Related papers: Kernel Smoothing, Mean Shift, and Their Learning T…
We propose new small-sphere distributional families for modeling multivariate directional data on $(\mathbb{S}^{p-1})^K$ for $p \ge 3$ and $K \ge 1$. In a special case of univariate directions in $\Re^3$, the new densities model random…
Mean Shift today, is widely used for mode detection and clustering. The technique though, is challenged in practice due to assumptions of isotropicity and homoscedasticity. We present an adaptive Mean Shift methodology that allows for full…
Diffusion models have achieved state-of-the-art performance, demonstrating remarkable generalisation capabilities across diverse domains. However, the mechanisms underpinning these strong capabilities remain only partially understood. A…
When analyzing modern machine learning algorithms, we may need to handle kernel density estimation (KDE) with intricate kernels that are not designed by the user and might even be irregular and asymmetric. To handle this emerging challenge,…
Biclustering algorithms partition data and covariates simultaneously, providing new insights in several domains, such as analyzing gene expression to discover new biological functions. This paper develops a new model-free biclustering…
We study the Stochastic Gradient Descent (SGD) algorithm in nonparametric statistics: kernel regression in particular. The directional bias property of SGD, which is known in the linear regression setting, is generalized to the kernel…
Spherical k-means is a widely used clustering algorithm for sparse and high-dimensional data such as document vectors. While several improvements and accelerations have been introduced for the original k-means algorithm, not all easily…
We study the data selection problem, whose aim is to select a small representative subset of data that can be used to efficiently train a machine learning model. We present a new data selection approach based on $k$-means clustering and…
We provide initial seedings to the Quick Shift clustering algorithm, which approximate the locally high-density regions of the data. Such seedings act as more stable and expressive cluster-cores than the singleton modes found by Quick…
We present a versatile formulation of the convolution operation that we term a "mapped convolution." The standard convolution operation implicitly samples the pixel grid and computes a weighted sum. Our mapped convolution decouples these…
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
Blurring mean shift (BMS) algorithm, a variant of the mean shift algorithm, is a kernel-based iterative method for data clustering, where data points are clustered according to their convergent points via iterative blurring. In this paper,…
This paper extends the blurring mean shift algorithm from vector-valued data to functional data, enabling effective clustering in infinite-dimensional settings without requiring specification of the number of clusters. To address the…
We derive analytical expressions for the generalization performance of kernel regression as a function of the number of training samples using theoretical methods from Gaussian processes and statistical physics. Our expressions apply to…
In this paper we present a new dynamical systems algorithm for clustering in hyperspectral images. The main idea of the algorithm is that data points are \`pushed\' in the direction of increasing density and groups of pixels that end up in…
Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the…
Timeseries generated from a dynamical source can often be modeled as sample paths of a stochastic differential equation (SDE). The timeseries thus reflects the motion of a particle which flows along the direction provided by a drift /…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…
Distance-based clustering and classification are widely used in various fields to group mixed numeric and categorical data. In many algorithms, a predefined distance measurement is used to cluster data points based on their dissimilarity.…
Spectral algorithms leverage spectral regularization techniques to analyze and process data, providing a flexible framework for addressing supervised learning problems. To deepen our understanding of their performance in real-world…