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Image recognition with prototypes is considered an interpretable alternative for black box deep learning models. Classification depends on the extent to which a test image “looks like” a prototype. However, perceptual similarity for humans can be different from the similarity learned by the classification model. Hence, only visualising prototypes can be insufficient for a user to understand what a prototype exactly represents, and why the model considers a prototype and an image to be similar. We address this ambiguity and argue that prototypes should be explained. We improve interpretability by automatically enhancing visual prototypes with quantitative information about visual characteristics deemed important by the classification model. Specifically, our method clarifies the meaning of a prototype by quantifying the influence of colour hue, shape, texture, contrast and saturation and can generate both global and local explanations. Because of the generality of our approach, it can improve the interpretability of any similarity-based method for prototypical image recognition. In our experiments, we apply our method to the existing Prototypical Part Network (ProtoPNet). Our analysis confirms that the global explanations are generalisable, and often correspond to the visually perceptible properties of a prototype. Our explanations are especially relevant for prototypes which might have been interpreted incorrectly otherwise. By explaining such ‘misleading’ prototypes, we improve the interpretability and simulatability of a prototype-based classification model. We also use our method to check whether visually similar prototypes have similar explanations, and are able to discover redundancy. Code is available at https://github.com/M-Nauta/Explaining_Prototypes.

One of the fundamental properties of dielectrics is to accumulate charges under an electric field. Even if this phenomena is exploited in some applications such as memories, it is the main cause of failure in a large amount of applications such as high voltage cables or microsystems. Numerous studies have demonstrated that dielectric/electrode interface has strong impact on complete system and particularly on charge injection phenomenon which induce failures. During the past decades, charge injection phenomena electrode / dielectric interface has been extensively studied. To explain the difference between experimental and modelling, the most plausible hypothesis is the presence of interface states between the electrode (metal or semiconductor) and the dielectric. This hypothesis explain the independence of injected charge density respect to the electrode meta (work function). However, interfaces properties remain poorly understood mainly because all nanometric phenomena accuring at its localization are characterized thanks to microscopic measurements. The aim of this PhD thesis is to characterize chemical and electrical properties of the interface through a rigorous control of its manufacturing process. The major contribution of this work is related to the use of Atomic Force Microscopy (AFM) to determine interface properties at nanoscale. In particular, interfaces are characterized morphologically (mechanical properties measurements by PFQNM - Peak Quantitative Quantum NanoMechanical) and electrically (surface potential measurements by KPFM - Kelvin Probe Force Microscopy). Thus, results demonstrate that the manufacturing process influenced the chemical properties (surface oxidation ...) of the interface without having any significant influence on the electrical properties. Indeed, the amount of injected charges remains quite the same regardless of the manufacturing process. AFM measurements showed that the morphological interface was abrupt whereas the electrical interface was progressive (several microns). A Matlab model permits us to extract interface charge density to KPFM surface potential measurements.; Une des propriétés fondamentales des diélectriques est d'accumuler des charges sous l'effet d'un champ électrique. Si cet effet est exploité dans certaines applications telles que les mémoires il est la plupart du temps la cause de défaillance dans de nombreux systèmes tels que les câbles haute tension ou les microsystèmes. De nombreuses études ont démontré que l'interface entre le diélectrique et l'électrode jouait un rôle prédominant dans le fonctionnement du système complet et en particulier influençait le phénomène d'injection de charge à l'origine des défaillances. Au cours des dernières années le phénomène d'injection de charges à l'interface électrode/diélectrique a largement été étudié. Pour expliquer la différence entre les résultats expérimentaux et les modèles, l'hypothèse la plus plausible est la présence d'états d'interfaces entre l'électrode (métal ou semiconducteur) et le diélectrique. Cette hypothèse permet en particulier d'expliquer l'indépendance de la quantité de charge injectée vis-à-vis du métal servant d'électrode. Toutefois, les propriétés des interfaces restent mal connues en particulier car ces phénomènes nanométriques sont caractérisés à partir de mesures microscopique. L'objectif de cette thèse est de caractériser les propriétés chimiques et électriques de l'interface grâce à un contrôle rigoureux de son procédé de fabrication. L'apport majeur de ces travaux est lié à l'utilisation de la microscopie à force atomique pour déterminer les propriétés de l'interface à l'échelle nanométrique. Nous avons en particulier caractérisé morphologiquement (mesure de propriétés mécaniques par PFQNM - Peak Force Quantitative NanoMechanical) et électriquement (mesure de potentiel de surface par KPFM - Kelvin Probe Force Microscopy). Nous avons ainsi pu montrer que le procédé de fabrication influençait les propriétés chimiques (oxydation de surface...) de l'interface sans que cela ait de conséquences notables sur les propriétés électriques. En effet, la quantité de charges injectées reste du même ordre de grandeur quel que soit le procédé de fabrication. Les mesures AFM ont montré que l'interface morphologique était abrupte alors que l'interface électrique était progressive (plusieurs microns). Grâce à un modèle nous avons pu extraire des mesures de potentiel de surface KPFM la densité de charge d'interface.

