A Unifying Framework and Comparison of Algorithms for Non-negative Matrix Factorisation

Non-negative matrix factorisation (NMF) is an increasingly popular unsupervised learning method. However, parameter estimation in the NMF model is a difficult high-dimensional optimisation problem. We consider algorithms of the alternating least squares type. Solutions to the least squares problem fall in two categories. The first category is iterative algorithms, which include algorithms such as the majorise–minimise (MM) algorithm, coordinate descent, gradient descent and the Févotte-Cemgil expectation–maximisation (FC-EM) algorithm. We introduce a new family of iterative updates based on a generalisation of the FC-EM algorithm. The coordinate descent, gradient descent and FC-EM algorithms are special cases of this new EM family of iterative procedures. Curiously, we show that the MM algorithm is never a member of our general EM algorithm. The second category is based on cone projection. We describe and prove a cone projection algorithm tailored to the non-negative least square problem. We compare the algorithms on a test case and on the problem of identifying mutational signatures in human cancer. We generally find that cone projection is an attractive choice. Furthermore, in the cancer application, we find that a mix-and-match strategy performs better than running each algorithm in isolation.     

Banks’ interconnections and peer effects: Evidence from Chile

In this paper, we identify and quantify the importance of endogenous peer effects in the interbank market, allowing for varying degrees of intensity of these peer effects. We base our analysis on a unique dataset that includes all interbank loans that have taken place between 15 banks in the Chilean interbank market representing more than 95% of the market between 2009 and 2016. This approach contrasts sharply with the geographical definition of peers used by most of the literature. As an application of our model, we examine an episode of liquidity shortage experienced by one Chilean bank in the interbank market, with the lenses of our model. We show evidence consistent with a herding behavior of the lender banks which, according to our model, were peers of the stressed bank.     

河南物流业产业波及效果现状分析

针对河南省物流业产业波及效果动态分析,可以探求物流业同国民经济体系中相关产业的技术经济联系,进而找出物流业发展的一般规律,认清物流业同其他产业的关联度,这对产业结构优化和产业政策的制定是非常重要的。     

Towns and rural industrialisation in Sweden 1850–1890: A spatial statistical approach

Abstract

Using a spatial statistical analysis we study the relation between rural industrial employment and distance to towns and access to communications in nineteenth century Sweden. Our results show that rural parishes with access to communications had a higher proportion of rural industrial workers than parishes without. In a region with few towns, the south-east of Sweden, parishes close to large towns had a higher proportion of industrial employees than distant parishes in 1850, while no significant correlation was observed in 1890. In a region with a relatively dense urban system, Mälardalen, only in 1890 did parishes close to large towns show a higher proportion of rural industrial workers than did more distant parishes. However, the mean positive effect was negligible beyond 10 km. Thus, in the second half of the nineteenth century the immediate urban hinterland was industrialising prior to large scale urbanisation and urban industrialisation.     

铁路大型客运站地区城市交通衔接组织研究

以北京站、北京南站为代表分析我国铁路大型客运站地区城市交通衔接的发展，借鉴国外柏林中央车站、巴黎拉德芳斯换乘枢纽设计经验，提出应以我国铁路大型客运站新建、改扩建为契机深化城市交通一体化工作。在我国的客运站设计中应增强信息引导、出入站口开设、站区交通规划、公共交通衔接、以及慢行交通的接入。     

Diversity of preferences in an unpredictable environment

The origin of preferences was viewed as related to the dominant eigenvalue of a Leslie matrix modelling reproductive strategies. In a variable environment, however, the coexistence of varying preferences no longer requires optimality, but is identified with the mathematical property of viability: a state of the population is viable if there exists at least one solution starting from it and remaining in the set of constraints until a given time horizon (or forever).The coexistence kernel of two competitors with varying preferences is computed for the case of scalar and 2 × 2 Leslie matrices, with either measurable or differentiable preferences. The homologue of indifference curves is the regulation map, the correspondence associating the set of viable preferences to a given state of the population.Among these viable trajectories, some are also optimal in the sense of dominance discounted in time. These viable optimal solutions are obtained as specific trajectories in an auxiliary dynamic system, and the associated maximal values constitute one boundary of the viability kernel of this auxiliary system (theorem). Hence, the perpetuation of varying preferences allows the diversity of economic preferences, as shown here using the example of the comparative history of fertility from mid-nineteenth century to nowadays in France and England.     

