Sketch-based subspace clustering of hyperspectral images

Sparse subspace clustering (SSC) techniques provide the state-of-the-art in clustering of hyperspectral images (HSIs). However, their computational complexity hinders their applicability to large-scale HSIs. In this paper, we propose a large-scale SSC-based method, which can effectively process large HSIs while also achieving improved clustering accuracy compared to the current SSC methods. We build our approach based on an emerging concept of sketched subspace clustering, which was to our knowledge not explored at all in hyperspectral imaging yet. Moreover, there are only scarce results on any large-scale SSC approaches for HSI. We show that a direct application of sketched SSC does not provide a satisfactory performance on HSIs but it does provide an excellent basis for an effective and elegant method that we build by extending this approach with a spatial prior and deriving the corresponding solver. In particular, a random matrix constructed by the Johnson-Lindenstrauss transform is first used to sketch the self-representation dictionary as a compact dictionary, which significantly reduces the number of sparse coefficients to be solved, thereby reducing the overall complexity. In order to alleviate the effect of noise and within-class spectral variations of HSIs, we employ a total variation constraint on the coefficient matrix, which accounts for the spatial dependencies among the neighbouring pixels. We derive an efficient solver for the resulting optimization problem, and we theoretically prove its convergence property under mild conditions. The experimental results on real HSIs show a notable improvement in comparison with the traditional SSC-based methods and the state-of-the-art methods for clustering of large-scale images

Automatic Relative Radiometric Normalization of Bi-Temporal Satellite Images Using a Coarse-to-Fine Pseudo-Invariant Features Selection and Fuzzy Integral Fusion Strategies

Relative radiometric normalization (RRN) is important for pre-processing and analyzing multitemporal remote sensing (RS) images. Multitemporal RS images usually include different land use/land cover (LULC) types; therefore, considering an identical linear relationship during RRN modeling may result in potential errors in the RRN results. To resolve this issue, we proposed a new automatic RRN technique that efficiently selects the clustered pseudo-invariant features (PIFs) through a coarse-to-fine strategy and uses them in a fusion-based RRN modeling approach. In the coarse stage, an efficient difference index was first generated from the down-sampled reference and target images by combining the spectral correlation, spectral angle mapper (SAM), and Chebyshev distance. This index was then categorized into three groups of changed, unchanged, and uncertain classes using a fast multiple thresholding technique. In the fine stage, the subject image was first segmented into different clusters by the histogram-based fuzzy c-means (HFCM) algorithm. The optimal PIFs were then selected from unchanged and uncertain regions using each cluster’s bivariate joint distribution analysis. In the RRN modeling step, two normalized subject images were first produced using the robust linear regression (RLR) and cluster-wise-RLR (CRLR) methods based on the clustered PIFs. Finally, the normalized images were fused using the Choquet fuzzy integral fusion strategy for overwhelming the discontinuity between clusters in the final results and keeping the radiometric rectification optimal. Several experiments were implemented on four different bi-temporal satellite images and a simulated dataset to demonstrate the efficiency of the proposed method. The results showed that the proposed method yielded superior RRN results and outperformed other considered well-known RRN algorithms in terms of both accuracy level and execution time.publishedVersio

