arXiv subjects

Eraldo Pereira Marinho

Publications and source records attributed to Eraldo Pereira Marinho.

7 recordsLinked to original sources

arXiv2026

Round-Trip KNN Clustering: multiscale hierarchical cluster detection on directed nearest-neighbour graphs

We introduce Round-Trip KNN Clustering (RTKNNC), a graph-based method for finding cluster structure at several neighbourhood scales without requiring the number of clusters in advance. Unlike approaches that first make a $k$-nearest-neighbour (KNN) graph undirected, RTKNNC keeps both directions of the neighbour relation: which points a given point selects and which points select it. Incoming selections are treated as weighted votes that help decide which local connections remain visible during a recursive forward-and-reverse traversal. Repeating the procedure for increasing $K$ reveals how groups persist or merge as the neighbourhood scale grows; for the reference inverse-square model before structural refinement, clusters can merge but do not split. Because graph connectivity can occasionally join distinct groups through a sparse bridge or a small region of overlap, we add an optional label-free refinement. It first tests whether an already formed component is better described by two or three Gaussian subpopulations, and accepts a subdivision only when the proposed groups are large enough and consistent with the visible KNN graph. Across eight synthetic datasets and $K=2,\ldots,16$, independent C and Python implementations produced identical partitions in all 120 reference runs. Refinement increased adjusted Rand index from $0.7817$ to $0.9627$ on a variable-density benchmark and from $0.8083$ to $0.9853$ on a sparse-bridge benchmark. Comparisons with seven external clustering methods show competitive performance while preserving a label-free cluster-construction process.

cs.LG↗

arXiv2026

Clustering Astronomical Orbital Synthetic Data Using Advanced Feature Extraction and Dimensionality Reduction Techniques

The dynamics of Saturn's satellite system offer a rich framework for studying orbital stability and resonance interactions. Traditional methods for analysing such systems, including Fourier analysis and stability metrics, struggle with the scale and complexity of modern datasets. This study introduces a machine learning-based pipeline for clustering approximately 22,300 simulated satellite orbits, addressing these challenges with advanced feature extraction and dimensionality reduction techniques. The key to this approach is using MiniRocket, which efficiently transforms 400 timesteps into a 9,996-dimensional feature space, capturing intricate temporal patterns. Additional automated feature extraction and dimensionality reduction techniques refine the data, enabling robust clustering analysis. This pipeline reveals stability regions, resonance structures, and other key behaviours in Saturn's satellite system, providing new insights into their long-term dynamical evolution. By integrating computational tools with traditional celestial mechanics techniques, this study offers a scalable and interpretable methodology for analysing large-scale orbital datasets and advancing the exploration of planetary dynamics.

astro-ph.EP↗

arXiv2022

Beyond z=0. The Deutsch-Jozsa decided monochromatic languages

The present work points out that the Deutsch-Jozsa algorithm was the first formal description of a quantum decider. In particular, it is studied here the class of languages whose indicator functions allow the Deutsch-Jozsa algorithm to output a monochromatic result, beyond the trivial case z = 0 for constant indicator functions. To illustrate examples of randomly balanced languages and some monochromatic cases, it was performed classical computational simulations of the Deutsch-Jozsa quantum algorithm for the specific cases of 4 and 6 qubits, respectively. The general case of the Deutsch-Jozsa decided languages are named balanced languages, and their outcomes from the simulation suggest that such languages are equivalent to the quantum superposition of the monochromatic cases.

quant-ph↗

arXiv2021

Covariance-based smoothed particle hydrodynamics. A machine-learning application to simulating disc fragmentation

A PCA-based, machine learning version of the SPH method is proposed. In the present scheme, the smoothing tensor is computed to have their eigenvalues proportional to the covariance's principal components, using a modified octree data structure, which allows the fast estimation of the anisotropic self-regulating kNN. Each SPH particle is the center of such an optimal kNN cluster, i.e., the one whose covariance tensor allows the find of the kNN cluster itself according to the Mahalanobis metric. Such machine learning constitutes a fixed point problem. The definitive (self-regulating) kNN cluster defines the smoothing volume, or properly saying, the smoothing ellipsoid, required to perform the anisotropic interpolation. Thus, the smoothing kernel has an ellipsoidal profile, which changes how the kernel gradients are computed. As an application, it was performed the simulation of collapse and fragmentation of a non-magnetic, rotating gaseous sphere. An interesting outcome was the formation of protostars in the disc fragmentation, shown to be much more persistent and much more abundant in the anisotropic simulation than in the isotropic case.

physics.comp-ph↗

arXiv2019

On the connection between Deutsch-Jozsa algorithm and bent functions

It is presently shown that the Deutsch-Jozsa algorithm is connected to the concept of bent function. Particularly, it is noticeable that the quantum circuit used to denote the well known quantum algorithm is by itself the quantum computer which performs the Walsh transform of a Boolean function. Consequently, the output from Deutsch-Jozsa algorithm, when the hidden function is bent, corresponds to a flat spectrum of quantum states.

cs.IT↗

arXiv2013

Pattern recognition issues on anisotropic smoothed particle hydrodynamics

This is a preliminary theoretical discussion on the computational requirements of the state of the art smoothed particle hydrodynamics (SPH) from the optics of pattern recognition and artificial intelligence. It is pointed out in the present paper that, when including anisotropy detection to improve resolution on shock layer, SPH is a very peculiar case of unsupervised machine learning. On the other hand, the free particle nature of SPH opens an opportunity for artificial intelligence to study particles as agents acting in a collaborative framework in which the timed outcomes of a fluid simulation forms a large knowledge base, which might be very attractive in computational astrophysics phenomenological problems like self-propagating star formation.

cs.AI↗

arXiv2011

Anisotropic k-Nearest Neighbor Search Using Covariance Quadtree

We present a variant of the hyper-quadtree that divides a multidimensional space according to the hyperplanes associated to the principal components of the data in each hyperquadrant. Each of the $2^λ$ hyper-quadrants is a data partition in a $λ$-dimension subspace, whose intrinsic dimensionality $λ\leq d$ is reduced from the root dimensionality $d$ by the principal components analysis, which discards the irrelevant eigenvalues of the local covariance matrix. In the present method a component is irrelevant if its length is smaller than, or comparable to, the local inter-data spacing. Thus, the covariance hyper-quadtree is fully adaptive to the local dimensionality. The proposed data-structure is used to compute the anisotropic K nearest neighbors (kNN), supported by the Mahalanobis metric. As an application, we used the present k nearest neighbors method to perform density estimation over a noisy data distribution. Such estimation method can be further incorporated to the smoothed particle hydrodynamics, allowing computer simulations of anisotropic fluid flows.

cs.CV↗