Proper Metrics Research Articles

Adaptive integration for Capon-type beamformers by exploring Riemannian geometry on covariance matrices

Adaptive, or Capon beamformers, offers several advantages compared to standard alternatives in underwater sensing. Furthermore, for hull mounted sensor arrays, adaptive beamformers is a convenient way of mitigating platform induced interference. The underlying difficulty in implementing a data-adaptive approach is how to obtain an accurate estimate of the data covariance matrix, R. The combination of high-dimensionality and time-variation renders significant challenges in maintaining accurate covariance estimates. A common way to approach this issue is to update the covariance matrix using a weighted Euclidean average, Rnew = a Rold + (1-a) Rinst, where Rinst is some instantaneous measurement. Meanwhile, the time-variation naturally form a trajectory on the covariance matrix manifold. With this in mind, it makes much more sense to smooth the trajectory on the space of covariance matrices using proper metrics. The purpose of this paper is to take the geometry of covariance matrices into account while performing adequate covariance matrix estimation. Specifically, we propose a simple and elegant algorithm to track the covariance based on an update through means on Riemannian manifolds. This solution is then incorporated into an adaptive beamformer, and initial evaluations based on both simulated and real data show slight improvements compared to standard approaches.

Riemann metric approach to optimal sampling of multidimensional free-energy landscapes.

Exploring the free-energy landscape along reaction coordinates or system parameters λ is central to many studies of high-dimensional model systems in physics, e.g., large molecules or spin glasses. In simulations this usually requires sampling conformational transitions or phase transitions, but efficient sampling is often difficult to attain due to the roughness of the energy landscape. For Boltzmann distributions, crossing rates decrease exponentially with free-energy barrier heights. Thus, exponential acceleration can be achieved in simulations by applying an artificial bias along λ tuned such that a flat target distribution is obtained. A flat distribution is, however, an ambiguous concept unless a proper metric is used and is generally suboptimal. Here we propose a multidimensional Riemann metric, which takes the local diffusion into account, and redefine uniform sampling such that it is invariant under nonlinear coordinate transformations. We use the metric in combination with the accelerated weight histogram method, a free-energy calculation and sampling method, to adaptively optimize sampling toward the target distribution prescribed by the metric. We demonstrate that for complex problems, such as molecular dynamics simulations of DNA base-pair opening, sampling uniformly according to the metric, which can be calculated without significant computational overhead, improves sampling efficiency by 50%-70%.

Developing a new energy performance indicator for the spindle system based on power flow analysis

The evaluation of the energy performance of spindle systems with a proper metric is extremely important for energy-efficient machine tools. However, there is a lack of appropriate index to achieve this evaluation. To close this gap, the additional power requirement, which is defined as the discrepancy between the material removal power and the power gap of the spindle system from air-cutting state to cutting state, was proposed as a new indicator based on a detailed power flow analysis. The additional power requirement universally exists in machining and results from the efficiency and power losses of the system, which makes it a good energy performance indicator candidate. A theoretical model for the additional power requirement of spindle systems was built and verified in a lathe machine, through which two causes of additional power requirement were pointed: less than 100% efficiency throughout the system and efficiency change of the spindle motor under a dynamic load and a variable speed. The first cause has a positive effect on the additional power requirement, whereas the second one generally plays a negative role. Furthermore, the additional power requirement can be negative because of the negative effect, which is different from previous studies. The close relation between the additional power requirement and the energy performance of the spindle is demonstrated by an in-depth analysis. This work is an important building block for energy-efficient machine tools.

The Shape Space of 3D Botanical Tree Models

We propose an algorithm for generating novel 3D tree model variations from existing ones via geometric and structural blending. Our approach is to treat botanical trees as elements of a tree-shape space equipped with a proper metric that quantifies geometric and structural deformations. Geodesics, or shortest paths under the metric, between two points in the tree-shape space correspond to optimal deformations that align one tree onto another, including the possibility of expanding, adding, or removing branches and parts. Central to our approach is a mechanism for computing correspondences between trees that have different structures and a different number of branches. The ability to compute geodesics and their lengths enables us to compute continuous blending between botanical trees, which, in turn, facilitates statistical analysis, such as the computation of averages of tree structures. We show a variety of 3D tree models generated with our approach from 3D trees exhibiting complex geometric and structural differences. We also demonstrate the application of the framework in reflection symmetry analysis and symmetrization of botanical trees.

