The Euclidean distance classifier: an alternative to the linear discriminant function

The sample linear discriminant function (LDF) is known to perform poorly when the number of features p is large relative to the size of the training samples, A simple and rarely applied alternative to the sample LDF is the sample Euclidean distance classifier (EDC). Raudys and Pikelis (1980) have compared the sample LDF with three other discriminant functions, including thesample EDC, when classifying individuals from two spherical normal populations. They have concluded that the sample EDC outperforms the sample LDF when p is large relative to the training sample size. This paper derives conditions for which the two classifiers are equivalent when all parameters are known and employs a Monte Carlo simulation to compare the sample EDC with the sample LDF no only for the spherical normal case but also for several nonspherical parameter configurations. Fo many practical situations, the sample EDC performs as well as or superior to the sample LDF, even for nonspherical covariance configurations.     

Minor speech with major significance: re-membering China in David Der-wei Wang's self-reflexive Monster ∗

The paper argues that a project to re-member China lies embedded in The Monster that Is History as Wang examines the monstrous violence which ravages modern China through the lenses of fiction. Through the alchemy of what the author calls ‘diasporic ambivalence’, it finally assumes the form of huawen wenxue, or Sinophone literature. As the project inevitably encounters resistance from the Taiwanese nativist, it falls into an aporia/differend between Sinophone and Taiwanese literature as struggling means to constitute a community formation.     

An information-theoretic approach to incorporating prior information in binomial sampling

The incorporation of prior information about θ, where θ is the success probability in a binomial sampling model, is an essential feature of Bayesian statistics. Methodology based on information-theoretic concepts is introduced which (a) quantifies the amount of information provided by the sample data relative to that provided by the prior distribution and (b) allows for a ranking of prior distributions with respect to conservativeness, where conservatism refers to restraint of extraneous information about θ which is embedded in any prior distribution. In effect, the most conservative prior distribution from a specified class (each member o f which carries the available prior information about θ) is that prior distribution within the class over which the likelihood function has the greatest average domination. The most conservative prior distributions from five different families of prior distributions over the interval (0,1) including the beta distribution are determined and compared for three situations: (1) no prior estimate of θ is available, (2) a prior point estimate or θ is available, and (3) a prior interval estimate of θ is available. The results of the comparisons not only advocate the use of the beta prior distribution in binomial sampling but also indicate which particular one to use in the three aforementioned situations.     

“From that Moment on My Life Changed”: Turning Points in the Healing Process for Men Recovering from Child Sexual Abuse

Recent research indicates that child sexual abuse often undermines the health of boys and men across the lifespan. However, some male survivors experience a turning point marking a positive change in their health trajectories and healing process. Although frequently discussed in reference to physical health problems or addictions, very little is known about turning points with respect to child sexual abuse for men. The purpose of this secondary qualitative analysis was to describe the different types of turning points experienced by male survivors who completed the 2010 Health and Well-Being Survey (N = 250). Using conventional content analysis, researchers identified seven types of turning points that were classified into three broad categories: influential relationships (professional and group support, personal relationships), insights and new meanings (cognitive realizations, necessity to change, spiritual transformation), and action-oriented communication (disclosure of CSA, pursuit of justice). Implications for clinical practice and future research are discussed.     

Household experience of gambling-related harm by socio-economic deprivation in New Zealand: increases in inequality between 2008 and 2012

Although problem gamblers make up a small proportion of the New Zealand population, those who are living in more deprived areas at higher risk of harm from their own or someone else's gambling. The global financial crisis in 2008 has been linked with changes in gambling behaviour and with increases in inequality between areas of relative deprivation. Nationally representative datasets from in-home face-to-face health surveys in 2008, 2010 and 2012 were analysed to investigate changes in gambling behaviour, experiences of household-level harm related to gambling, and the association with economic deprivation. Although overall gambling participation had dropped, the experience of gambling harm at the household level was significantly higher in 2012 compared with 2008 and 2010. The increase in harm was experienced disproportionately by those in more deprived areas, who were 4.5 times as likely to experience gambling-related arguments or money problems. We consider possible explanations including more harmful gambling behaviour as a response to financial stresses, decreasing household resilience to financial stresses, and the concentration of more harmful forms of gambling product in more deprived areas. Causes of gambling harm in deprived communities, and the vulnerability of households in these communities, should be addressed if inequalities are to be reduced.     

