity propagation is an exemplar-based clustering algorithm that finds a set of data-points that best exemplify the data, and associates each datapoint with one exemplar. We extend affinity propagation in a principled way to solve the hierarchical clustering problem, which arises in a variety of domains including bi…
A recently proposed clustering method, called the Nearest Descent (ND), can organize the whole dataset into a sparsely connected graph, called the In-tree. This ND-based Intree structure proves able to reveal the clustering structure underlying the dataset, except one imperfect place, that is, there are some undesired …
Training Deep Neural Networks that are robust to norm bounded adversarial attacks remains an elusive problem. While exact and inexact verification-based methods are generally too expensive to train large networks, it was demonstrated that bounded input intervals can be inexpensively propagated from a layer to another t…
EAP clusters evolving data, promoting temporal smoothness and automatic cluster tracking.
problem Clustering time-evolving data with temporal smoothness and automatic cluster identification.
method Evolutionary Affinity Propagation (EAP) on a factor graph exchanging messages between adjacent data snapshots.
result EAP clusters data with temporal smoothness and automatically tracks clusters, outperforming existing methods.
A new method improves label propagation for unsupervised domain adaptation.
problem Improving unsupervised domain adaptation through semi-supervised learning techniques.
method Label Propagation with Augmented Anchors (ALP) for UDA.
result ALP improves over representative UDA methods and benchmarks.
The paper studies Hawkes processes under mean-field limits and criticality conditions.
problem Analyzing nearly unstable Hawkes processes in a mean-field regime.
method Extending the method by Jaisson and Rosenbaum, establishing scaling limits and propagation of chaos.
result Scaling limits of Hawkes processes are stochastic Volterra diffusions of affine type, with three distinct limiting regimes.
The paper studies distributions and controllability in quantum mechanical systems.
problem Controlling quantum mechanical systems and their evolution.
method Analysis of distributions, controllability, and geodesics on sub-Finsler manifolds.
result Proves the Lie group decomposition and geodesics equivalence for quantum system steering.
In this paper we tackle the issue of clustering trajectories of geolocalized observations. Using clustering technics based on the choice of a distance between the observations, we first provide a comprehensive review of the different distances used in the literature to compare trajectories. Then based on the limitation…
Two wave fronts and that originated at some points of the manifold are said to be causally related if one of them passed through the origin of the other before the other appeared. We define the causality relation invariant to be the algebraic number of times the earlier born front pass…
InteractionNet models noncovalent protein-ligand interactions with GNNs and explains predictions.
problem Modeling noncovalent protein-ligand interactions with graph neural networks.
method InteractionNet uses a GNN architecture with separated covalent and noncovalent convolution layers and layer-wise relevance propagation for explainability.
result InteractionNet successfully predicts noncovalent protein-ligand interactions with chemical relevance.
Exemplar-based clustering methods have been shown to produce state-of-the-art results on a number of synthetic and real-world clustering problems. They are appealing because they offer computational benefits over latent-mean models and can handle arbitrary pairwise similarity measures between data points. However, when…
A novel approach for semi-supervised learning using regularized optimal transport.
problem Improving model performance with unlabeled data.
method Regularized optimal transport between empirical measures for affinity matrix construction, incremental label propagation, and certainty score.
result Surpasses state-of-the-art results on 12 benchmark datasets.
New method improves neural network verification by considering multivariate input space of ReLU neurons.
problem Improving the effectiveness of neural network verification algorithms.
method A new tightened convex relaxation for ReLU neurons considering multivariate input space.
result Our convex relaxation is significantly stronger than the commonly used univariate-input relaxation.
The Straight-Through Estimator (STE) is widely used for back-propagating gradients through the quantization function, but the STE technique lacks a complete theoretical understanding. We propose an alternative methodology called alpha-blending (AB), which quantizes neural networks to low-precision using stochastic grad…
BNN-DP improves robustness analysis of Bayesian Neural Networks.
problem Ensuring robustness of Bayesian Neural Networks against adversarial attacks.
method Dynamic Programming applied to Bayesian Neural Networks as stochastic dynamical systems.
result BNN-DP provides tighter and more efficient bounds on prediction ranges compared to existing methods.
