Related papers: Applying Self-organizing Maps to the Inverse Probl…
We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an…
By suitable examples we illustrate an algorithm for composition of inverse problems.
We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a…
We propose a new clustering approach, called optimality-based clustering, that clusters data points based on their latent decision-making preferences. We assume that each data point is a decision generated by a decision-maker who…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
An approach to the classification problem of machine learning, based on building local classification rules, is developed. The local rules are considered as projections of the global classification rules to the event we want to classify. A…
The linear ordering problem (LOP), which consists in ordering M objects from their pairwise comparisons, is commonly applied in many areas of research. While efforts have been made to devise efficient LOP algorithms, verification of whether…
We exhibit an analogy between the problem of pushing forward measurable sets under measure preserving maps and linear relaxations in combinatorialoptimization. We show how invariance of hyperfiniteness of graphings under local isomorphism…
We design a new iterative algorithm, called REINFORCE-OPT, for solving a general type of optimization problems. This algorithm parameterizes the solution search rule and iteratively updates the parameter using a reinforcement learning (RL)…
We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…
Scene graphs are a powerful structured representation of the underlying content of images, and embeddings derived from them have been shown to be useful in multiple downstream tasks. In this work, we employ a graph convolutional network to…
In this work, we propose a model order reduction framework to deal with inverse problems in a non-intrusive setting. Inverse problems, especially in a partial differential equation context, require a huge computational load due to the…
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…
The last decade has seen the parallel emergence in computational neuroscience and machine learning of neural network structures which spread the input signal randomly to a higher dimensional space; perform a nonlinear activation; and then…
Machine-learning classifiers can be leveraged as a two-sample statistical test. Suppose each sample is assigned a different label and that a classifier can obtain a better-than-chance result discriminating them. In this case, we can infer…
Neural network algorithms have been recently applied to construct Parton Distribution Function (PDF) parametrizations which provide an alternative to standard global fitting procedures. We propose a technique based on an interactive neural…
This paper defines a new learning architecture, Layered Self-Organizing Maps (LSOMs), that uses the SOM and supervised-SOM learning algorithms. The architecture is validated with the MNIST database of hand-written digit images. LSOMs are…
A self-organizing map (SOM) is a type of competitive artificial neural network, which projects the high-dimensional input space of the training samples into a low-dimensional space with the topology relations preserved. This makes SOMs…
Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem,…