Spectral Clustering with Imbalanced Data

Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data since they tend to emphasize cut sizes over cut values. We propose a graph partitioning problem that seeks minimum cut partitions under minimum size constraints on partitions to deal with imbalanced data. Our approach parameterizes a family of graphs, by adaptively modulating node degrees on a fixed node set, to yield a set of parameter dependent cuts reflecting varying levels of imbalance. The solution to our problem is then obtained by optimizing over these parameters. We present rigorous limit cut analysis results to justify our approach. We demonstrate the superiority of our method through unsupervised and semi-supervised experiments on synthetic and real data sets.Comment: 24 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1302.513

Clustering and Community Detection with Imbalanced Clusters

Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced cluster sizes since they tend to emphasize cut sizes over cut values. We propose a graph partitioning problem that seeks minimum cut partitions under minimum size constraints on partitions to deal with imbalanced cluster sizes. Our approach parameterizes a family of graphs by adaptively modulating node degrees on a fixed node set, yielding a set of parameter dependent cuts reflecting varying levels of imbalance. The solution to our problem is then obtained by optimizing over these parameters. We present rigorous limit cut analysis results to justify our approach and demonstrate the superiority of our method through experiments on synthetic and real datasets for data clustering, semi-supervised learning and community detection.Comment: Extended version of arXiv:1309.2303 with new applications. Accepted to IEEE TSIP

Why U.S. States Need Pension Waiver Credits

[A] new tax expenditure concept, which is described for the first time in this article, achieves its goal by providing fresh consideration for each of the parties. This additional consideration takes two forms: a new tax credit allocation (i.e., this tax expenditure provides early access to retirement benefits, which would otherwise be accessible upon retirement, and thereby provides fresh consideration for public employees) and the right to discontinue offering defined-benefit pension plans (i.e., the waiver of this legal duty, which would otherwise need to be discharged, serves as fresh consideration for public employers). Because this fresh consideration is not tied to any pre-existing duty, and meets every other requirement, Pension Waiver Credits resolve the fresh consideration dilemma for public pension contract

A characterization of irreducible infeasible subsystems in flow networks

Infeasible network flow problems with supplies and demands can be characterized via violated cut-inequalities of the classical Gale-Hoffman theorem. Written as a linear program, irreducible infeasible subsystems (IISs) provide a different means of infeasibility characterization. In this article, we answer a question left open in the literature by showing a one-to-one correspondence between IISs and Gale-Hoffman-inequalities in which one side of the cut has to be weakly connected. We also show that a single max-flow computation allows one to compute an IIS. Moreover, we prove that finding an IIS of minimal cardinality in this special case of flow networks is strongly NP-hard

Haemoglobin status of adult non-pregnant Kazakh women living in Kzyl-Orda region, Kazakhstan.

OBJECTIVE: To estimate the prevalence of anaemia among adult non-pregnant women in the Kzyl-Orda region of Kazakhstan, and to determine the association between haemoglobin concentration and anthropometric, socioeconomic, reproductive and dietary factors. DESIGN: A cross-sectional study using a randomly selected sample. Subjects were interviewed, and finger-prick blood samples and anthropometric measurements were collected. Associations between haemoglobin concentration and anthropometric and questionnaire data were evaluated by sequential linear regression analysis. SETTING: Health centres in Kazalinsk, Djalagash and Zhanakorgan districts of Kzyl-Orda region, Kazakhstan. SUBJECTS: Three-thousand six-hundred and twenty-five non-pregnant women aged 18-45 y randomly selected from health centre records. RESULTS: Iron deficiency anaemia, as reflected by low haemoglobin levels (Hb<12 g/dl), was detected in 40.2% of the total sample. There was a significant curvilinear relationship between haemoglobin concentration and age, with the nadir of the curve in the 30-40 y age-group. Haemoglobin concentration was found to be positively associated with body mass index (BMI) and socioeconomic factors. Significant negative associations were found between haemoglobin concentration and duration of menses, use of the intra-uterine contraceptive device and the consumption of tea. CONCLUSIONS: This study demonstrates that iron deficiency anaemia is present at considerable levels among adult women living in Kzyl-Orda region, Kazakhstan, and provides important baseline information for future research and public health interventions. SPONSORSHIP: Funding was provided by the United States Agency for International Development, Office of Nutrition, the United Kingdom Department for International Development, and the Polden-Puckham Trust