Efficient Algorithms and Implementations for Optimizing the Sum of Linear Fractional Functions,with Applications

This paper presents an improved algorithm for solving the sum of linear fractional functions (SOLF) problem in 1-D and 2-D. A key subproblem to our solution is the off-line ratio query (OLRQ) problem, which asks to find the optimal values of a sequence of m linear fractional functions (called ratios), each ratio subject to a feasible domain defined by O(n) linear constraints. Based on some geometric properties and the parametric linear programming technique, we develop an algorithm that solves the OLRQ problem in O((m+n)log (m+n)) time. The OLRQ algorithm can be used to speed up every iteration of a known iterative SOLF algorithm, from O(m(m+n)) time to O((m+n)log (m+n)), in 1-D and 2-D. Implementation results of our improved 1-D and 2-D SOLF algorithm have shown that in most cases it outperforms the commonly-used approaches for the SOLF problem. We also apply our techniques to some problems in computational geometry and other areas, improving the previous results.This research was supported in part by the National Science Foundation under Grant CCR-9623585.The research of this author was supported in part by National Science Foundation under grant CCF-0430366.Grant-in-Aid of Ministry of Science, Culture and Education of Japan, No. 10780274.The research of this author was supported in part by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Researchon Priority Areas     

光·影

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Mobile facility location: combinatorial filtering via weighted occupancy

An instance of the mobile facility location problem consists of a complete directed graph \(G = (V, E)\) , in which each arc \((u, v) \in E\) is associated with a numerical attribute \(\mathcal M (u,v)\) , representing the cost of moving any object from \(u\) to \(v\) . An additional ingredient of the input is a collection of servers \(S = \{ s_1, \ldots , s_k \}\) and a set of clients \(C = \{ c_1, \ldots , c_\ell \}\) , which are located at nodes of the underlying graph. With this setting in mind, a movement scheme is a function \(\psi : S \rightarrow V\) that relocates each server \(s_i\) to a new position, \(\psi ( s_i )\) . We refer to \(\mathcal M ( s_i, \psi ( s_i ) )\) as the relocation cost of \(s_i\) , and to \(\min _{i \in [k]} \mathcal M (c_j, \psi ( s_i ) )\) , the cost of assigning client \(c_j\) to the nearest final server location, as the service cost of \(c_j\) . The objective is to compute a movement scheme that minimizes the sum of relocation and service costs. In this paper, we resolve an open question posed by Demaine et al. (SODA ’07) by characterizing the approximability of mobile facility location through LP-based methods. We also develop a more efficient algorithm, which is based on a combinatorial filtering approach. The latter technique is of independent interest, as it may be applicable in other settings as well. In this context, we introduce a weighted version of the occupancy problem, for which we establish interesting tail bounds, not before demonstrating that existing bounds cannot be extended.     

Approximating <Emphasis Type="Italic">k</Emphasis>-generalized connectivity via collapsing HSTs

An instance of the k -generalized connectivity problem consists of an undirected graph G=(V,E), whose edges are associated with non-negative costs, and a collection \({\mathcal{D}}=\{(S_{1},T_{1}),\ldots,(S_{d},T_{d})\}\) of distinct demands, each of which comprises a pair of disjoint vertex sets. We say that a subgraph ??G connects a demand (S _i ,T _i ) when it contains a path with one endpoint in S _i and the other in T _i . Given an integer parameter k, the goal is to identify a minimum cost subgraph that connects at least k demands in \({\mathcal{D}}\).Alon, Awerbuch, Azar, Buchbinder and Naor (SODA ’04) seem to have been the first to consider the generalized connectivity paradigm as a unified machinery for incorporating multiple-choice decisions into network formation settings. Their main contribution in this context was to devise a multiplicative-update online algorithm for computing log-competitive fractional solutions, and to propose provably-good rounding procedures for important special cases. Nevertheless, approximating the generalized connectivity problem in its unconfined form, where one makes no structural assumptions about the underlying graph and collection of demands, has remained an open question up until a recent O(log?² nlog?² d) approximation due to Chekuri, Even, Gupta and Segev (SODA ’08). Unfortunately, the latter result does not extend to connecting a pre-specified number of demands. Furthermore, even the simpler case of singleton demands has been established as a challenging computational task, when Hajiaghayi and Jain (SODA ’06) related its inapproximability to that of dense k -subgraph.In this paper, we present the first non-trivial approximation algorithm for k-generalized connectivity, which is derived by synthesizing several techniques originating in probabilistic embeddings of finite metrics, network design, and randomization. Specifically, our algorithm constructs, with constant probability, a feasible subgraph whose cost is within a factor of O(n ^2/3?polylog(n,k)) of optimal. We believe that the fundamental approach illustrated in the current writing is of independent interest, and may be applicable in other settings as well.