820 resultados para Lanczos, Linear systems, Generalized cross validation
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Recommendation systems aim to help users make decisions more efficiently. The most widely used method in recommendation systems is collaborative filtering, of which, a critical step is to analyze a user's preferences and make recommendations of products or services based on similarity analysis with other users' ratings. However, collaborative filtering is less usable for recommendation facing the "cold start" problem, i.e. few comments being given to products or services. To tackle this problem, we propose an improved method that combines collaborative filtering and data classification. We use hotel recommendation data to test the proposed method. The accuracy of the recommendation is determined by the rankings. Evaluations regarding the accuracies of Top-3 and Top-10 recommendation lists using the 10-fold cross-validation method and ROC curves are conducted. The results show that the Top-3 hotel recommendation list proposed by the combined method has the superiority of the recommendation performance than the Top-10 list under the cold start condition in most of the times.
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Ce mémoire s’intéresse à l’étude du critère de validation croisée pour le choix des modèles relatifs aux petits domaines. L’étude est limitée aux modèles de petits domaines au niveau des unités. Le modèle de base des petits domaines est introduit par Battese, Harter et Fuller en 1988. C’est un modèle de régression linéaire mixte avec une ordonnée à l’origine aléatoire. Il se compose d’un certain nombre de paramètres : le paramètre β de la partie fixe, la composante aléatoire et les variances relatives à l’erreur résiduelle. Le modèle de Battese et al. est utilisé pour prédire, lors d’une enquête, la moyenne d’une variable d’intérêt y dans chaque petit domaine en utilisant une variable auxiliaire administrative x connue sur toute la population. La méthode d’estimation consiste à utiliser une distribution normale, pour modéliser la composante résiduelle du modèle. La considération d’une dépendance résiduelle générale, c’est-à-dire autre que la loi normale donne une méthodologie plus flexible. Cette généralisation conduit à une nouvelle classe de modèles échangeables. En effet, la généralisation se situe au niveau de la modélisation de la dépendance résiduelle qui peut être soit normale (c’est le cas du modèle de Battese et al.) ou non-normale. L’objectif est de déterminer les paramètres propres aux petits domaines avec le plus de précision possible. Cet enjeu est lié au choix de la bonne dépendance résiduelle à utiliser dans le modèle. Le critère de validation croisée sera étudié à cet effet.
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This study focuses on multiple linear regression models relating six climate indices (temperature humidity THI, environmental stress ESI, equivalent temperature index ETI, heat load HLI, modified HLI (HLI new), and respiratory rate predictor RRP) with three main components of cow’s milk (yield, fat, and protein) for cows in Iran. The least absolute shrinkage selection operator (LASSO) and the Akaike information criterion (AIC) techniques are applied to select the best model for milk predictands with the smallest number of climate predictors. Uncertainty estimation is employed by applying bootstrapping through resampling. Cross validation is used to avoid over-fitting. Climatic parameters are calculated from the NASA-MERRA global atmospheric reanalysis. Milk data for the months from April to September, 2002 to 2010 are used. The best linear regression models are found in spring between milk yield as the predictand and THI, ESI, ETI, HLI, and RRP as predictors with p-value < 0.001 and R2 (0.50, 0.49) respectively. In summer, milk yield with independent variables of THI, ETI, and ESI show the highest relation (p-value < 0.001) with R2 (0.69). For fat and protein the results are only marginal. This method is suggested for the impact studies of climate variability/change on agriculture and food science fields when short-time series or data with large uncertainty are available.
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Las organizaciones y sus entornos son sistemas complejos. Tales sistemas son difíciles de comprender y predecir. Pese a ello, la predicción es una tarea fundamental para la gestión empresarial y para la toma de decisiones que implica siempre un riesgo. Los métodos clásicos de predicción (entre los cuales están: la regresión lineal, la Autoregresive Moving Average y el exponential smoothing) establecen supuestos como la linealidad, la estabilidad para ser matemática y computacionalmente tratables. Por diferentes medios, sin embargo, se han demostrado las limitaciones de tales métodos. Pues bien, en las últimas décadas nuevos métodos de predicción han surgido con el fin de abarcar la complejidad de los sistemas organizacionales y sus entornos, antes que evitarla. Entre ellos, los más promisorios son los métodos de predicción bio-inspirados (ej. redes neuronales, algoritmos genéticos /evolutivos y sistemas inmunes artificiales). Este artículo pretende establecer un estado situacional de las aplicaciones actuales y potenciales de los métodos bio-inspirados de predicción en la administración.