A Sub-Exponential FPT Algorithm and a Polynomial Kernel for Minimum Directed Bisection on Semicomplete Digraphs

Given an n-vertex digraph D and a non-negative integer k, the Minimum Directed Bisection problem asks if the vertices of D can be partitioned into two parts, say L and R, such that |L| and |R| differ by at most 1 and the number of arcs from R to L is at most k. This problem, in general, is W-hard as it is known to be NP-hard even when k=0. We investigate the parameterized complexity of this problem on semicomplete digraphs. We show that Minimum Directed Bisection on semicomplete digraphs is one of a handful of problems that admit sub-exponential time fixed-parameter tractable algorithms. That is, we show that the problem admits a 2^{O(sqrt{k} log k)}n^{O(1)} time algorithm on semicomplete digraphs. We also show that Minimum Directed Bisection admits a polynomial kernel on semicomplete digraphs. To design the kernel, we use (n,k,k^2)-splitters. To the best of our knowledge, this is the first time such pseudorandom objects have been used in the design of kernels. We believe that the framework of designing kernels using splitters could be applied to more problems that admit sub-exponential time algorithms via chromatic coding. To complement the above mentioned results, we prove that Minimum Directed Bisection is NP-hard on semicomplete digraphs, but polynomial time solvable on tournaments

On the preference for form and abstract architecture spaces with distinct geometric characteristics