On the stability of asymptotic property C for products and some group extensions

We show that Dranishnikov's asymptotic property C is preserved by direct products and the free product of discrete metric spaces. In particular, if $G$ and $H$ are groups with asymptotic property C, then both $G \times H$ and $G * H$ have asymptotic property C. We also prove that a group~$G$ has asymptotic property C if $1\to K\to G\to H\to 1$ is exact, if $\operatorname{asdim} K<\infty$, and if $H$ has asymptotic property C. The groups are assumed to have left-invariant proper metrics and need not be finitely generated. These results settle questions of Dydak and Virk, of Bell and Moran, and an open problem in topology from the Lviv Topological Seminar.

Document Classification via Nonlinear Metric Learning

Learning a proper distance metric is an important problem in document classification, because the similarities of samples in many problems are usually measured by distance metric. In this paper, we address the nonlinear metric leaning problem with applying in the document classification. First, we propose a new representation about nonlinear metric by using a linear combination of some basic kernels. Second, we give a linear metric learning method by a triplet constraint and k-nearest neighbors, and then we develop it to a nonlinear method based on multiple kernel by above nonlinear metric. Further, the corresponding problem can be rewritten as an unconstrained optimization problem on positive definite matrices groups. At last, to ensure the learned distance matrix must be a positive definite matrix, we provide an improved intrinsic steepest descent algorithm with adaptive step-size to solve this unconstrained optimization. The experimental results show that our proposed method is effective on some document classification problems.

Forbidden versus permitted interactions: Disentangling processes from patterns in ecological network analysis.

Several studies have identified the tendency for species to share interacting partners as a key property to the functioning and stability of ecological networks. However, assessing this pattern has proved challenging in several regards, such as finding proper metrics to assess node overlap (sharing), and using robust null modeling to disentangle significance from randomness. Here, we bring attention to an additional, largely neglected challenge in assessing species’ tendency to share interacting partners. In particular, we discuss and illustrate with two different case studies how identifying the set of “permitted” interactions for a given species (i.e. interactions that are not impeded, e.g. by lack of functional trait compatibility) is paramount to understand the ecological and co‐evolutionary processes at the basis of node overlap and segregation patterns.

Global helioseismology (WP4.1): From the Sun to the stars &amp; solar analogs

Sun-as-a star observations put our star as a reference for stellar observations. Here, I review the activities in which the SPACEINN global seismology team (Working Package WP4.1) has worked during the past 3 years. In particular, we will explain the new deliverables available on the SPACEINN seismic+ portal. Moreover, special attention will be given to surface dynamics (rotation and magnetic fields). After characterizing the rotation and the magnetic properties of around 300 solar-like stars and defining proper metrics for that, we use their seismic properties to characterize 18 solar analogues for which we study their surface magnetic and seismic properties. This allows us to put the Sun into context compared to its siblings.

Prognostic and Health Management System for Fly-by-wire Electro-hydraulic Servo Actuators for Detection and Tracking of Actuator Faults

Maintenance of flight control actuation systems is currently performed on a scheduled basis, however air fleet operators and component manufacturers are willing to move from scheduled maintenance to Condition Based Maintenance (CBM) in order to reduce maintenance costs and improve aircraft dispatchability. Prognostics and Health Management (PHM) systems are a critical part of CBM and are perceived as a breakthrough technology to effectively respond to an urgent and critical need to improve the readiness, availability, reliability, safety and maintainability of aerospace vehicles. This paper presents the results of an ongoing research activity focused on the development of a PHM system for fly-by-wire Electro-Hydraulic Servo Actuators (EHSA) without adding new sensors. The PHM system is being developed with the objective of detecting the most common faults, according to a failure mode effects and criticality analysis (FMECA). The paper describes in particular the tools used for detection and tracking of internal leakage faults of the hydraulic actuator, which is one of the most common faults of hydraulic servo-actuators in service, and for predicting its remaining useful life (RUL). The research work has been supported by the development of a nonlinear model for a reference EHSA, that has been implemented using physical equations and system parameters, taking into account environmental condition and disturbances. The model was validated through tests runs on a flight control actuator of a civil aircraft. Simulations are performed in nominal conditions and with progressive injection of degradation to verify the PHM algorithm. The performances of the PHM algorithms are evaluated by means of proper metrics.

