Related papers: Unsupervised Discovery of Formulas for Mathematica…
The CLASSIX algorithm is a fast and explainable approach to data clustering. In its original form, this algorithm exploits the sorting of the data points by their first principal component to truncate the search for nearby data points, with…
This book provides a comprehensive and accessible introduction to the emerging field of AI for mathematics. It covers the core principles and diverse applications of using artificial intelligence to advance mathematical research. Through…
The Science of Science (SoS) explores the mechanisms underlying scientific discovery, and offers valuable insights for enhancing scientific efficiency and fostering innovation. Traditional approaches often rely on simplistic assumptions and…
The use of a finite mixture of normal distributions in model-based clustering allows to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by…
Clustering uncertain data has emerged as a challenging task in uncertain data management and mining. Thanks to a computational complexity advantage over other clustering paradigms, partitional clustering has been particularly studied and a…
In this comprehensive review, we describe a new mathematical problem in artificial intelligence (AI) from a mathematical modeling perspective, following the philosophy stated by Rudolf E. Kalman that "Once you get the physics right, the…
We propose a new clustering technique that can be regarded as a numerical method to compute the proximity gestalt. The method analyzes edge length statistics in the MST of the dataset and provides an a contrario cluster detection criterion.…
We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analysis. We demonstrate that conventional machine learning models…
Monitoring network traffic data to detect any hidden patterns of anomalies is a challenging and time-consuming task that requires high computing resources. To this end, an appropriate summarization technique is of great importance, where it…
Clustering aims to group unlabeled objects based on similarity inherent among them into clusters. It is important for many tasks such as anomaly detection, database sharding, record linkage, and others. Some clustering methods are taken as…
In scientific inference problems, the underlying statistical modeling assumptions have a crucial impact on the end results. There exist, however, only a few automatic means for validating these fundamental modelling assumptions. The…
Nine popular clustering methods are applied to 42 real data sets. The aim is to give a detailed characterisation of the methods by means of several cluster validation indexes that measure various individual aspects of the resulting clusters…
This paper presents a comprehensive overview on the applications of artificial intelligence (AI) in mathematical research, highlighting the transformative role AI has begun to play in this domain. Traditionally, AI advancements have heavily…
New intent discovery is of great value to natural language processing, allowing for a better understanding of user needs and providing friendly services. However, most existing methods struggle to capture the complicated semantics of…
Modern inference and learning often hinge on identifying low-dimensional structures that approximate large scale data. Subspace clustering achieves this through a union of linear subspaces. However, in contemporary applications data is…
Forensic toolmark analysis traditionally relies on subjective human judgment, leading to inconsistencies and lack of transparency. The multitude of variables, including angles and directions of mark generation, further complicates…
Throughout more than two millennia many formulas have been obtained, some of them beautiful, to calculate the number pi. Among them, we can find series, infinite products, expansions as continued fractions and expansions using radicals.…
The rapid ascent of artificial intelligence (AI) is often portrayed as a revolution born from computer science and engineering. This narrative, however, obscures a fundamental truth: the theoretical and methodological core of AI is, and has…
The monitoring of rotating machinery is an essential task in today's production processes. Currently, several machine learning and deep learning-based modules have achieved excellent results in fault detection and diagnosis. Nevertheless,…
Linear multistep methods (LMMs) are popular time discretization techniques for the numerical solution of differential equations. Traditionally they are applied to solve for the state given the dynamics (the forward problem), but here we…