One of the fundamental properties of dielectrics is to accumulate charges under an electric field. Even if this phenomena is exploited in some applications such as memories, it is the main cause of failure in a large amount of applications such as high voltage cables or microsystems. Numerous studies have demonstrated that dielectric/electrode interface has strong impact on complete system and particularly on charge injection phenomenon which induce failures. During the past decades, charge injection phenomena electrode / dielectric interface has been extensively studied. To explain the difference between experimental and modelling, the most plausible hypothesis is the presence of interface states between the electrode (metal or semiconductor) and the dielectric. This hypothesis explain the independence of injected charge density respect to the electrode meta (work function). However, interfaces properties remain poorly understood mainly because all nanometric phenomena accuring at its localization are characterized thanks to microscopic measurements. The aim of this PhD thesis is to characterize chemical and electrical properties of the interface through a rigorous control of its manufacturing process. The major contribution of this work is related to the use of Atomic Force Microscopy (AFM) to determine interface properties at nanoscale. In particular, interfaces are characterized morphologically (mechanical properties measurements by PFQNM - Peak Quantitative Quantum NanoMechanical) and electrically (surface potential measurements by KPFM - Kelvin Probe Force Microscopy). Thus, results demonstrate that the manufacturing process influenced the chemical properties (surface oxidation ...) of the interface without having any significant influence on the electrical properties. Indeed, the amount of injected charges remains quite the same regardless of the manufacturing process. AFM measurements showed that the morphological interface was abrupt whereas the electrical interface was progressive (several microns). A Matlab model permits us to extract interface charge density to KPFM surface potential measurements.; Une des propriétés fondamentales des diélectriques est d'accumuler des charges sous l'effet d'un champ électrique. Si cet effet est exploité dans certaines applications telles que les mémoires il est la plupart du temps la cause de défaillance dans de nombreux systèmes tels que les câbles haute tension ou les microsystèmes. De nombreuses études ont démontré que l'interface entre le diélectrique et l'électrode jouait un rôle prédominant dans le fonctionnement du système complet et en particulier influençait le phénomène d'injection de charge à l'origine des défaillances. Au cours des dernières années le phénomène d'injection de charges à l'interface électrode/diélectrique a largement été étudié. Pour expliquer la différence entre les résultats expérimentaux et les modèles, l'hypothèse la plus plausible est la présence d'états d'interfaces entre l'électrode (métal ou semiconducteur) et le diélectrique. Cette hypothèse permet en particulier d'expliquer l'indépendance de la quantité de charge injectée vis-à-vis du métal servant d'électrode. Toutefois, les propriétés des interfaces restent mal connues en particulier car ces phénomènes nanométriques sont caractérisés à partir de mesures microscopique. L'objectif de cette thèse est de caractériser les propriétés chimiques et électriques de l'interface grâce à un contrôle rigoureux de son procédé de fabrication. L'apport majeur de ces travaux est lié à l'utilisation de la microscopie à force atomique pour déterminer les propriétés de l'interface à l'échelle nanométrique. Nous avons en particulier caractérisé morphologiquement (mesure de propriétés mécaniques par PFQNM - Peak Force Quantitative NanoMechanical) et électriquement (mesure de potentiel de surface par KPFM - Kelvin Probe Force Microscopy). Nous avons ainsi pu montrer que le procédé de fabrication influençait les propriétés chimiques (oxydation de surface...) de l'interface sans que cela ait de conséquences notables sur les propriétés électriques. En effet, la quantité de charges injectées reste du même ordre de grandeur quel que soit le procédé de fabrication. Les mesures AFM ont montré que l'interface morphologique était abrupte alors que l'interface électrique était progressive (plusieurs microns). Grâce à un modèle nous avons pu extraire des mesures de potentiel de surface KPFM la densité de charge d'interface.

