Stochastic Optimization in Robust Statistic

2000 Mathematics Subject Classification: 62J05, 62G35

Non-monotone averaging aggregation

We advance the theory of aggregation operators and introduce non-monotone aggregation methods based on minimization of a penalty for inputs disagreements. The application in mind is processing data sets which may contain noisy values. Our aim is to filter out noise while at the same time preserve signs of unusual values. We review various methods of robust estimators of location, and then introduce a new estimator based on penalty minimisation.

Image reduction operators based on non-monotonic averaging functions

Image reduction is a crucial task in image processing, underpinning many practical applications. This work proposes novel image reduction operators based on non-monotonic averaging aggregation functions. The technique of penalty function minimisation is used to derive a novel mode-like estimator capable of identifying the most appropriate pixel value for representing a subset of the original image. Performance of this aggregation function and several traditional robust estimators of location are objectively assessed by applying image reduction within a facial recognition task. The FERET evaluation protocol is applied to confirm that these non-monotonic functions are able to sustain task performance compared to recognition using nonreduced images, as well as significantly improve performance on query images corrupted by noise. These results extend the state of the art in image reduction based on aggregation functions and provide a basis for efficiency and accuracy improvements in practical computer vision applications.

Weakly monotone averaging functions

Averaging behaviour of aggregation functions depends on the fundamental property of monotonicity with respect to all arguments. Unfortunately this is a limiting property that ensures that many important averaging functions are excluded from the theoretical framework. We propose a definition for weakly monotone averaging functions to encompass the averaging aggregation functions in a framework with many commonly used non-monotonic means. Weakly monotonic averages are robust to outliers and noise, making them extremely important in practical applications. We show that several robust estimators of location are actually weakly monotone and we provide sufficient conditions for weak monotonicity of the Lehmer and Gini means and some mixture functions. In particular we show that mixture functions with Gaussian kernels, which arise frequently in image and signal processing applications, are actually weakly monotonic averages. Our concept of weak monotonicity provides a sound theoretical and practical basis for understanding both monotone and non-monotone averaging functions within the same framework. This allows us to effectively relate these previously disparate areas of research and gain a deeper understanding of averaging aggregation methods. © Springer International Publishing Switzerland 2014.

Weakly monotonic averaging functions

Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions. It is also a limiting property that results in many important nonmonotonic averaging functions being excluded from the theoretical framework. This work proposes a definition for weakly monotonic averaging functions, studies some properties of this class of functions, and proves that several families of important nonmonotonic means are actually weakly monotonic averaging functions. Specifically, we provide sufficient conditions for weak monotonicity of the Lehmer mean and generalized mixture operators. We establish weak monotonicity of several robust estimators of location and conditions for weak monotonicity of a large class of penalty-based aggregation functions. These results permit a proof of the weak monotonicity of the class of spatial-tonal filters that include important members such as the bilateral filter and anisotropic diffusion. Our concept of weak monotonicity provides a sound theoretical and practical basis by which (monotonic) aggregation functions and nonmonotonic averaging functions can be related within the same framework, allowing us to bridge the gap between these previously disparate areas of research.

UNIFORM DISSIPATIVENESS, ROBUST SYNCHRONIZATION AND LOCATION OF THE ATTRACTOR OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS

In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance principle in the autonomous case. The Liapunov function is allowed to have positive derivative along solutions of the system inside a bounded set, and this reduces substantially the difficulty of constructing a Liapunov function for a given system. In particular, we develop an approach that incorporates the classical Lagrange multiplier into the Liapunov function method to naturally extend those Liapunov functions from continuous dynamical system to their discretizations, so that the corresponding uniform dispativeness results are valid when the step size of the discretization is small. Applications to the discretized Lorenz system and the discretization of a time-periodic chaotic system are given to illustrate the general results. We also show how to obtain uniform estimation of attractors for parametrized linear stable systems with nonlinear perturbation.

Influence functions of two families of robust estimators under proportional scatter matrices

In this paper, under a proportional model, two families of robust estimates for the proportionality constants, the common principal axes and their size are discussed. The first approach is obtained by plugging robust scatter matrices on the maximum likelihood equations for normal data. A projection- pursuit and a modified projection-pursuit approach, adapted to the proportional setting, are also considered. For all families of estimates, partial influence functions are obtained and asymptotic variances are derived from them. The performance of the estimates is compared through a Monte Carlo study. © 2006 Springer-Verlag.

Robust design of multiple trailing edge flaps for helicopter vibration reduction: A multi-objective bat algorithm approach

The objective of this study is to determine an optimal trailing edge flap configuration and flap location to achieve minimum hub vibration levels and flap actuation power simultaneously. An aeroelastic analysis of a soft in-plane four-bladed rotor is performed in conjunction with optimal control. A second-order polynomial response surface based on an orthogonal array (OA) with 3-level design describes both the objectives adequately. Two new orthogonal arrays called MGB2P-OA and MGB4P-OA are proposed to generate nonlinear response surfaces with all interaction terms for two and four parameters, respectively. A multi-objective bat algorithm (MOBA) approach is used to obtain the optimal design point for the mutually conflicting objectives. MOBA is a recently developed nature-inspired metaheuristic optimization algorithm that is based on the echolocation behaviour of bats. It is found that MOBA inspired Pareto optimal trailing edge flap design reduces vibration levels by 73% and flap actuation power by 27% in comparison with the baseline design.

