Cristiano Tamborrino | Searcharxiv

arXiv2026

Random Indexing for Image Change Detection: A Distance-Threshold Vocabulary Approach

Random Indexing (RI), used almost exclusively in text analysis (notably Temporal Random Indexing, TRI, for tracking word meaning over time), represents a discrete vocabulary with fixed random vectors and accumulates context by vector summation. We explore transplanting this mechanism to change detection in multitemporal images. A naive transplant using k-means to build the visual vocabulary is unstable: pixels are frequently reassigned between acquisition dates due to small radiometric shifts, destroying the pixel-to-vector correspondence RI depends on. We propose a distance-threshold (leader) clustering vocabulary instead, and give a short formal argument -- a stability radius from the vocabulary covering/packing properties -- for why this is provably more robust to acquisition noise than k-means. Combined with spatial context accumulation, this yields a training-free change detection pipeline, evaluated on four bi-temporal remote-sensing datasets (agriculture, river, urban PolSAR, wildfire) against a Change Vector Analysis baseline, which it consistently approaches but does not surpass. Multi-seed validation exposed and let us fix a degenerate-vector failure mode in a probabilistic-sparsity RI variant, and revealed a second, unresolved source of variability -- sensitivity to the leader-clustering visitation order -- which we characterize but, despite three attempted corrections, could not eliminate, reporting it as the main open problem. Results are cross-checked against an independent re-implementation. We report an ablation, a hyperparameter sensitivity analysis, an Otsu-vs-Gaussian-mixture thresholding comparison, and discuss RI incremental accumulation for future long time-series monitoring.

math.NA↗

arXiv2024

Empirical Density Estimation based on Spline Quasi-Interpolation with applications to Copulas clustering modeling

Density estimation is a fundamental technique employed in various fields to model and to understand the underlying distribution of data. The primary objective of density estimation is to estimate the probability density function of a random variable. This process is particularly valuable when dealing with univariate or multivariate data and is essential for tasks such as clustering, anomaly detection, and generative modeling. In this paper we propose the mono-variate approximation of the density using spline quasi interpolation and we applied it in the context of clustering modeling. The clustering technique used is based on the construction of suitable multivariate distributions which rely on the estimation of the monovariate empirical densities (marginals). Such an approximation is achieved by using the proposed spline quasi-interpolation, while the joint distributions to model the sought clustering partition is constructed with the use of copulas functions. In particular, since copulas can capture the dependence between the features of the data independently from the marginal distributions, a finite mixture copula model is proposed. The presented algorithm is validated on artificial and real datasets.

stat.ML↗