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We study the problem of explainability-first clustering where explainability becomes a first-class citizen for clustering. Previous clustering approaches use decision trees for explanation, but only after the clustering is completed. In…

A main puzzle of deep neural networks (DNNs) revolves around the apparent absence of "overfitting", defined in this paper as follows: the expected error does not get worse when increasing the number of neurons or of iterations of gradient…

Clustering is a fundamental task in data mining and machine learning, particularly for analyzing large-scale data. In this paper, we introduce Clust-Splitter, an efficient algorithm based on nonsmooth optimization, designed to solve the…

Can we identify the weights of a neural network by probing its input-output mapping? At first glance, this problem seems to have many solutions because of permutation, overparameterisation and activation function symmetries. Yet, we show…

The objective functions used in spectral clustering are usually composed of two terms: i) a term that minimizes the local quadratic variation of the cluster assignments on the graph and; ii) a term that balances the clustering partition and…

This paper studies the dynamics of a network of diffusively-coupled bistable systems. Under mild conditions and without requiring smoothness of the vector field, we analyze the network dynamics and show that the solutions converge globally…

In many contexts, simpler models are preferable to more complex models and the control of this model complexity is the goal for many methods in machine learning such as regularization, hyperparameter tuning and architecture design. In deep…

In this paper, we prove the existence of minimizers of a class of multi-constrained variational problems. We consider systems involving a nonlinearity that does not satisfy compactness, monotonicity, neither symmetry properties. Our…

Despite their overwhelming capacity to overfit, deep learning architectures tend to generalize relatively well to unseen data, allowing them to be deployed in practice. However, explaining why this is the case is still an open area of…

We study a variational problem motivated by models of species population density in a nonhomogeneous environment. We first analyze local minimizers and the structure of the saturated region (where the population attains its maximal density)…

Convex clustering is a well-regarded clustering method, resembling the similar centroid-based approach of Lloyd's $k$-means, without requiring a predefined cluster count. It starts with each data point as its centroid and iteratively merges…

This study concerns the mean-clustering approach to modelling the evolution of lattice dynamics. Instead of tracking the state of individual lattice sites, this approach describes the time evolution of the concentrations of different…

The use of high-dimensional features has become a normal practice in many computer vision applications. The large dimension of these features is a limiting factor upon the number of data points which may be effectively stored and processed,…

The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of…

We study nonconvex optimization landscapes for learning overcomplete representations, including learning (i) sparsely used overcomplete dictionaries and (ii) convolutional dictionaries, where these unsupervised learning problems find many…

We study the loss surface of a feed-forward neural network with ReLU non-linearities, regularized with weight decay. We show that the regularized loss function is piecewise strongly convex on an important open set which contains, under some…

In this work, we consider multitask learning problems where clusters of nodes are interested in estimating their own parameter vector. Cooperation among clusters is beneficial when the optimal models of adjacent clusters have a good number…

This paper analyzes the convergence and generalization of training a one-hidden-layer neural network when the input features follow the Gaussian mixture model consisting of a finite number of Gaussian distributions. Assuming the labels are…

Deep clustering is an emerging topic in deep learning where traditional clustering is performed in deep learning feature space. However, clustering and deep learning are often mutually exclusive. In the autoencoder based deep clustering,…

We consider grouping as a general characterization for problems such as clustering, community detection in networks, and multiple parametric model estimation. We are interested in merging solutions from different grouping algorithms,…