Robust Extraction of Text from Camera Images using Colour and Spatial Information Simultaneously

The importance and use of text extraction from camera based coloured scene images is rapidly increasing with time. Text within a camera grabbed image can contain a huge amount of meta data about that scene. Such meta data can be useful for identification, indexing and retrieval purposes. While the segmentation and recognition of text from document images is quite successful, detection of coloured scene text is a new challenge for all camera based images. Common problems for text extraction from camera based images are the lack of prior knowledge of any kind of text features such as colour, font, size and orientation as well as the location of the probable text regions. In this paper, we document the development of a fully automatic and extremely robust text segmentation technique that can be used for any type of camera grabbed frame be it single image or video. A new algorithm is proposed which can overcome the current problems of text segmentation. The algorithm exploits text appearance in terms of colour and spatial distribution. When the new text extraction technique was tested on a variety of camera based images it was found to out perform existing techniques (or something similar). The proposed technique also overcomes any problems that can arise due to an unconstraint complex background. The novelty in the works arises from the fact that this is the first time that colour and spatial information are used simultaneously for the purpose of text extraction.

Robust dynamics of Amazon dieback to climate change with perturbed ecosystem model parameters

Climate change science is increasingly concerned with methods for managing and integrating sources of uncertainty from emission storylines, climate model projections, and ecosystem model parameterizations. In tropical ecosystems, regional climate projections and modeled ecosystem responses vary greatly, leading to a significant source of uncertainty in global biogeochemical accounting and possible future climate feedbacks. Here, we combine an ensemble of IPCC-AR4 climate change projections for the Amazon Basin (eight general circulation models) with alternative ecosystem parameter sets for the dynamic global vegetation model, LPJmL. We evaluate LPJmL simulations of carbon stocks and fluxes against flux tower and aboveground biomass datasets for individual sites and the entire basin. Variability in LPJmL model sensitivity to future climate change is primarily related to light and water limitations through biochemical and water-balance-related parameters. Temperature-dependent parameters related to plant respiration and photosynthesis appear to be less important than vegetation dynamics (and their parameters) for determining the magnitude of ecosystem response to climate change. Variance partitioning approaches reveal that relationships between uncertainty from ecosystem dynamics and climate projections are dependent on geographic location and the targeted ecosystem process. Parameter uncertainty from the LPJmL model does not affect the trajectory of ecosystem response for a given climate change scenario and the primary source of uncertainty for Amazon 'dieback' results from the uncertainty among climate projections. Our approach for describing uncertainty is applicable for informing and prioritizing policy options related to mitigation and adaptation where long-term investments are required.

Robust classification of SAR imagery

In this work the G(A)(0) distribution is assumed as the universal model for amplitude Synthetic Aperture (SAR) imagery data under the Multiplicative Model. The observed data, therefore, is assumed to obey a G(A)(0) (alpha; gamma, n) law, where the parameter n is related to the speckle noise, and (alpha, gamma) are related to the ground truth, giving information about the background. Therefore, maps generated by the estimation of (alpha, gamma) in each coordinate can be used as the input for classification methods. Maximum likelihood estimators are derived and used to form estimated parameter maps. This estimation can be hampered by the presence of corner reflectors, man-made objects used to calibrate SAR images that produce large return values. In order to alleviate this contamination, robust (M) estimators are also derived for the universal model. Gaussian Maximum Likelihood classification is used to obtain maps using hard-to-deal-with simulated data, and the superiority of robust estimation is quantitatively assessed.