Bayesian Gaussian Processes layer detects out-of-distribution data in medical imaging.
problem Detecting out-of-distribution data in medical imaging tasks.
method Parameter-efficient hierarchical convolutional Gaussian Processes in Wasserstein-2 space.
result Uncertainty estimates enable superior out-of-distribution detection compared to previous methods.
Generalized belief propagation converges to optimal solutions on graphs with motifs.
problem Understanding belief propagation on loopy graphs.
method Study of generalized belief propagation on graphs with motifs.
result Generalized belief propagation converges to the global optimum of the Bethe free energy.
Bayesian layer improves image segmentation and out-of-distribution detection.
problem Outlier detection in image segmentation.
method Parameter-efficient hierarchical convolutional Gaussian Processes in Wasserstein-2 space.
result Uncertainty estimates improve out-of-distribution detection.
Belief propagation recovers backpropagation results.
problem Connection between backpropagation and belief propagation poorly understood.
method Converted backpropagation input to belief propagation input and showed results.
result Backpropagation is a special case of belief propagation.
Business taxonomies are indispensable tools for investors to do equity research and make professional decisions. However, to identify the structure of industry sectors in an emerging market is challenging for two reasons. First, existing taxonomies are designed for mature markets, which may not be the appropriate class…
Susceptibility Propagation by Using Diagonal Consistencycond-mat.stat-mech
A susceptibility propagation that is constructed by combining a belief propagation and a linear response method is used for approximate computation for Markov random fields. Herein, we formulate a new, improved susceptibility propagation by using the concept of a diagonal matching method that is based on mean-field app…
Expectation Propagationstat.ML
Variational inference is a powerful concept that underlies many iterative approximation algorithms; expectation propagation, mean-field methods and belief propagations were all central themes at the school that can be perceived from this unifying framework. The lectures of Manfred Opper introduce the archetypal example…
Almost Zoll affine surface found on cylinder.
problem Finding surfaces with special geodesic properties.
method Exhibited an affine structure on a cylinder.
result Affine structure on cylinder is almost Zoll.
Fibres affinesmath.DG
We study affine maps between affine manifolds. Even when the fibers are compact and diffeomorphic, two of them can inherit different affine structures from the source space. This leads to a fixed linear holonomy deformation theory of the affine structure of an affine manifold. We found various conditions which make the…
This paper proposes an alternating back-propagation algorithm for learning the generator network model. The model is a non-linear generalization of factor analysis. In this model, the mapping from the continuous latent factors to the observed signal is parametrized by a convolutional neural network. The alternating bac…
Study reveals decurve flows in graph propagation models.
problem Limitations of traditional graph analysis and propagation mechanisms.
method Introduces Generalized Propagation Neural Networks (GPNNs) and Continuous Unified Ricci Curvature (CURC).
result Observation of decurve flow during training of graph neural networks, revealing propagation dynamics.
Unified model combines feature and label propagation for semi-supervised classification.
problem Combining feature and label propagation for effective semi-supervised classification.
method Unified Message Passing Model (UniMP) using Graph Transformer and masked label prediction.
result Obtains new state-of-the-art results in Open Graph Benchmark (OGB).
Improved error correction using neural networks and belief propagation.
problem Inference in factor graphs with loops or poor approximations.
method Hybrid model combining FG-GNN and belief propagation.
result Hybrid model outperforms belief propagation in error correction tasks.
A new approach estimates propagators for trading risky assets.
problem Estimating price impact kernel from static data for optimal trading.
method Nonparametric estimation of propagator using offline reinforcement learning.
result Pessimistic trading strategy optimises execution costs under uncertainty.
In this article, we propose the notion of the general -affine capacity and prove some basic properties for the general -affine capacity, such as affine invariance and monotonicity. The newly proposed general -affine capacity is compared with several classical geometric quantities, e.g., the volume, the -var…
In this paper, we show that a compact affine manifold endowed with an Affine Anosov transformation is finitely covered by a complete affine nilmanifold.
