Sonia Djebali

Pablo Thomassin, Guillaume Guerard, Sonia Djebali et al.

Effectively encoding inequality constraints is a primary obstacle in applying quantum algorithms to financial optimization. A quantum model for Markowitz portfolio optimization is presented that resolves this by embedding slack variables directly into the problem Hamiltonian. The method maps each slack variable to a dedicated ancilla qubit, transforming the problem into a Quadratic Unconstrained Binary Optimization (QUBO) formulation suitable for the Quantum Approximate Optimization Algorithm (QAOA). This process internalizes the constraints within the quantum state, altering the problem's energy landscape to facilitate optimization. The model is empirically validated through simulation, showing it consistently finds the optimal portfolio where a standard penalty-based QAOA fails. This work demonstrates that modifying the Hamiltonian architecture via a slack-ancilla scheme provides a robust and effective pathway for solving constrained optimization problems on quantum computers. A fundamental quantum limit on the simultaneous precision of portfolio risk and return is also posited.

Sonia Djebali, Quentin Gabot, Guillaume Guerard

With the recent digital revolution, analyzing of tourists' behaviors and research fields associated with it have changed profoundly. It is now easier to examine behaviors of tourists using digital traces they leave during their travels. The studies conducted on diverse aspects of tourism focus on quantitative aspects of digital traces to reach its conclusions. In this paper, we suggest a study focused on both qualitative and quantitative aspect of digital traces to understand the dynamics governing tourist behavior, especially those concerning attractions networks.

Loup-Noe Levy, Guillaume Guerard, Sonia Djebali et al.

This article presents a novel pretopology-based algorithm designed to address the challenges of clustering mixed data without the need for dimensionality reduction. Leveraging Disjunctive Normal Form, our approach formulates customizable logical rules and adjustable hyperparameters that allow for user-defined hierarchical cluster construction and facilitate tailored solutions for heterogeneous datasets. Through hierarchical dendrogram analysis and comparative clustering metrics, our method demonstrates superior performance by accurately and interpretably delineating clusters directly from raw data, thus preserving data integrity. Empirical findings highlight the algorithm's robustness in constructing meaningful clusters and reveal its potential in overcoming issues related to clustered data explainability. The novelty of this work lies in its departure from traditional dimensionality reduction techniques and its innovative use of logical rules that enhance both cluster formation and clarity, thereby contributing a significant advancement to the discourse on clustering mixed data.

Guillaume Guerard, Sonia Djebali

The advent of the big data paradigm has transformed how industries manage and analyze information, ushering in an era of unprecedented data volume, velocity, and variety. Within this landscape, mixed-data clustering has become a critical challenge, requiring innovative methods that can effectively exploit heterogeneous data types, including numerical and categorical variables. Traditional clustering techniques, typically designed for homogeneous datasets, often struggle to capture the additional complexity introduced by mixed data, underscoring the need for approaches specifically tailored to this setting. Hierarchical and explainable algorithms are particularly valuable in this context, as they provide structured, interpretable clustering results that support informed decision-making. This paper introduces a clustering method grounded in pretopological spaces. In addition, benchmarking against classical numerical clustering algorithms and existing pretopological approaches yields insights into the performance and effectiveness of the proposed method within the big data paradigm.

Theo Demessance, Chongke Bi, Sonia Djebali et al.

Nowadays, social networks are becoming a popular way of analyzing tourist behavior, thanks to the digital traces left by travelers during their stays on these networks. The massive amount of data generated; by the propensity of tourists to share comments and photos during their trip; makes it possible to model their journeys and analyze their behavior. Predicting the next movement of tourists plays a key role in tourism marketing to understand demand and improve decision support. In this paper, we propose a method to understand and to learn tourists' movements based on social network data analysis to predict future movements. The method relies on a machine learning grammatical inference algorithm. A major contribution in this paper is to adapt the grammatical inference algorithm to the context of big data. Our method produces a hidden Markov model representing the movements of a group of tourists. The hidden Markov model is flexible and editable with new data. The capital city of France, Paris is selected to demonstrate the efficiency of the proposed methodology.