A Robust Parser of Czech

Mr. Kubon's project was inspired by the growing need for an automatic, syntactic analyser (parser) of Czech, which could be used in the syntactic processing of large amounts of texts. Mr. Kubon notes that such a tool would be very useful, especially in the field of corpus linguistics, where creating a large-scale "tree bank" (a collection of syntactic representations of natural language sentences) is a very important step towards the investigation of the properties of a given language. The work involved in syntactically parsing a whole corpus in order to get a representative set of syntactic structures would be almost inconceivable without the help of some kind of robust (semi)automatic parser. The need for the automatic natural language parser to be robust increases with the size of the linguistic data in the corpus or in any other kind of text which is going to be parsed. Practical experience shows that apart from syntactically correct sentences, there are many sentences which contain a "real" grammatical error. These sentences may be corrected in small-scale texts, but not generally in the whole corpus. In order to be able to complete the overall project, it was necessary to address a number of smaller problems. These were; 1. the adaptation of a suitable formalism able to describe the formal grammar of the system; 2. the definition of the structure of the system's dictionary containing all relevant lexico-syntactic information, and the development of a formal grammar able to robustly parse Czech sentences from the test suite; 3. filling the syntactic dictionary with sample data allowing the system to be tested and debugged during its development (about 1000 words); 4. the development of a set of sample sentences containing a reasonable amount of grammatical and ungrammatical phenomena covering some of the most typical syntactic constructions being used in Czech. Number 3, building a formal grammar, was the main task of the project. The grammar is of course far from complete (Mr. Kubon notes that it is debatable whether any formal grammar describing a natural language may ever be complete), but it covers the most frequent syntactic phenomena, allowing for the representation of a syntactic structure of simple clauses and also the structure of certain types of complex sentences. The stress was not so much on building a wide coverage grammar, but on the description and demonstration of a method. This method uses a similar approach as that of grammar-based grammar checking. The problem of reconstructing the "correct" form of the syntactic representation of a sentence is closely related to the problem of localisation and identification of syntactic errors. Without a precise knowledge of the nature and location of syntactic errors it is not possible to build a reliable estimation of a "correct" syntactic tree. The incremental way of building the grammar used in this project is also an important methodological issue. Experience from previous projects showed that building a grammar by creating a huge block of metarules is more complicated than the incremental method, which begins with the metarules covering most common syntactic phenomena first, and adds less important ones later, especially from the point of view of testing and debugging the grammar. The sample of the syntactic dictionary containing lexico-syntactical information (task 4) now has slightly more than 1000 lexical items representing all classes of words. During the creation of the dictionary it turned out that the task of assigning complete and correct lexico-syntactic information to verbs is a very complicated and time-consuming process which would itself be worth a separate project. The final task undertaken in this project was the development of a method allowing effective testing and debugging of the grammar during the process of its development. The problem of the consistency of new and modified rules of the formal grammar with the rules already existing is one of the crucial problems of every project aiming at the development of a large-scale formal grammar of a natural language. This method allows for the detection of any discrepancy or inconsistency of the grammar with respect to a test-bed of sentences containing all syntactic phenomena covered by the grammar. This is not only the first robust parser of Czech, but also one of the first robust parsers of a Slavic language. Since Slavic languages display a wide range of common features, it is reasonable to claim that this system may serve as a pattern for similar systems in other languages. To transfer the system into any other language it is only necessary to revise the grammar and to change the data contained in the dictionary (but not necessarily the structure of primary lexico-syntactic information). The formalism and methods used in this project can be used in other Slavic languages without substantial changes.

The Dissociation of Location and Object Working Memory using fMRI and MEG

Visual working memory (VWM) involves maintaining and processing visual information, often for the purpose of making immediate decisions. Neuroimaging experiments of VWM provide evidence in support of a neural system mainly involving a fronto-parietal neuronal network, but the role of specific brain areas is less clear. A proposal that has recently generated considerable debate suggests that a dissociation of object and location VWM occurs within the prefrontal cortex, in dorsal and ventral regions, respectively. However, re-examination of the relevant literature presents a more robust distribution suggestive of a general caudal-rostral dissociation from occipital and parietal structures, caudally, to prefrontal regions, rostrally, corresponding to location and object memory, respectively. The purpose of the present study was to identify a dissociation of location and object VWM across two imaging methods (magnetoencephalography, MEG, and functional magnetic imaging, fMRI). These two techniques provide complimentary results due the high temporal resolution of MEG and the high spatial resolution of fMRI. The use of identical location and object change detection tasks was employed across techniques and reported for the first time. Moreover, this study is the first to use matched stimulus displays across location and object VWM conditions. The results from these two imaging methods provided convergent evidence of a location and object VWM dissociation favoring a general caudal-rostral rather than the more common prefrontal dorsal-ventral view. Moreover, neural activity across techniques was correlated with behavioral performance for the first time and provided convergent results. This novel approach of combining imaging tools to study memory resulted in robust evidence suggesting a novel interpretation of location and object memory. Accordingly, this study presents a novel context within which to explore the neural substrates of WM across imaging techniques and populations.

R-estimator of location of the generalized secant hyperbolic distribution

The generalized secant hyperbolic distribution (GSHD) proposed in Vaughan (2002) includes a wide range of unimodal symmetric distributions, with the Cauchy and uniform distributions being the limiting cases, and the logistic and hyperbolic secant distributions being special cases. The current article derives an asymptotically efficient rank estimator of the location parameter of the GSHD and suggests the corresponding one- and two-sample optimal rank tests. The rank estimator derived is compared to the modified MLE of location proposed in Vaughan (2002). By combining these two estimators, a computationally attractive method for constructing an exact confidence interval of the location parameter is developed. The statistical procedures introduced in the current article are illustrated by examples.

Enhancing the trust of location acquisition systems for critical applications and location-based security services

This paper identifies a number of critical infrastructure applications that are reliant on location services from cooperative location technologies such as GPS and GSM. We show that these location technologies can be represented in a general location model, such that the model components can be used for vulnerability analysis. We perform a vulnerability analysis on these components of GSM and GPS location systems as well as a number of augmentations to these systems.