Modes and ridges of the probability density function behind observed data are useful geometric features. Mode-seeking clustering assigns cluster labels by associating data samples with the nearest modes, and estimation of density ridges enables us to find lower-dimensional structures hidden in data. A key technical cha…
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48 results for “density mode”
Density mode clustering is a nonparametric clustering method. The clusters are the basins of attraction of the modes of a density estimator. We study the risk of mode-based clustering. We show that the clustering risk over the cluster cores --- the regions where the density is high --- is very small even in high dimens…
New method uses random projections to estimate densities and modes efficiently.
problem Estimating densities and modes from sparse representations.
method Expand-and-sparsify representations followed by linear function and mode recovery algorithms.
result Optimal rates for density and mode estimation achieved.
A new online method estimates mode from samples using ODE analysis.
problem Estimating mode from samples when analytical density is unknown.
method Online iterative algorithm using ODE analysis for asymptotic convergence and stability.
result Asymptotic convergence and stability of estimates demonstrated.
An image pattern can be represented by a probability distribution whose density is concentrated on different low-dimensional subspaces in the high-dimensional image space. Such probability densities have an astronomical number of local modes corresponding to typical pattern appearances. Related groups of modes can join…
Study finds the number of modes in Gaussian kernel density estimators scales with sqrt(β log β).
problem Determining the number of clusters in Transformers.
method Used Kac-Rice formula and Edgeworth expansion to prove scaling.
result The expected number of modes scales as Θ(√(β log β)).
A new GAN variant avoids mode collapse and generates high-quality images.
problem Mode collapse in GANs.
method Mixture Density GAN uses Gaussian mixtures to encourage the discriminator to form clusters, leading the generator to discover multiple data modes.
result Mixture Density GAN generates images with high quality and avoids mode collapse, as shown by FID metrics.
Estimates modes and ridges in mixed Euclidean and directional spaces.
problem Estimating local modes and density ridges in product spaces combining Euclidean and directional metrics.
method Extends mean shift algorithm to product spaces, addressing challenges in generalization.
result Established convergence of the proposed methods and demonstrated effectiveness on real-world datasets.
Advances scalable clustering and density mode finding.
problem Joint clustering and density mode finding for large datasets.
method Proposes a concave-convex relaxation with parallel algorithm optimization.
result Optimizes a tight bound for cluster assignment variables.
Bayesian taut splines estimate modes in probability densities.
problem Estimating the number of modes in probability density functions.
method Bayesian inference with flexible kernel estimators and compositional splines.
result The new method provides more accurate results than traditional approaches.
New tools for constructing disintegrations and studying their modes.
problem Difficulty in constructing disintegrations and understanding their modes.
method Developed comprehensive mathematical tools for constructing disintegrations and analyzing their modes.
result Disagreement between restricted density and disintegration density in certain cases.
Study guarantees convergence of mean shift mode estimation.
problem Ensuring reliable mode estimation in KDE using mean shift.
method Utilizes Łojasiewicz inequality to prove convergence rate.
result Extends convergence guarantees to biweight kernel.
Mean shift clustering finds the modes of the data probability density by identifying the zero points of the density gradient. Since it does not require to fix the number of clusters in advance, the mean shift has been a popular clustering algorithm in various application fields. A typical implementation of the mean shi…
Develops an MS-inspired algorithm for regression mode finding and space partitioning.
problem Finding local modes of regression functions and partitioning input space.
method Mean-shift-inspired algorithm for iterative gradient ascent.
result Proves convergence and rates of convergence for estimated local modes.
Kernel methods are popular in clustering due to their generality and discriminating power. However, we show that many kernel clustering criteria have density biases theoretically explaining some practically significant artifacts empirically observed in the past. For example, we provide conditions and formally prove the…
A natural way to characterize the cluster structure of a dataset is by finding regions containing a high density of data. This can be done in a nonparametric way with a kernel density estimate, whose modes and hence clusters can be found using mean-shift algorithms. We describe the theory and practice behind clustering…
We propose an estimation method for the conditional mode when the conditioning variable is high-dimensional. In the proposed method, we first estimate the conditional density by solving quantile regressions multiple times. We then estimate the conditional mode by finding the maximum of the estimated conditional density…
Learning an optimal policy from a multi-modal reward function is a challenging problem in reinforcement learning (RL). Hierarchical RL (HRL) tackles this problem by learning a hierarchical policy, where multiple option policies are in charge of different strategies corresponding to modes of a reward function and a gati…
BDMBC clusters data with varying densities using a new PLLS measure.
problem Finding clusters with varying densities in data.
method Bagged -distance with PLLS for mode estimation.
result BDMBC achieves optimal convergence rates for mode and level set estimation.