The role of developers’ social relationships in improving service selection

Purpose Modern Enterprise Web Application development can exploit third-party software components, both internal and external to the enterprise, that provide access to huge and valuable data sets, tested by millions of users and often available as Web application programming interfaces (APIs). In this context, the developers have to select the right data services and might rely, to this purpose, on advanced techniques, based on functional and non-functional data service descriptive features. This paper focuses on this selection task where data service selection may be difficult because the developer has no control on services, and source reputation could be only partially known. Design/methodology/approach The proposed framework and methodology are apt to provide advanced search and ranking techniques by considering: lightweight data service descriptions, in terms of (semantic) tags and technical aspects; previously developed aggregations of data services, to use in the selection process of a service the past experiences with the services when used in similar applications; social relationships between developers (social network) and their credibility evaluations. This paper also discusses some experimental results regarding the plan to expand other experiments to check how developers feel using the approach. Findings In this paper, a data service selection framework that extends and specializes an existing one for Web APIs selection is presented. The revised multi-layered model for data services is discussed and proper metrics relying on it, meant for supporting the selection of data services in a context of Web application design, are introduced. Model and metrics take into account the network of social relationships between developers, to exploit them for estimating the importance that a developer assigns to other developers’ experience. Originality/value This research, with respect to the state of the art, focuses attention on developers’ social networks in an enterprise context, integrating the developers’ credibility assessment and implementing the social network-based data service selection on top of a rich framework based on a multi-perspective model for data services.

Perceptron ensemble of graph-based positive-unlabeled learning for disease gene identification

Identification of disease genes, using computational methods, is an important issue in biomedical and bioinformatics research. According to observations that diseases with the same or similar phenotype have the same biological characteristics, researchers have tried to identify genes by using machine learning tools. In recent attempts, some semi-supervised learning methods, called positive-unlabeled learning, is used for disease gene identification. In this paper, we present a Perceptron ensemble of graph-based positive-unlabeled learning (PEGPUL) on three types of biological attributes: gene ontologies, protein domains and protein-protein interaction networks. In our method, a reliable set of positive and negative genes are extracted using co-training schema. Then, the similarity graph of genes is built using metric learning by concentrating on multi-rank-walk method to perform inference from labeled genes. At last, a Perceptron ensemble is learned from three weighted classifiers: multilevel support vector machine, k-nearest neighbor and decision tree. The main contributions of this paper are: (i) incorporating the statistical properties of gene data through choosing proper metrics, (ii) statistical evaluation of biological features, and (iii) noise robustness characteristic of PEGPUL via using multilevel schema. In order to assess PEGPUL, we have applied it on 12950 disease genes with 949 positive genes from six class of diseases and 12001 unlabeled genes. Compared with some popular disease gene identification methods, the experimental results show that PEGPUL has reasonable performance.

Resources versus Capabilities in Social Justice

Over the last decades, economists, political theorists and philosophers have debated the question of what the proper metric of justice is. In other words, they have sought to answer the questions what should we look at, when evaluating whether one state of affairs is more or less just than another? Should we evaluate the distribution of happiness? Or wealth? Or some combination of these and other factors? The resourcist approach and the capability approach as egalitarian theories of social justice are two prominent answers to these questions. While the former approach has been developed by the studies of John Rawls and Donald Dworkin, the latter approach has been associated with the studies of Amartya Sen and Martha Nussbaum. A fundamental debate between these approaches continues over what should be distributed. This paper attempts to bridge the gap between these approaches. By this we aim to bring their different perspectives together to reconsider the relationship between resource and the capability approach, and to open up a new insight to understand both approaches as complementary theories, rather than purely rival theories of justice. JEL: D30, D63

Co-Saliency Detection via a Self-Paced Multiple-Instance Learning Framework.