Advances in robust clustering methods with applications

Robust methods in statistics are mainly concerned with deviations from model assumptions. As already pointed out in Huber (1981) and in Huber & Ronchetti (2009) \these assumptions are not exactly true since they are just a mathematically convenient rationalization of an often fuzzy knowledge or belief". For that reason \a minor error in the mathematical model should cause only a small error in the nal conclusions". Nevertheless it is well known that many classical statistical procedures are \excessively sensitive to seemingly minor deviations from the assumptions". All statistical methods based on the minimization of the average square loss may suer of lack of robustness. Illustrative examples of how outliers' in uence may completely alter the nal results in regression analysis and linear model context are provided in Atkinson & Riani (2012). A presentation of classical multivariate tools' robust counterparts is provided in Farcomeni & Greco (2015). The whole dissertation is focused on robust clustering models and the outline of the thesis is as follows. Chapter 1 is focused on robust methods. Robust methods are aimed at increasing the eciency when contamination appears in the sample. Thus a general denition of such (quite general) concept is required. To do so we give a brief account of some kinds of contamination we can encounter in real data applications. Secondly we introduce the \Spurious outliers model" (Gallegos & Ritter 2009a) which is the cornerstone of the robust model based clustering models. Such model is aimed at formalizing clustering problems when one has to deal with contaminated samples. The assumption standing behind the \Spurious outliers model" is that two dierent random mechanisms generate the data: one is assumed to generate the \clean" part while the another one generates the contamination. This idea is actually very common within robust models like the \Tukey-Huber model" which is introduced in Subsection 1.2.2. Outliers' recognition, especially in the multivariate case, plays a key role and is not straightforward as the dimensionality of the data increases. An overview of the most widely used (robust) methods for outliers detection is provided within Section 1.3. Finally, in Section 1.4, we provide a non technical review of the classical tools introduced in the Robust Statistics' literature aimed at evaluating the robustness properties of a methodology. Chapter 2 is focused on model based clustering methods and their robustness' properties. Cluster analysis, \the art of nding groups in the data" (Kaufman & Rousseeuw 1990), is one of the most widely used tools within the unsupervised learning context. A very popular method is the k-means algorithm (MacQueen et al. 1967) which is based on minimizing the Euclidean distance of each observation from the estimated clusters' centroids and therefore it is aected by lack of robustness. Indeed even a single outlying observation may completely alter centroids' estimation and simultaneously provoke a bias in the standard errors' estimation. Cluster's contours may be in ated and the \real" underlying clusterwise structure might be completely hidden. A rst attempt of robustifying the k- means algorithm appeared in Cuesta-Albertos et al. (1997), where a trimming step is inserted in the algorithm in order to avoid the outliers' exceeding in uence. It shall be noticed that k-means algorithm is ecient for detecting spherical homoscedastic clusters. Whenever more exible shapes are desired the procedure becomes inecient. In order to overcome this problem Gaussian model based clustering methods should be adopted instead of k-means algorithm. An example, among the other proposals described in Chapter 2, is the TCLUST methodology (Garca- Escudero et al. 2008), which is the cornerstone of the thesis. Such methodology is based on two main characteristics: trimming a xed proportion of observations and imposing a constraint on the estimates of the scatter matrices. As it will be explained in Chapter 2, trimming is used to protect the results from outliers' in uence while the constraint is involved as spurious maximizers may completely spoil the solution. Chapter 3 and 4 are mainly focused on extending the TCLUST methodology. In particular, in Chapter 3, we introduce a new contribution (compare Dotto et al. 2015 and Dotto et al. 2016b), based on the TCLUST approach, called reweighted TCLUST or RTCLUST for the sake of brevity. The idea standing behind such method is based on reweighting the observations initially agged as outlying. This is helpful both to gain eciency in the parameters' estimation process and to provide a reliable estimation of the true contamination level. Indeed, as the TCLUST is based on trimming a xed proportion of observations, a proper choice of the trimming level is required. Such choice, especially in the applications, can be cumbersome. As it will be claried later on, RTCLUST methodology allows the user to overcome such problem. Indeed, in the RTCLUST approach the user is only required to impose a high preventive trimming level. The procedure, by iterating through a sequence of decreasing trimming levels, is aimed at reinserting the discarded observations at each step and provides more precise estimation of the parameters and a nal estimation of the true contamination level ^. The theoretical properties of the methodology are studied in Section 3.6 and proved in Appendix A.1, while, Section 3.7, contains a simulation study aimed at evaluating the properties of the methodology and the advantages with respect to some other robust (reweigthed and single step procedures). Chapter 4 contains an extension of the TCLUST method for fuzzy linear clustering (Dotto et al. 2016a). Such contribution can be viewed as the extension of Fritz et al. (2013a) for linear clustering problems, or, equivalently, as the extension of Garca-Escudero, Gordaliza, Mayo-Iscar & San Martn (2010) to the fuzzy clustering framework. Fuzzy clustering is also useful to deal with contamination. Fuzziness is introduced to deal with overlapping between clusters and the presence of bridge points, to be dened in Section 1.1. Indeed bridge points may arise in case of overlapping between clusters and may completely alter the estimated cluster's parameters (i.e. the coecients of a linear model in each cluster). By introducing fuzziness such observations are suitably down weighted and the clusterwise structure can be correctly detected. On the other hand, robustness against gross outliers, as in the TCLUST methodology, is guaranteed by trimming a xed proportion of observations. Additionally a simulation study, aimed at comparing the proposed methodology with other proposals (both robust and non robust) is also provided in Section 4.4. Chapter 5 is entirely dedicated to real data applications of the proposed contributions. In particular, the RTCLUST method is applied to two dierent datasets. The rst one is the \Swiss Bank Note" dataset, a well known benchmark dataset for clustering models, and to a dataset collected by Gallup Organization, which is, to our knowledge, an original dataset, on which no other existing proposals have been applied yet. Section 5.3 contains an application of our fuzzy linear clustering proposal to allometry data. In our opinion such dataset, already considered in the robust linear clustering proposal appeared in Garca-Escudero, Gordaliza, Mayo-Iscar & San Martn (2010), is particularly useful to show the advantages of our proposed methodology. Indeed allometric quantities are often linked by a linear relationship but, at the same time, there may be overlap between dierent groups and outliers may often appear due to errors in data registration. Finally Chapter 6 contains the concluding remarks and the further directions of research. In particular we wish to mention an ongoing work (Dotto & Farcomeni, In preparation) in which we consider the possibility of implementing robust parsimonious Gaussian clustering models. Within the chapter, the algorithm is briefly described and some illustrative examples are also provided. The potential advantages of such proposals are the following. First of all, by considering the parsimonious models introduced in Celeux & Govaert (1995), the user is able to impose the shape of the detected clusters, which often, in the applications, plays a key role. Secondly, by constraining the shape of the detected clusters, the constraint on the eigenvalue ratio can be avoided. This leads to the removal of a tuning parameter of the procedure and, at the same time, allows the user to obtain ane equivariant estimators. Finally, since the possibility of trimming a xed proportion of observations is allowed, then the procedure is also formally robust