PresGANs improve GANs by mitigating mode collapse and enhancing log-likelihood.
problem GANs struggle with mode collapse and lack a reliable way to evaluate generalization.
method PresGANs add noise to density networks and use entropy regularization to stabilize training and capture all modes.
result PresGANs reduce the gap in predictive log-likelihood between GANs and VAEs.
CNFs model conditional densities efficiently and avoid mode collapse.
problem Capturing strong correlations between output dimensions in structured prediction tasks.
method Conditional normalizing flows (CNFs) with a likelihood-based objective.
result CNFs achieve competitive performance in super-resolution and vessel segmentation tasks.
Mode clustering is a nonparametric method for clustering that defines clusters using the basins of attraction of a density estimator's modes. We provide several enhancements to mode clustering: (i) a soft variant of cluster assignment, (ii) a measure of connectivity between clusters, (iii) a technique for choosing the …
We introduce the functional mean-shift algorithm, an iterative algorithm for estimating the local modes of a surrogate density from functional data. We show that the algorithm can be used for cluster analysis of functional data. We propose a test based on the bootstrap for the significance of the estimated local modes …
The two most extended density-based approaches to clustering are surely mixture model clustering and modal clustering. In the mixture model approach, the density is represented as a mixture and clusters are associated to the different mixture components. In modal clustering, clusters are understood as regions of high d…
New method trains neural samplers to sample from multi-modal distributions efficiently.
problem Mode-seeking behavior of reverse KL divergence hinders effective sampling from multi-modal target distributions.
method Minimizing reverse diffusive KL divergence along diffusion trajectories of model and target densities.
result Demonstrated enhanced sampling performance across various multi-modal distributions.
VB approximates posterior mean perfectly in linear Gaussian VAR models.
problem Unknown approximation error of VB in VAR models.
method Derive approximation error in terms of mean, mode, variance, predictive density, and KL divergence.
result VB approximates posterior mean perfectly.
RAHMC improves sampling from multimodal distributions using dissipative dynamics.
problem Sampling from multimodal distributions efficiently.
method RAHMC uses mode-repelling and mode-attracting stages with a single tuning parameter.
result RAHMC generates proposals that cross low-probability barriers efficiently.
Paper proposes a new method for robust modal regression.
problem Estimating the global mode of conditional density functions robustly.
method Directly approximates the gradient of modal regression risk using kernelized and neural-network-based log-density derivative estimators.
result Proposed methods achieve superior performance on various datasets.
Measures mode separation in high-dimensional densities via a reversible diffusion process.
problem Quantifying how sharply a distribution fragments into barrier-separated clusters in high dimensions.
method A unique reversible diffusion process with f as stationary distribution, extracting SSA and DA from its autocovariance matrix.
result Empirical autocovariance spectrum and readouts (SSA, DA) quantify mode separation using only samples and pretrained score-based models.
Learning Compact Physics-Aware Delayed Photocurrent Models Using Dynamic Mode Decompositionphysics.comp-ph
Compact models learn photocurrent dynamics from radiation-induced excess carrier density.
problem Accurate but computationally expensive physics-based photocurrent models for semiconductor devices.
method Dynamic Mode Decomposition (DMD) for learning reduced order models from internal state data.
result Physics-aware, compact delayed photocurrent models accurately approximate internal excess carrier dynamics.
Chia and Nakano (2009) introduced the concept of M-decomposability of probability densities in one-dimension. In this paper, we generalize M-decomposability to any dimension. We prove that all elliptical unimodal densities are M-undecomposable. We also derive an inequality to show that it is better to represent an M-de…
Efficient clustering in high dimensions with Quick Shift and LSH.
problem Density-based clustering in high-dimensional data.
method Combines Quick Shift and LSH for efficient density estimation.
result Achieves almost linear time complexity for consistency.
