10 research outputs found
Towards Theoretical Foundations of Clustering
Clustering is a central unsupervised learning task with a wide variety of applications. Unlike in supervised learning, different clustering algorithms may yield dramatically different outputs for the same input sets. As such, the choice of algorithm is crucial. When selecting a clustering algorithm, users tend to focus on cost-related considerations, such as running times, software purchasing costs, etc. Yet differences concerning the output of the algorithms are a more primal consideration. We propose an approach for selecting clustering algorithms based on differences in their input-output behaviour. This approach relies on identifying significant properties of clustering algorithms and classifying algorithms based on the properties that they satisfy.
We begin with Kleinberg's impossibility result, which relies on concise abstract properties that are well-suited for our approach. Kleinberg showed that three specific properties cannot be satisfied by the same algorithm. We illustrate that the impossibility result is a consequence of the formalism used, proving that these properties can be formulated without leading to inconsistency in the context of clustering quality measures or algorithms whose input requires the number of clusters.
Combining Kleinberg's properties with newly proposed ones, we provide an extensive property-base classification of common clustering paradigms. We use some of these properties to provide a novel characterization of the class of linkage-based algorithms. That is, we distil a small set of properties that uniquely identify this family of algorithms.
Lastly, we investigate how the output of algorithms is affected by the addition of small, potentially adversarial, sets of points. We prove that given clusterable input, the output of -means is robust to the addition of a small number of data points. On the other hand, clusterings produced by many well-known methods, including linkage-based techniques, can be changed radically by adding a small number of elements
Expedition in Data and Harmonic Analysis on Graphs
The graph Laplacian operator is widely studied in spectral graph theory largely due to its importance in modern data analysis. Recently, the Fourier transform and other time-frequency operators have been defined on graphs using Laplacian eigenvalues and eigenvectors. We extend these results and prove that the translation operator to the i’th node is invertible if and only if all eigenvectors are nonzero on the i’th node. Because of this dependency on the support of eigenvectors we study the characteristic set of Laplacian eigenvectors. We prove that the Fiedler vector of a planar graph cannot vanish on large neighborhoods and then explicitly construct a family of non-planar graphs that do exhibit this property.
We then prove original results in modern analysis on graphs. We extend results on spectral graph wavelets to create vertex-dyanamic spectral graph wavelets whose support depends on both scale and translation parameters. We prove that Spielman’s Twice-Ramanujan graph sparsifying algorithm cannot outperform his conjectured optimal sparsification constant. Finally, we present numerical results on graph conditioning, in which edges of a graph are rescaled to best approximate the complete graph and reduce average commute time
Biometric Systems
Biometric authentication has been widely used for access control and security systems over the past few years. The purpose of this book is to provide the readers with life cycle of different biometric authentication systems from their design and development to qualification and final application. The major systems discussed in this book include fingerprint identification, face recognition, iris segmentation and classification, signature verification and other miscellaneous systems which describe management policies of biometrics, reliability measures, pressure based typing and signature verification, bio-chemical systems and behavioral characteristics. In summary, this book provides the students and the researchers with different approaches to develop biometric authentication systems and at the same time includes state-of-the-art approaches in their design and development. The approaches have been thoroughly tested on standard databases and in real world applications
LIPIcs, Volume 244, ESA 2022, Complete Volume
LIPIcs, Volume 244, ESA 2022, Complete Volum
Algorithms and mathematical methods for extraction of functional information from magnetic resonance images of the heart
Imperial Users onl
Towards Cognition-Guided Patient-Specific Numerical Simulation for Cardiac Surgery Assistance
Motivation.
Patient-specific, knowledge-based, holistic surgical treatment planning is of utmost importance when dealing with complex surgery. Surgeons need to account for all available medical patient data, keep track of technical developments, and stay on top of current surgical expert knowledge to define a suitable surgical treatment strategy.
There is a large potential for computer assistance, also, and in particular, regarding surgery simulation which gives surgeons the opportunity not only to plan but to simulate,
too, some steps of an intervention and to forecast relevant surgical situations.
Purpose.
In this work, we particularly look at mitral valve reconstruction (MVR) surgery, which is to re-establish the functionality of an incompetent mitral valve (MV) through implantation of an artificial ring that reshapes the valvular morphology. We aim at supporting MVR by providing surgeons with biomechanical FEM-based MVR surgery simulations that enable them to assess the simulated behavior of the MV after an MVR. However, according to the above requirements, such surgery simulation is really beneficial to surgeons only if it is patient-specific, surgical expert knowledge-based, comprehensive in terms of the underlying model and the patient’s data, and if its setup and execution is fully automated and integrated into the surgical treatment workflow.
Methods.
This PhD work conducts research on simulation-enhanced, cognition-guided, patient-specific cardiac surgery assistance. First, we derive a biomechanical MV/MVR model and develop an FEM-based MVR surgery simulation using the FEM software toolkit HiFlow3. Following, we outline the functionality and features of the Medical Simulation Markup Language (MSML) and how it simplifies the biomechanical modeling workflow. It is then detailed, how, by means of the MSML and a set of dedicated MVR simulation reprocessing operators, patient-individual medical data can comprehensively be analyzed and processed in order for the fully automated setup of MVR simulation scenarios. Finally, the presented work is integrated into the cognitive system architecture of the joint research project Cognition-Guided Surgery. We particularly look at its semantic knowledge and data infrastructure as well as at the setup of its cognitive software components, which eventually facilitate cognition-guidance and patient-specifity for the overall simulation-enhanced MVR assistance pipeline.
Results and Discussion.
We have proposed and implemented, for the first time, a prototypic system for simulation-enhanced, cognition-guided, patient-specific cardiac surgery assistance. The overall system was evaluated in terms of functionality and performance. Through its cognitive, data-driven pipeline setup, medical patient data and surgical information is analyzed and processed comprehensively, efficiently and fully automatically, and the hence set-up simulation scenarios yield reliable, patient-specific MVR surgery simulation results. This indicates the system’s usability and applicability. The proposed work thus presents an important step towards a simulation-enhanced, cognition-guided, patient-specific cardiac surgery assistance, and can – once operative – be expected to significantly enhance MVR surgery. Concluding, we discuss possible further research contents and promising applications to build upon the presented work