An affine manifold is a manifold with torsion-free flat affine connection. A geometric topologist's definition of an affine manifold is a manifold with an atlas of charts to the affine space with affine transition functions; a radiant affine manifold is an affine manifold with holonomy consisting of affine transformati…
This thesis investigates belief propagation's performance in graphical models with loops.
problem Belief propagation's performance and convergence guarantees in models with loops are uncertain.
method Investigates how model parameters affect belief propagation's performance, convergence, and approximation quality.
result Model parameters influence the number of fixed points, convergence properties, and approximation quality of belief propagation.
LNPE enhances local connections in embeddings using extended neighbor propagation.
problem Improving local connections and interactions in nonlinear dimensionality reduction.
method Inspired by GCN, LNPE extends 1-hop neighbors to n-hop neighbors in LLE.
result LNPE produces more faithful and robust embeddings with better topological and geometrical properties.
Decoupled GCN is shown to be equivalent to label propagation.
problem Improving semi-supervised node classification in graph learning.
method The paper proves the equivalence of decoupled GCN and label propagation, and proposes a new method named PTA.
result Decoupled GCN is equivalent to two-step label propagation and can automatically assign weights to pseudo-labels.
Backprop Evolutioncs.NE
The back-propagation algorithm is the cornerstone of deep learning. Despite its importance, few variations of the algorithm have been attempted. This work presents an approach to discover new variations of the back-propagation equation. We use a domain specific lan- guage to describe update equations as a list of primi…
Proofs for decomposing branched affine surfaces into triangles and cylinders.
problem Decomposing branched affine surfaces into simpler geometric shapes.
method Proof of Veech's theorem and introduction of invariant α.
result Any pair of decompositions can be connected by flips.
An affine manifold is said to be geodesically complete if all affine geodesics extend for all time. It is said to be affine Killing complete if the integral curves for any affine Killing vector field extend for all time. We use the solution space of the quasi-Einstein equation to examine these concepts in the setting o…
A new method for target propagation using iterative approximations converges fast and is more biologically plausible.
problem Improving target propagation methods for neural networks.
method Iterative approximate inverses and local auto-encoders.
result The method converges exponentially fast under certain conditions.
Belief Propagation algorithms are instruments used broadly to solve graphical model optimization and statistical inference problems. In the general case of a loopy Graphical Model, Belief Propagation is a heuristic which is quite successful in practice, even though its empirical success, typically, lacks theoretical gu…
Global propagator for massless Dirac operator defined and analyzed.
problem Analyzing the massless Dirac operator on 3-manifolds.
method Constructing propagator as sum of oscillatory integrals, providing global definitions and small time expansions.
result Explicit calculation of propagators' symbols and coefficients in eigenvalue counting functions.
General affine surface areasmath.MG
Two families of general affine surface areas are introduced. Basic properties and affine isoperimetric inequalities for these new affine surface areas as well as for affine surface areas are established.
Study on completeness in affine and statistical geometry.
problem Completeness of affine connections on statistical manifolds and affine hypersurfaces.
method Collect basic facts, prove new theorems, provide examples.
result New theorems on completeness of affine connections.
This thesis is devoted to the study of affine processes and their applications in financial mathematics. In the first part we consider the theory of time-inhomogeneous affine processes on general state spaces. We present a concise setup for time-inhomogeneous Markov processes. For stochastically continuous affine proce…
We study affine Jacobi structures on an affine bundle , i.e. Jacobi brackets that close on affine functions. We prove that there is a one-to-one correspondence between affine Jacobi structures on and Lie algebroid structures on the vector bundle of affine functionals. Som…
A (flat) affine -manifold is a -manifold with an atlas of charts to an affine space with transition maps in the affine transformation group . We will show that a connected closed affine -manifold is either an affine Hopf -manifold or decomposes canonically to conca…
In this paper, we consider affine self-similar solutions for the affine curve shortening flow in the Euclidean plane. We obtain the equations of all affine self-similar solutions up to affine transformations and solve the equations or give descriptions of the solutions for the degenerate case. Some new special solution…