As an interesting and emerging topic, co-saliency detection aims at simultaneously extracting common salient objects from a group of images. On one hand, traditional co-saliency detection approaches rely heavily on human knowledge for designing hand-crafted metrics to possibly reflect the faithful properties of the co-salient regions. Such strategies, however, always suffer from poor generalization capability to flexibly adapt various scenarios in real applications. On the other hand, most current methods pursue co-saliency detection in unsupervised fashions. This, however, tends to weaken their performance in real complex scenarios because they are lack of robust learning mechanism to make full use of the weak labels of each image. To alleviate these two problems, this paper proposes a new SP-MIL framework for co-saliency detection, which integrates both multiple instance learning (MIL) and self-paced learning (SPL) into a unified learning framework. Specifically, for the first problem, we formulate the co-saliency detection problem as a MIL paradigm to learn the discriminative classifiers to detect the co-saliency object in the "instance-level". The formulated MIL component facilitates our method capable of automatically producing the proper metrics to measure the intra-image contrast and the inter-image consistency for detecting co-saliency in a purely self-learning way. For the second problem, the embedded SPL paradigm is able to alleviate the data ambiguity under the weak supervision of co-saliency detection and guide a robust learning manner in complex scenarios. Experiments on benchmark datasets together with multiple extended computer vision applications demonstrate the superiority of the proposed framework beyond the state-of-the-arts.

Antipodally Invariant Metrics for Fast Regression-Based Super-Resolution

Dictionary-based super-resolution (SR) algorithms usually select dictionary atoms based on the distance or similarity metrics. Although the optimal selection of the nearest neighbors is of central importance for such methods, the impact of using proper metrics for SR has been overlooked in literature, mainly due to the vast usage of Euclidean distance. In this paper, we present a very fast regression-based algorithm, which builds on the densely populated anchored neighborhoods and sublinear search structures. We perform a study of the nature of the features commonly used for SR, observing that those features usually lie in the unitary hypersphere, where every point has a diametrically opposite one, i.e., its antipode, with same module and angle, but the opposite direction. Even though, we validate the benefits of using antipodally invariant metrics, most of the binary splits use Euclidean distance, which does not handle antipodes optimally. In order to benefit from both the worlds, we propose a simple yet effective antipodally invariant transform that can be easily included in the Euclidean distance calculation. We modify the original spherical hashing algorithm with this metric in our antipodally invariant spherical hashing scheme, obtaining the same performance as a pure antipodally invariant metric. We round up our contributions with a novel feature transform that obtains a better coarse approximation of the input image thanks to iterative backprojection. The performance of our method, which we named antipodally invariant SR, improves quality (Peak Signal to Noise Ratio) and it is faster than any other state-of-the-art method.

Policies Towards the OFDI and IFDI in the European Union after the 2008+ Crisis

Objective : The objective of this paper is to evaluate the (post)crisis FDI policies in Europe, taken the significant drop in international foreign direct investment (FDI) flows as observed in the aftermath of 2008+ crisis as well as the accompanying ideological shifts as to the role of the State in the economy. Research Design & Methods : By synthesising the available sources – critical literature review, evaluation of rankings and scoreboards and experts’ survey - this paper seeks to classify the EU member states according to their policies pursued towards outward and inward foreign direct investment (IFDI, OFDI) in the context of 2008+ crisis. Findings : A matrix with for possible combinations of FDI policy has been proposed. It distinguishes: an open model with “a double positive strategy”, closed with “a double negative strategy”, competitive with “a positive outward and negative inward strategy”, and a capital model with “a positive inward, negative outward strategy”. Obtained results point to the dominance of two opposite models where countries seem to apply combinations of rather friendly IFDI (or OFDI) and unfriendly OFDI (or IFDI) policies. Implications & Recommendations : Current scarcity of a proper metric of FDI policy has made it necessary to draw on some imperfect substitutes, hence findings must be treated with caution. Properly designed, reliable international database enabling crosscountry comparisons in terms of FDI policies would certainly improve the quality of future research. Contribution & Value Added : Presented research findings can be seen as a voice in the discussion on FDI policy in Europe, in particular on the issue of operationalisation of such policy.

