Prof. Dr. Ana Carpio: Professor of Applied Mathematics at Universidad Complutense de Madrid, Spain
Article Details
The article “Hierarchical topological clustering and meaningful outliers” by Ana Carpio & Gema Duro was published in Soft Computing on 07 February 2026. It presents a mathematical and computational framework that integrates topological data analysis with hierarchical clustering to detect clusters of any shape and identify meaningful outliers in datasets. The approach is demonstrated using MATLAB on datasets from diverse domains, including biological, physical, and economic data.
Novelty
The work introduces a hierarchical topological clustering (HTC) algorithm that combines persistence-based topological analysis with clustering, a method not found in traditional algorithms like K-means, K-medoids, or DBSCAN. Its novelty lies in enabling multiscale clustering of arbitrary shapes while providing a mathematically grounded method to quantify cluster stability and identify significant outliers.
Impact
The algorithm has the potential to transform how researchers analyze complex, high-dimensional data where conventional clustering fails. By accurately identifying clusters and meaningful outliers, it can impact fields such as genomics, image analysis, swarm robotics, and economic modeling. Its robustness to noise also enhances the reliability of insights drawn from real-world datasets.
Originality
The approach is original because it integrates persistent homology from topological data analysis into a hierarchical clustering framework. Unlike other methods, it does not rely on pre-set parameters or assume convexity of clusters. The identification of “meaningful outliers” adds a layer of interpretability uncommon in standard clustering techniques.
Experimental Rigor
The authors validate the algorithm across multiple datasets of moderate size, employing different distance measures (Euclidean, Wasserstein, Fermat). MATLAB simulations demonstrate its ability to detect both complex cluster structures and significant outliers. However, large-scale computational benchmarking and comparisons with state-of-the-art topological clustering methods could further strengthen rigor.
Sustainability Impact
By efficiently identifying key data patterns and reducing misclassification, the method may indirectly support sustainable decision-making, for example, in resource allocation, disease diagnosis, and trade analysis, where misinterpretation of data can lead to resource waste or inefficiency. Its computational efficiency also reduces unnecessary computational load compared to repeated parameter tuning in traditional clustering methods.
Applicability
The HTC algorithm is highly applicable across domains requiring nuanced data analysis. Its ability to handle non-convex clusters, hierarchical structures, and meaningful outliers makes it suitable for bioinformatics, materials science, social network analysis, economic modeling, robotics, and image compression. The flexibility in distance metrics further broadens its applicability across varied datasets.
Research Portfolio
Ana Carpio is a Professor of Applied Mathematics at the Universidad Complutense de Madrid, specializing in numerical analysis and its applications to physical and biological systems. She has built an international reputation for bridging rigorous mathematical theory with real-world problems in fluid dynamics, biomedicine, and complex systems modeling. Throughout her career, she has supervised numerous Ph.D. students, led interdisciplinary research projects, and collaborated with top institutions worldwide.
Online Profile
Carpio maintains a verified academic profile at UCM and a personal homepage detailing her research, publications, collaborations, and ongoing projects. Her work is widely cited, with over 3,600 total citations, an h-index of 35, and an i10-index of 91, reflecting her substantial impact in applied mathematics. Her profile highlights both theoretical contributions and practical applications, emphasizing the relevance of mathematics to engineering, biology, and computational science.
Education
Carpio earned her B.S. and M.S. in Mathematics (Numerical Analysis) from Universidad Politécnica de Valencia in 1988. She completed her DEA d’Analyse Numérique at Université Pierre et Marie Curie (Paris VI) in 1989 and obtained her Ph.D. in Mathematics in 1993 under the supervision of A. Haraux, focusing on numerical methods for partial differential equations. In 2004, she earned her Habilitation as Full Professor of Applied Mathematics from the MEC, Spain, marking her qualification for senior academic leadership.
Research Focus
Her research centers on the development and application of mathematical models and numerical methods to complex systems, with a focus on physical and biological phenomena. She works on partial differential equations, fluid dynamics, and microbiome interactions, integrating computational tools to solve problems in biomedicine and industry. Her interdisciplinary approach emphasizes both theoretical rigor and the translation of mathematics into actionable scientific and technological solutions.
Experience
Carpio’s professional experience spans multiple institutions and countries. She began as a predoctoral researcher at Université Pierre et Marie Curie, followed by assistant and associate professorships at UCM, and postdoctoral research at Oxford. She has held visiting scholar and researcher positions at Stanford, Harvard, NYU Courant Institute, Institut Henri Poincaré, the University of Iceland, and the Fields Institute. Currently, she is Professor of Applied Mathematics at UCM and directs the Research Group on Mathematics Applied to Physical and Biological Systems.
Research Timeline & Activities
Her research timeline reflects a continuous evolution from foundational numerical analysis in the late 1980s and 1990s to interdisciplinary applications in fluid dynamics, biomedicine, and computational modeling from 2005 onward. She has led projects that connect mathematics with industrial, environmental, and health-related applications, and has collaborated with international research centers and institutes. Her activities include supervising graduate students, organizing workshops, and contributing to collaborative scientific networks.
Awards & Honors
Carpio has received multiple awards recognizing both her research excellence and innovative contributions. She won the Best Ph.D. Thesis Award at UCM in 1993, the SEMA Prize for Young Researchers in 1998, a mention from the Madrid-MIT Vision Program for innovative ideas in biomedicine in 2013, and a winning project in the Repsol Inspire Program in 2013. These honors reflect her sustained impact in applied mathematics and her leadership in interdisciplinary research initiatives.
Prof. Dr. Ana Carpio the Innovative Researcher Award based:
1. Pioneering Research in Applied Mathematics
Prof. Carpio has consistently developed novel mathematical frameworks that bridge theory and practice. Her work on hierarchical topological clustering exemplifies her ability to translate advanced mathematical concepts, such as persistent homology, into actionable tools for data analysis across biology, economics, and engineering. This demonstrates a forward-thinking, innovative approach in applied mathematics.
2. Interdisciplinary Impact
Her research seamlessly integrates mathematics with biomedicine, fluid dynamics, microbiome studies, and complex systems modeling. By tackling real-world problems with rigorous mathematical methods, she has created solutions that cross traditional disciplinary boundaries, exemplifying innovation through interdisciplinary application.
3. Methodological Originality and Novelty
The hierarchical topological clustering algorithm she co-developed introduces new ways to detect non-convex clusters and meaningful outliers. This method addresses limitations of conventional clustering techniques, showing her strength in creating original, high-impact methodologies that advance both theoretical and practical aspects of data science.
4. Global Academic Leadership and Collaboration
Carpio’s career demonstrates international leadership and collaboration, with research positions and partnerships at top institutions like Stanford, Harvard, NYU, Institut Henri Poincaré, and the Fields Institute. Her ability to lead interdisciplinary projects and mentor future scientists reflects her innovative influence on global research networks.
5. Sustained Excellence and Recognition
Her numerous awards—Best Ph.D. Thesis, SEMA Prize, Madrid-MIT Vision Program recognition, and Repsol Inspire Program winner—highlight her sustained excellence and innovation. Coupled with an h-index of 35 and over 3,600 citations, this underscores her impact as a researcher whose innovations have both academic and societal relevance.