Related papers: A theory of stratification learning
We show how, given a sufficiently large point cloud sampled from an embedded 2-manifold in $\mathbb{R}^n$, we may obtain a global representation as a cell complex with vertices given by a representative subset of the point cloud. The vertex…
Modeling of high-dimensional data is very important to categorize different classes. We develop a new mixture model called Multinomial cluster-weighted model (MCWM). We derive the identifiability of a general class of MCWM. We estimate the…
The problem of dimension reduction is of increasing importance in modern data analysis. In this paper, we consider modeling the collection of points in a high dimensional space as a union of low dimensional subspaces. In particular we…
Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…
Subspace clustering algorithms are notorious for their scalability issues because building and processing large affinity matrices are demanding. In this paper, we introduce a method that simultaneously learns an embedding space along…
This paper describes a new approach for learning structures of large Bayesian networks based on blocks resulting from feature space clustering. This clustering is obtained using normalized mutual information. And the subsequent aggregation…
A multilayered particle is illuminated by plane acoustic or electromagnetic waves of one or several frequencies. We consider the inverse scattering problem for the identification of the layers and of the refraction coefficients of the…
We define a class of probability distributions that we call simplicial mixture models, inspired by simplicial complexes from algebraic topology. The parameters of these distributions represent their topology and we show that it is possible…
This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…
Additive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such…
Point cloud data are widely used in manufacturing applications for process inspection, modeling, monitoring and optimization. The state-of-art tensor regression techniques have effectively been used for analysis of structured point cloud…
Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes…
We present Submatrix-wise Vector Embedding Learner (Swivel), a method for generating low-dimensional feature embeddings from a feature co-occurrence matrix. Swivel performs approximate factorization of the point-wise mutual information…
As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…
Large parallax between images is an intractable issue in image stitching. Various warping-based methods are proposed to address it, yet the results are unsatisfactory. In this paper, we propose a novel image stitching method using…
We present a novel framework exploiting the cascade of phase transitions occurring during a simulated annealing of the Expectation-Maximisation algorithm to cluster datasets with multi-scale structures. Using the weighted local covariance,…
This article introduces a novel, geometric approach for multi-manifold clustering (MMC), i.e. for clustering a collection of potentially intersecting, d-dimensional manifolds into the individual manifold components. We first compute a…
Graph-based clustering methods have demonstrated the effectiveness in various applications. Generally, existing graph-based clustering methods first construct a graph to represent the input data and then partition it to generate the…
The performance of a machine learning system is usually evaluated by using i.i.d.\ observations with true labels. However, acquiring ground truth labels is expensive, while obtaining unlabeled samples may be cheaper. Stratified sampling can…
Multi-model fitting has been extensively studied from the random sampling and clustering perspectives. Most assume that only a single type/class of model is present and their generalizations to fitting multiple types of models/structures…