Boosting for multi-graph classification

© 2014 IEEE. In this paper, we formulate a novel graph-based learning problem, multi-graph classification (MGC), which aims to learn a classifier from a set of labeled bags each containing a number of graphs inside the bag. A bag is labeled positive, if at least one graph in the bag is positive, and negative otherwise. Such a multi-graph representation can be used for many real-world applications, such as webpage classification, where a webpage can be regarded as a bag with texts and images inside the webpage being represented as graphs. This problem is a generalization of multi-instance learning (MIL) but with vital differences, mainly because instances in MIL share a common feature space whereas no feature is available to represent graphs in a multi-graph bag. To solve the problem, we propose a boosting based multi-graph classification framework (bMGC). Given a set of labeled multi-graph bags, bMGC employs dynamic weight adjustment at both bag- and graph-levels to select one subgraph in each iteration as a weak classifier. In each iteration, bag and graph weights are adjusted such that an incorrectly classified bag will receive a higher weight because its predicted bag label conflicts to the genuine label, whereas an incorrectly classified graph will receive a lower weight value if the graph is in a positive bag (or a higher weight if the graph is in a negative bag). Accordingly, bMGC is able to differentiate graphs in positive and negative bags to derive effective classifiers to form a boosting model for MGC. Experiments and comparisons on real-world multi-graph learning tasks demonstrate the algorithm performance

Multi-Target Tracking with Probabilistic Graphical Models

Thanks to revolutionary developments in microscopy techniques such as robotic high-throughput setups or light sheet microscopy, vast amounts of data can be acquired at unprecedented temporal and spatial resolution. The mass of data naturally prohibits manual analysis, though, and life scientists thus have to rely more and more on automated cell tracking methods. However, automated cell tracking involves intricacies that are not commonly found in traditional tracking applications. For instance, cells may undergo mitosis, which results in variable numbers of tracking targets across successive frames. These difficulties have been addressed by tracking-by-assignment models in the past, which dissect the task into two stages, detection and tracking. However, as with every two-stage framework, the approach hinges on the quality of the first stage, and errors propagate partially irrevocably from the detection to the tracking phase. The research in this thesis thus focuses on methods to advance tracking-by-assignment models in order to avoid these errors by exploiting synergy effects between the two (previously) separate stages. We propose two approaches, both in terms of probabilistic graphical models, which allow for information exchange between the detection and the tracking step to different degrees. The first algorithm, termed Conservation tracking, models both possible over- and undersegmentation errors and implements global consistency constraints in order to reidentify target identities even across occlusion or erroneous detections. Wrong detections from the first step can hence be corrected in the second stage. The second method goes one step further and optimizes the two stages completely jointly in one holistic model. In this way, the detection and tracking step can maximally benefit from each other and reach the overall most likely interpretation of the data. Both algorithms yield notable results which are state-of-the-art. In spite of the distinguished results achieved with these methods, automated cell tracking methods are still error-prone and manual proof-reading is often unavoidable for life scientists. To avoid the time-consuming manual identification of errors on very large datasets, most ambiguous predictions ought to be detected automatically so that these can be corrected by a human expert with minimal effort. In response, we propose two easy-to-use methods to sample multiple solutions from a tracking-by-assignment graphical model and derive uncertainty measures from the variations across the samples. We showcase the usefulness for guided proof-reading on the cell tracking model proposed in this work. Finally, the successful application of structured output learning algorithms to cell tracking in previous work inspired us to advance the state-of-the-art by an algorithm called Coulomb Structured Support Vector Machine (CSSVM). The CSSVM improves the expected generalization error for unseen test data by the training of multiple concurrent graphical models. Through the novel diversity encouraging term, motivated from experimental design, the ensemble of graphical models is learned to yield diverse predictions for test data. The best prediction amongst these models may then be selected by an oracle or with respect to a more complex loss. Experimental evaluation shows significantly better results than using only one model and achieves state-of-the-art performance on challenging computer vision tasks