Performance and robustness analysis of stochastic jump linear systems using Wasserstein metric

This paper focuses on the performance and robustness analysis of stochastic jump linear systems. In the presence of stochastic jumps, state variables evolve as random process, with associated time varying probability density functions. Consequently, system analysis is performed at the density level and a proper metric is necessary to quantify the system performance. In this paper, Wasserstein metric that measures a distance between probability density functions is employed to develop new results for the performance analysis of stochastic jump linear systems. Both transient and steady-state performance of the systems, with given initial state uncertainties, can be analyzed in this framework. Also, we prove that the convergence of the Wasserstein metric implies the mean square stability. We present a novel “Split-and-Merge” algorithm for propagation of state uncertainty in such systems. Overall, this study provides a unifying framework for the performance and robustness analysis of general stochastic jump linear systems, and not necessarily Markovian that is commonly assumed. The usefulness and efficiency of the proposed method are verified through numerical examples.

The Law and Finance of Anti-Takeover Statutes

Lawyers and financial economists have fundamentally different views of anti-takeover statutes. While corporate lawyers and academics generally dismiss these statutes as irrelevant, economists study them empirically and conclude that they – and hence the threat of a takeover – affect firm and managerial behavior. This article seeks to examine the divide between the law and the finance approach to anti-takeover statutes. We first explain why these statutes, as used by financial economists, are not a proper metric of the potential takeover threat facing a firm. This poses the question of why finance studies of these statutes find results. We therefore examine in greater detail three finance studies and show that their results are due to omitted variables or improper specifications. When corrected for these problems, the association between anti-takeover statutes and the hypothesized effect disappeared. We then supplement this specific critique with a more general critique that identifies three flaws – coding errors, failure to account for managerial share ownership, and selection bias – that pervade the finance studies on anti-takeover statutes and bias their results. Broadly, our paper calls into question most of the understanding of the effect of takeover threat, which is based to a large extent on finance studies of anti-takeover statutes.

Dissimilarities in Alignment-Free Methods for Phylogenetic Analysis Based on Genomes

Whole genome sequences are generally accepted as excellent tools for studying evolutionary relationships. Due to the problems caused by the uncertainty in alignment, existing tools for phylogenetic analysis based on multiple alignments could not be directly applied to the whole-genome comparison and phylogenomic studies. There has been a growing interest in alignment-free methods for phylogenetic analysis using complete genome data. The “distances” used in these alignment-free methods are not proper distance metrics in the strict mathematical sense. In this study, we first review them in a more general frame — dissimilarity. Then we propose some new dissimilarities for phylogenetic analysis. Last three genome datasets are employed to evaluate these dissimilarities from a biological point of view.

Maximum Likelihood Sequence Detection for Mitigating Nonlinear Effects

Coherent detection allows for a more effective compensation of transmission impairments in the electrical domain. However, in order to be effective, a detection strategy should be based on an accurate channel model capable of providing sufficiently accurate signal statistics. While in the linear regime such a model is available and linear impairments such as chromatic dispersion and polarization-mode dispersion can be almost fully compensated by adaptive equalizers, this is not the case for nonlinear impairments, whose mitigation is essentially based on heuristic strategies. One of the most considered strategies is the back-propagation (BP) technique, based on channel inversion. It is shown that BP is most effective only in dispersion-unmanaged links, while a low-complexity Viterbi detector with proper metrics can achieve better results in the case of dispersion-managed links. It is also shown that, in the cases where it is effective, BP is far from approaching optimal performance. Indeed, proper processing after BP can significantly increase performance.

Analysis of spike train data: Alignment and comparisons using the extended Fisher-Rao metric

We present a metric-based framework for analyzing statistical variability of the neural spike train data that was introduced in an earlier paper on this section [14]. Treating the smoothed spike trains as functional data, we apply the extended Fisher-Rao Riemannian metric, first introduced in Srivastava et al. [9], to perform: (1) pairwise alignment of spike functions, (2) averaging of multiple functions, and (3) alignment of spike functions to the mean. The last item results in separation phase and amplitude components from the functional data. Further, we utilize proper metrics on these components for classification of activities represented by spike trains. This approach is based on the square-root slope function (SRSF) representation of functions that transforms the Fisher-Rao metric into the standard $\mathbb{L}^{2}$ metric and, thus, simplifies computations. We compare our registration results with some current methods and demonstrate an application of our approach in neural decoding to infer motor behaviors.