arXiv subjects

Jesús García

Publications and source records attributed to Jesús García.

3 recordsLinked to original sources

arXiv2025

Architecture for Trajectory-Based Fishing Ship Classification with AIS Data

This paper proposes a data preparation process for managing real-world kinematic data and detecting fishing vessels. The solution is a binary classification that classifies ship trajectories into either fishing or non-fishing ships. The data used are characterized by the typical problems found in classic data mining applications using real-world data, such as noise and inconsistencies. The two classes are also clearly unbalanced in the data, a problem which is addressed using algorithms that resample the instances. For classification, a series of features are extracted from spatiotemporal data that represent the trajectories of the ships, available from sequences of Automatic Identification System (AIS) reports. These features are proposed for the modelling of ship behavior but, because they do not contain context-related information, the classification can be applied in other scenarios. Experimentation shows that the proposed data preparation process is useful for the presented classification problem. In addition, positive results are obtained using minimal information.

cs.LG↗

arXiv2008

New results on lower bounds for the number of (at most k)-facets

In this paper we present three different results dealing with the number of $(\leq k)$-facets of a set of points: 1. We give structural properties of sets in the plane that achieve the optimal lower bound $3\binom{k+2}{2}$ of $(\leq k)$-edges for a fixed $0\leq k\leq \lfloor n/3 \rfloor -1$; 2. We give a simple construction showing that the lower bound $3\binom{k+2}{2}+3\binom{k-\lfloor \frac{n}{3} \rfloor+2}{2}$ for the number of $(\leq k)$-edges of a planar point set appeared in [Aichholzer et al. New lower bounds for the number of ($\leq k$)-edges and the rectilinear crossing number of $K_n$. {\em Disc. Comput. Geom.} 38:1 (2007), 1--14] is optimal in the range $\lfloor n/3 \rfloor \leq k \leq \lfloor 5n/12 \rfloor -1$; 3. We show that for $k < \lfloor n/(d+1) \rfloor$ the number of $(\leq k)$-facets of a set of $n$ points in general position in $\mathbb{R}^d$ is at least $(d+1)\binom{k+d}{d}$, and that this bound is tight in the given range of $k$.

math.CO↗

arXiv2006

New lower bounds for the number of $(\leq k)$-edges and the rectilinear crossing number of $K_n$

We provide a new lower bound on the number of $(\leq k)$-edges of a set of $n$ points in the plane in general position. We show that for $0 \leq k \leq\lfloor\frac{n-2}{2}\rfloor$ the number of $(\leq k)$-edges is at least $$ E_k(S) \geq 3\binom{k+2}{2} + \sum_{j=\lfloor\frac{n}{3}\rfloor}^k (3j-n+3), $$ which, for $k\geq \lfloor\tfrac{n}{3}\rfloor$, improves the previous best lower bound in [J. Balogh, G. Salazar, Improved bounds for the number of ($\leq k$)-sets, convex quadrilaterals, and the rectilinear crossing number of $K_n$]. As a main consequence, we obtain a new lower bound on the rectilinear crossing number of the complete graph or, in other words, on the minimum number of convex quadrilaterals determined by $n$ points in the plane in general position. We show that the crossing number is at least $$ \Bigl({41/108}+ε\Bigr) \binom{n}{4} + O(n^3) \geq 0.379631 \binom{n}{4} + O(n^3), $$ which improves the previous bound of $0.37533 \binom{n}{4} + O(n^3)$ in [J. Balogh, G. Salazar, Improved bounds for the number of ($\leq k$)-sets, convex quadrilaterals, and the rectilinear crossing number of $K_n$] and approaches the best known upper bound $0.38058\binom{n}{4}$ in [O. Aichholzer, H. Krasser, Abstract order type extension and new results on the rectilinear crossing number].

math.CO↗