定量包装商品净含量检验的必要性

随着我国市场经济的发展,定量包装商品的数量和种类也在迅速增加,因定量包装商品与广大人民群众的生活息息相关,所以对定量包装商品净含量的检验是十分必要的。     

Rejuvenating wood carving industry in Taiwan Sanyi： A perspective of strategic management

This research aimed at providing suggestions to rejuvenate the wood carving industry in Taiwan Sanyi. The authors conducted interviews with representative store keepers and sculptors to gain industrial insights, and applied the strategic matrix analysis developed by Dr. Seetoo to examine industrial conditions and formulate strategic suggestions for wood carving companies. The industry was found lack of market orientation, which was considered as the critical factor of the long term depression. However, a market of tourism for nostalgic and cultural experience started developing in the near area, providing opportunities for Sanyi wood carving industry to recover. The main suggestions the authors made are （1） restructuring the product scope to respond to the market, and （2） branding with resorts in near area.     

Interpolation of Air Quality Measures in Hedonic House Price Models: Spatial Aspects

Abstract

This paper investigates the sensitivity of hedonic models of house prices to the spatial interpolation of measures of air quality. We consider three aspects of this question: the interpolation technique used, the inclusion of air quality as a continuous vs discrete variable in the model, and the estimation method. Using a sample of 115,732 individual house sales for 1999 in the South Coast Air Quality Management District of Southern California, we compare Thiessen polygons, inverse distance weighting, Kriging and splines to carry out spatial interpolation of point measures of ozone obtained at 27 air quality monitoring stations to the locations of the houses. We take a spatial econometric perspective and employ both maximum-likelihood and general method of moments techniques in the estimation of the hedonic. A high degree of residual spatial autocorrelation warrants the inclusion of a spatially lagged dependent variable in the regression model. We find significant differences across interpolators in the coefficients of ozone, as well as in the estimates of willingness to pay. Overall, the Kriging technique provides the best results in terms of estimates (signs), model fit and interpretation. There is some indication that the use of a categorical measure for ozone is superior to a continuous one.

RÉSUMÉ

Interpolation des Mesures de la Qualité de l'Air dans les Modèles Hédoniste de l'Estimation Immobilière: Aspects Spatiaux

Cet article examine la sensibilité de l’évaluation hédoniste des prix de l'immobilier à l'interpolation spatiale des mesures de la qualité de l'air. Nous avons envisagé la question sous trois aspects: la technique d'interpolation utilisée, l'introduction de la qualité de l'air comme variable continue ou discrète dans le modèle et la méthode d'estimation. Nous avons utilisé un échantillon de 115 732 ventes de maisons individuelles, en 1999, dans le district Côte Sud de la gestion de la Qualité de l'Air en Californie du Sud. Nous avons comparé les polygônes de Thiessen, la pondération inversement proportionnelle à la distance, le krigeage et les courbes splines pour mener l'interpolation des mesures ponctuelles de l'ozone, obtenues dans 27 stations de suivi de la qualité de l'air en fonction des lieux où étaient situées les maisons. Nous avons pris une perspective spatiale économétrique et employé aussi bien la probabilité maximale que la méthode générale des moments techniques dans l’évaluation de l'hédonique. Un degré élevé d'auto corrélation spatiale résiduelle garantie l'inclusion d'une variable dépendante spatialement décalée dans le modèle de régression. Nous avons trouvé des différences importantes parmi les interpolateurs dans les coefficients d'ozone, ainsi que parmi les indicateurs de la volonté de payer. Surtout, la technique de krigeage donne les meilleurs résultats pour les estimations (signes), l'ajustement du modèle et l'interprétation. L'utilisation d'une mesure nominale pour l'ozone est supérieure à une mesure continue, semble-t-il.

RESUMEN

Interpolación de las medidas de la calidad del aire en los modelos de los precios hedónicos de la vivienda: aspectos espaciales

En este ensayo investigamos la sensibilidad de los modelos de lo precios hedónicos de la vivienda para la interpolación espacial de medidas de la calidad del aire. Tenemos en cuenta tres aspectos al respecto: la técnica de interpolación utilizada, la inclusión de la calidad del aire como variable continua, en vez de discreta, en el modelo, y el método de cálculo. Con una muestra de 115.732 ventas de viviendas individuales durante 1999 en el Distrito de Gestión de Calidad del Aire de la Costa Sur en California, comparamos los polígonos de Thiessen, la ponderación de la distancia inversa, métodos geoestadísticos o Kriging y métodos basados en splines para llevar a cabo la interpolación espacial de las mediciones puntuales de ozono obtenidas en 27 estaciones de control de calidad del aire en los lugares donde están situadas las viviendas. Desde la perspectiva econométrica espacial empleamos las técnicas de la probabilidad máxima del método general de momentos en el cálculo de precios hedónicos. Debido a un alto grado de autocorrelación espacial residual debemos incluir una variable dependiente espacialmente rezagada en el modelo de regresión. Se observan diferencias importantes entre los interpoladores en los coeficientes del ozono y en los cálculos de la disposición a pagar. En general, la técnica Kriging da los mejores resultados en cuanto a los cálculos (señales), la idoneidad del modelo y la interpretación. Hay indicios de que es mejor usar una medida categórica para el ozono en vez de una continua.