Since at least the Greek classic period that thought, within the western civilizations, has been sharing a strict relationship with Euclidean principles, which have influenced and characterized it, leading to a specific type of reasoning and identity. In turn, as expressions of the mind, the forms that we have been thinking about and have brought to material reality, have been following these same Euclidean principles. Thought has shared also a closed relationship with architecture and architecture space form. A relationship that became even more pronounced with the incoming phenomenon of the Industrial Revolution with its standardization and mass production techniques and technologies. Ever since, the majority of architecture spaces that we have been thinking about and eventually building, follow and share Euclidean-orthogonal principles and relationships. However, with the arrival of the 20th and 21st centuries’ Digital Revolutions and their novel representation, visualization and production techniques and technologies, the forms that we think about and manage to produce, have achieved an unprecedented range of freedom, in which both Euclidean and non-Euclidean free forms are considered. This happening opened a pertinent and relevant thinking and discussion on whether humans, in their nature and within a valid freedom of choice, tend to prefer the long settled Euclidean, orthogonal-based architecture spaces, with all the elements that such geometry implies, namely, the presence of angular, sharp edges and vertices, or, on the contrary, they tend to prefer non-Euclidean, curved, rounded architecture spaces. This thesis proposes to address the problem of the preference for form, namely architecture space form, divided in two sub-problems that the literature review helped to identify: aesthetic judgements and approach-avoidance decisions, two judgements that, in turn, may rely in two knowledge ‘databases’: a subjective-based one, build through our life time sensible and rational experiences, and, a more objective-based one, which hides behind our genetic legacy and lays on basic evolutionary defense functions or mechanisms. We will approach this thesis Problem and Research Question, through (i) a free discourse on historic key events that, through our evolutionary stages, may have contributed to the fact that we have been closer to some elements, namely forms and architecture form, with certain geometric characteristics, over others; (ii) the evolution of aesthetics and our basic evolutionary defense functions or mechanisms, through qualitative and quantitative research methodologies, (iii) state-of-the-art review on the topic of preference for elements with distinct geometric characteristics, and (iv) our own developed experimental user study on abstract architecture spaces with distinct geometric characteristics at the contour level, which, based on the thesis two sub-problems, tried to validate our raised hypotheses. The results of this thesis suggest that humans prefer abstract architecture spaces with curved, rounded elements, rather than those equipped with angular, sharp ones. On the other hand, they were inconclusive on whether we prefer Euclidean-orthogonal or full non-Euclidean abstract architecture spaces, possibly due to familiarity (“mere-exposure”) and ‘strangeness’ effects. These results validate and partial validate hypotheses ‘H1’ and ‘H2’, respectively, the two major hypotheses of this thesis.Desde pelo menos o período grego clássico que o pensamento das civilizações ocidentais têm partilhado uma relação estreita com princípios Euclidianos, algo que tem influenciado e caracterizado este pensamento, orientando-o para uma forma específica de raciocínio e identidade. Por sua vez, enquanto expressões da mente, as formas que temos vindo a pensar e a trazer para a realidade material têm seguido estes mesmos princípios Euclidianos. Enquanto extensão do pensamento, o mesmo se tem aplicado à arquitetura, nomeadamente à sua forma. Esta relação tornou-se ainda mais pronunciada com a chegada do fenómeno da Revolução Industrial e as suas técnicas e tecnologias de estandardização e produção em série. Desde então, a maioria dos espaços de arquitetura que temos pensado e construído seguem e partilham princípios e relações ortogonais-Euclidianos. No entanto, com a entrada em cena das revoluções digitais dos séculos XX e XXI e as suas inovadoras técnicas e tecnologias de representação, visualização e produção, as formas que temos vindo a pensar e a conseguir produzir, atingiram um grau de liberdade sem precedentes, no qual entram em consideração tanto as formas Euclidianas como não-Euclidianas. Este acontecimento abriu uma discussão pertinente e relevante sobre se, na eventualidade de uma válida liberdade de escolha, os humanos efetivamente preferem os, tão presentes e enraizados, espaços de arquitetura ortogonais-Euclidianos, com todos os elementos que esta geometria implica, nomeadamente, a presença de arestas e vértices angulares e afiados, ou, pelo contrário, preferem espaços de arquitetura não-Euclidianos, com elementos curvos e arredondados. Esta tese de doutoramento propõe, neste sentido, abordar o problema da preferência pela forma, nomeadamente, pela forma dos espaços de arquitetura, dividido pelos dois sub-problemas que a revisão bibliográfica ajudou a identificar: Julgamentos estéticos e decisões de aproximação ou afastamento, dois julgamentos que, por sua vez, podem estar baseados em duas ‘bases de dados’ de conhecimento: uma subjetiva, construída ao longo das nossas experiências sensíveis e racionais, e, uma mais objetiva, que se esconde atrás do nosso legado genético e assenta em funções ou mecanismos básicos de defesa evolutiva. O Problema e a Pergunta de Investigação desta tese serão abordados através de (i) um discurso livre sobre eventos históricos chave que, ao longo da nossa evolução, possam ter contribuído para o facto de podermos ter mantido um maior grau de aproximação em relação a determinados elementos, nomeadamente, formas e a forma da arquitetura, com determinadas características geométricas, sobre outros; (ii) a evolução do estudo da estética e as nossas funções ou mecanismos básicos de defesa evolutiva, através metodologias de investigação qualitativa e quantitativa, (iii) a revisão do estado-da-arte sobre a preferência de elementos com características geométricas distintas e (iv) o desenvolvimento de um estudo experimental sobre espaços abstratos de arquitetura com características geométricas distintas ao nível do contorno, que, baseado nos dois sub-problemas desta tese, procurou validar as hipóteses de estudo levantadas. Os resultados desta tese sugerem que os humanos preferem espaços abstratos de arquitetura com elementos curvos e arredondados em relação àqueles dotados de elementos angulares e afiados. Por outro lado, foram inconclusivos quanto ao facto de podermos preferir espaços de arquitetura Euclidianos-ortogonais àqueles puramente não-Euclidianos. Estes resultados validam e validam parcialmente as hipóteses H1 e H2, respetivamente, as duas hipóteses principais desta tese de doutoramento