A strategy for short-term load forecasting in Ireland

Electric utilities require short-term forecasts of electricity demand (load) in order to schedule generating plant up to several days ahead on an hourly basis. Errors in the forecasts may lead to generation plant operation that is not required or sub-optimal scheduling of generation plants. In addition, with the introduction of the Electricity Regulation Act 1999, a deregulated market structure has been introduced, adding increased impetus to reducing forecast error and the associated costs. This thesis presents a strategy for reducing costs from electrical demand forecast error using models designed specifically for the Irish system. The differences in short-term load forecasting models are examined under three independent categories: how the data is segmented prior to modelling, the modelling technique and the approach taken to minimise the effect of weather forecast errors present in weather inputs to the load forecasting models. A novel approach is presented to determine whether the data should be segmented by hour of the day prior to modelling. Several segmentation strategies are analysed and the one appropriate for Irish data identified. Furthermore, both linear and nonlinear techniques are compared with a view to evaluating the optimal model type. The effect of weather forecast errors on load forecasting models, though significant, has largely been ignored in the literature. Thus, the underlying issues are examined and a novel method is presented which minimises the effect of weather forecast errors

On motion in dynamic magnetic resonance imaging: Applications in cardiac function and abdominal diffusion

La imagen por resonancia magnética (MRI), hoy en día, representa una potente herramienta para el diagnóstico clínico debido a su flexibilidad y sensibilidad a un amplio rango de propiedades del tejido. Sus principales ventajas son su sobresaliente versatilidad y su capacidad para proporcionar alto contraste entre tejidos blandos. Gracias a esa versatilidad, la MRI se puede emplear para observar diferentes fenómenos físicos dentro del cuerpo humano combinando distintos tipos de pulsos dentro de la secuencia. Esto ha permitido crear distintas modalidades con múltiples aplicaciones tanto biológicas como clínicas. La adquisición de MR es, sin embargo, un proceso lento, lo que conlleva una solución de compromiso entre resolución y tiempo de adquisición (Lima da Cruz, 2016; Royuela-del Val, 2017). Debido a esto, la presencia de movimiento fisiológico durante la adquisición puede conllevar una grave degradación de la calidad de imagen, así como un incremento del tiempo de adquisición, aumentando así tambien la incomodidad del paciente. Esta limitación práctica representa un gran obstáculo para la viabilidad clínica de la MRI. En esta Tesis Doctoral se abordan dos problemas de interés en el campo de la MRI en los que el movimiento fisiológico tiene un papel protagonista. Éstos son, por un lado, la estimación robusta de parámetros de rotación y esfuerzo miocárdico a partir de imágenes de MR-Tagging dinámica para el diagnóstico y clasificación de cardiomiopatías y, por otro, la reconstrucción de mapas del coeficiente de difusión aparente (ADC) a alta resolución y con alta relación señal a ruido (SNR) a partir de adquisiciones de imagen ponderada en difusión (DWI) multiparamétrica en el hígado.Departamento de Teoría de la Señal y Comunicaciones e Ingeniería TelemáticaDoctorado en Tecnologías de la Información y las Telecomunicacione