The paper introduces new estimators for multivariate functions using Fourier methods.
problem Estimating multivariate functions like densities and regression functions.
method Monte Carlo estimators based on the Fourier integral theorem.
result Established rates of convergence for new estimators, often superior to existing methods.
Multimodal clustering is an unsupervised technique for mining interesting patterns in -adic binary relations or -mode networks. Among different types of such generalized patterns one can find biclusters and formal concepts (maximal bicliques) for 2-mode case, triclusters and triconcepts for 3-mode case, closed $n…
We propose a new definition for the abelian magnetic charge density of a non-abelian monopole, based on zero-modes of an associated Dirac operator. Unlike the standard definition of the charge density, this density is smooth in the core of the monopole. We show that this charge density induces a magnetic field whose ex…
Model financial markets using open quantum systems to understand market imperfections.
problem Understanding market imperfections through imperfect trading mechanisms.
method Using open quantum systems to represent financial markets, characterizing orbits, and analyzing reduced density matrices.
result Non-classical modes of time evolution can incorporate factors like illiquid trades and imperfect trading mechanisms.
Study classifies mappings of bivariate normal densities, revealing three types with distinct geometric and statistical properties.
problem Understanding the properties of two-component bivariate normal mixtures.
method Classification via -equivalence and statistical analysis.
result Three distinct types of mappings with specific geometric and statistical properties, and upper bounds for the number of modes.
Method uses normalizing flows to efficiently sample from complex target densities.
problem Sampling from complex target densities with zero values in regions of transformation.
method Normalizing flows to address exploding reverse Kullback-Leibler divergence.
result Demonstrated efficient sampling from multi-mode complex density function.
Implicit generative models are difficult to train as no explicit density functions are defined. Generative adversarial nets (GANs) present a minimax framework to train such models, which however can suffer from mode collapse due to the nature of the JS-divergence. This paper presents a learning by teaching (LBT) approa…
We present a nonparametric method for selecting informative features in high-dimensional clustering problems. We start with a screening step that uses a test for multimodality. Then we apply kernel density estimation and mode clustering to the selected features. The output of the method consists of a list of relevant f…
Unified framework for sampling from complex densities using PDEs and neural networks.
problem Sampling from complicated probability densities.
method Dynamical measure transport via PDEs and physics-informed neural networks (PINNs).
result Significantly better mode coverage and high accuracy in sampling.
A new method improves posterior approximation for complex distributions.
problem Difficulty in capturing multimodal and heavy-tailed posteriors with standard normalizing flows.
method StiCTAF: stick-breaking mixture base with component-wise tail adaptation.
result Improved tail recovery and better mode coverage compared to benchmarks.
The paper studies kernel smoothing and mean shift for directional data, deriving convergence rates and mode estimation.
problem Statistical and computational problems of kernel smoothing for directional data.
method Generalization of mean shift to directional data, derivation of convergence rates, and investigation of mode estimation.
result Statistical convergence rates of directional KDE and its derivatives, ascending property of directional mean shift, and mode estimation.
Given i.i.d samples from some unknown continuous density on hyper-rectangle , we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a binary split of and built up sequentially according to discrepancy crite…
New method for k-modes algorithm improves clustering performance.
problem Improving initial solution selection for k-modes algorithm.
method Uses Hospital-Resident Assignment Problem to find initial cluster centroids.
result Outperforms other initialisations in most cases, especially for low-density data.
In addition to finding meaningful clusters, centroid-based clustering algorithms such as K-means or mean-shift should ideally find centroids that are valid patterns in the input space, representative of data in their cluster. This is challenging with data having a nonconvex or manifold structure, as with images or text…
Log-density gradient estimation is a fundamental statistical problem and possesses various practical applications such as clustering and measuring non-Gaussianity. A naive two-step approach of first estimating the density and then taking its log-gradient is unreliable because an accurate density estimate does not neces…
Many clustering algorithms exist that estimate a cluster centroid, such as K-means, K-medoids or mean-shift, but no algorithm seems to exist that clusters data by returning exactly K meaningful modes. We propose a natural definition of a K-modes objective function by combining the notions of density and cluster assignm…