This work presents a data-driven approach for the indoor localization of an observer on a 2D topological map of the environment. State-of-the-art techniques may yield accurate estimates only when they are tailor-made for a specific data modality like camera-based system that prevents their applicability to broader domains. Here, we establish a modality-agnostic framework (called OT-Isomap) and formulate the localization problem in the context of parametric manifold learning while leveraging optimal transportation. This framework allows jointly learning a lowdimensional embedding as well as correspondences with a topological map. We examine the generalizability of the proposed algorithm by applying it to data from diverse modalities such as image sequences and radio frequency signals. The experimental results demonstrate decimeter-level accuracy for localization using different sensory inputs.

The matching principles behind optimal transport (OT) play an increasingly important role in machine learning, a trend which can be observed when OT is used to disambiguate datasets in applications (e.g.

Neural circuits undergo developmental processes which can be influenced by experience. Here we explore a bio-inspired development process to form the connections in a network used for locality sensitive hashing. The network is a simplified model of the insect mushroom body, which has sparse connections from the input layer to a second layer of higher dimension, forming a sparse code. In previous versions of this model, connectivity between the layers is random. We investigate whether the performance of the hash, evaluated in nearest neighbour query tasks, can be improved by process of developing the connections, in which the strongest input dimensions in successive samples are wired to each successive coding dimension. Experiments show that the accuracy of searching for nearest neighbours is improved, although performance is dependent on the parameter values and datasets used. Our approach is also much faster than alternative methods that have been proposed for training the connections in this model. Importantly, the development process does not impact connections built at an earlier stage, which should provide stable coding results for simultaneous learning in a downstream network.

For both GP-VAE and CP-VAE, the number of attention heads is empirically set to 4. We customize a fixed weight 0.2 to the KL divergence such that we can bias more towards the reconstruction loss in Eq. (5) and Eq.

Given a graph or similarity matrix, we consider the problem of recovering a notion of true distance between the nodes, and so their true positions. We show that this can be accomplished in two steps: matrix factorisation, followed by nonlinear dimension reduction. This combination is effective because the point cloud obtained in the first step lives close to a manifold in which latent distance is encoded as geodesic distance. Hence, a nonlinear dimension reduction tool, approximating geodesic distance, can recover the latent positions, up to a simple transformation. We give a detailed account of the case where spectral embedding is used, followed by Isomap, and provide encouraging experimental evidence for other combinations of techniques.

Clustering, in particular k-means clustering, is a central topic in data analysis. Clustering with Bregman divergences is a recently proposed generalization of k-means clustering which has already been widely used in applications. In this paper we analyze theoretical properties of Bregman clustering when the number of the clusters k is large. We establish quantization rates and describe the limiting distribution of the centers as k, extending well-known results for k-means clustering.

Multi-view data analysis seeks to integrate multiple representations of the same samples in order to recover a coherent low-dimensional structure. Classical approaches often rely on feature concatenation or explicit alignment assumptions, which become restrictive under heterogeneous geometries or nonlinear distortions. In this work, we propose two geometry-aware multi-view embedding strategies grounded in Gromov-Wasserstein (GW) optimal transport. The first, termed Mean-GWMDS, aggregates view-specific relational information by averaging distance matrices and applying GW-based multidimensional scaling to obtain a representative embedding. The second strategy, referred to as Multi-GWMDS, adopts a selection-based paradigm in which multiple geometry-consistent candidate embeddings are generated via GW-based alignment and a representative embedding is selected. Experiments on synthetic manifolds and real-world datasets show that the proposed methods effectively preserve intrinsic relational structure across views. These results highlight GW-based approaches as a flexible and principled framework for multi-view representation learning.