Uncertainty and the curse of dimensionality are two crucial problems that usually a®ect data clustering. Uncertainty in data clustering may be typically considered at data level or clustering level. Data level uncertainty is inherently present in the repre- sentation of several kinds of data objects from various application contexts (e.g., sensor networks, moving objects databases, biomedicine). This kind of uncertainty should be carefully taken into account in a clustering task in order to achieve adequate accuracy; unfortunately, traditional clustering methods are designed to work only on deterministic vectorial representations of data objects. Clustering uncertainty is related to the output of any clustering algo- rithm. Indeed, the ill-posed nature of clustering leads to clustering algorithms that cannot be generally valid for any input dataset, i.e., their output results are necessarily uncertain. Clustering ensembles has been recognized as a pow- erful solution to overcome clustering uncertainty. It aims to derive a single clustering solution (i.e., the consensus partition) from a set of clusterings rep- resenting di®erent partitions of the same input dataset (i.e., the ensemble). A major weakness of the existing clustering ensembles methods is that they compute the consensus partition by equally considering all the solutions in the ensemble. The curse of dimensionality in data clustering concerns all the issues that naturally arise from data objects represented by a large set of features and are responsible of poor accuracy and e±ciency achieved by traditional clustering methods working on high dimensional data. Classic approaches to the curse of dimensionality include global and local dimensionality reduction. Global techniques aim at reducing the dimensionality of the input dataset by applying the same algorithm(s) to all the input data objects. Local dimensionality reduction acts by considering subsets of the input dataset and performing dimensionality reduction speci¯c for any of such subsets. Projective clustering is an e®ective class of methods falling into the category of local dimensionality reduction. It aims to discover clusters of objects along with the corresponding subspaces, following the principle that objects in the same cluster are close to each other if and only if they are projected onto the subspace associated to that cluster. viii Abstract The focus of this thesis is on the development of proper techniques for overcoming the crucial problems of uncertainty and the curse of dimension- ality arising from data clustering. This thesis provides the following main contributions. Uncertainty. Uncertainty at a representation level is addressed by proposing: UK-medoids, which is a new partitional algorithm for clustering un- certain objects, which is designed to overcome e±ciency and accuracy issues of some existing state-of-the-art methods; U-AHC, i.e., the ¯rst (agglomerative) hierarchical algorithm for clus- tering uncertain objects; a methodology to exploit U-AHC for clustering microarray biomedical data with probe-level uncertainty. Clustering uncertainty is addressed by focusing on the problem of weighted consensus clustering, which aims to automatically determine weighting schemes to discriminate among clustering solutions in a given ensemble. In particular: three novel diversity-based, general schemes for weighting the individ- ual clusterings in a given ensemble are proposed, i.e., Single-Weighting (SW), Group-Weighting (GW), and Dendrogram-Weighting (DW); three algorithms, called WICE, WCCE, and WHCE, are de¯ned to eas- ily involve clustering weighting schemes into any clustering ensembles algorithm falling into one of the main classes of clustering ensembles approaches, i.e., instance-based, cluster-based, and hybrid. The curse of dimensionality. Global dimensionality reduction is addressed by focusing on the time series data application context: the Derivative time series Segment Approximation (DSA) model is proposed as a new time series dimensionality reduction method de- signed for accurate and fast similarity detection and clustering; Mass Spectrometry Data Analysis (MaSDA) system is presented; it mainly aims at analyzing mass spectrometry (MS) biomedical data by exploiting DSA to model such data according to a time series-based representation; DSA is exploited for pro¯ling low-voltage electricity customers. Regarding local dimensionality reduction, a uni¯ed view of projective clus- tering and clustering ensembles is provided. In particular: the novel Projective Clustering Ensembles (PCE) problem is addressed and formally de¯ned according two speci¯c optimization formulations, i.e., two-objective PCE and single-objective PCE; MOEA-PCE and EM-PCE algorithms are proposed as novel heuristics to solve two-objective PCE and single-objective PCE, respectively. Absolute accuracy and e±ciency performance achieved by the proposed techniques, as well as the performance with respect to the prominent state- of-the-art methods are evaluated by performing extensive sets of experiments on benchmark, synthetically generated, and real-world datasets Dottorato di Ricerca in Ingegneria dei Sistemi ed Informatica, XXII Ciclo, 2009 Università della Calabria