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Peer to peer systems have been widely used in the internet. However, most of the peer to peer information systems are still missing some of the important features, for example cross-language IR (Information Retrieval) and collection selection / fusion features. Cross-language IR is the state-of-art research area in IR research community. It has not been used in any real world IR systems yet. Cross-language IR has the ability to issue a query in one language and receive documents in other languages. In typical peer to peer environment, users are from multiple countries. Their collections are definitely in multiple languages. Cross-language IR can help users to find documents more easily. E.g. many Chinese researchers will search research papers in both Chinese and English. With Cross-language IR, they can do one query in Chinese and get documents in two languages. The Out Of Vocabulary (OOV) problem is one of the key research areas in crosslanguage information retrieval. In recent years, web mining was shown to be one of the effective approaches to solving this problem. However, how to extract Multiword Lexical Units (MLUs) from the web content and how to select the correct translations from the extracted candidate MLUs are still two difficult problems in web mining based automated translation approaches. Discovering resource descriptions and merging results obtained from remote search engines are two key issues in distributed information retrieval studies. In uncooperative environments, query-based sampling and normalized-score based merging strategies are well-known approaches to solve such problems. However, such approaches only consider the content of the remote database but do not consider the retrieval performance of the remote search engine. This thesis presents research on building a peer to peer IR system with crosslanguage IR and advance collection profiling technique for fusion features. Particularly, this thesis first presents a new Chinese term measurement and new Chinese MLU extraction process that works well on small corpora. An approach to selection of MLUs in a more accurate manner is also presented. After that, this thesis proposes a collection profiling strategy which can discover not only collection content but also retrieval performance of the remote search engine. Based on collection profiling, a web-based query classification method and two collection fusion approaches are developed and presented in this thesis. Our experiments show that the proposed strategies are effective in merging results in uncooperative peer to peer environments. Here, an uncooperative environment is defined as each peer in the system is autonomous. Peer like to share documents but they do not share collection statistics. This environment is a typical peer to peer IR environment. Finally, all those approaches are grouped together to build up a secure peer to peer multilingual IR system that cooperates through X.509 and email system.
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The selection criteria for contractor pre-qualification are characterized by the co-existence of both quantitative and qualitative data. The qualitative data is non-linear, uncertain and imprecise. An ideal decision support system for contractor pre-qualification should have the ability of handling both quantitative and qualitative data, and of mapping the complicated nonlinear relationship of the selection criteria, such that rational and consistent decisions can be made. In this research paper, an artificial neural network model was developed to assist public clients identifying suitable contractors for tendering. The pre-qualification criteria (variables) were identified for the model. One hundred and twelve real pre-qualification cases were collected from civil engineering projects in Hong Kong, and eighty-eight hypothetical pre-qualification cases were also generated according to the “If-then” rules used by professionals in the pre-qualification process. The results of the analysis totally comply with current practice (public developers in Hong Kong). Each pre-qualification case consisted of input ratings for candidate contractors’ attributes and their corresponding pre-qualification decisions. The training of the neural network model was accomplished by using the developed program, in which a conjugate gradient descent algorithm was incorporated for improving the learning performance of the network. Cross-validation was applied to estimate the generalization errors based on the “re-sampling” of training pairs. The case studies show that the artificial neural network model is suitable for mapping the complicated nonlinear relationship between contractors’ attributes and their corresponding pre-qualification (disqualification) decisions. The artificial neural network model can be concluded as an ideal alternative for performing the contractor pre-qualification task.
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Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.
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Background The majority of peptide bonds in proteins are found to occur in the trans conformation. However, for proline residues, a considerable fraction of Prolyl peptide bonds adopt the cis form. Proline cis/trans isomerization is known to play a critical role in protein folding, splicing, cell signaling and transmembrane active transport. Accurate prediction of proline cis/trans isomerization in proteins would have many important applications towards the understanding of protein structure and function. Results In this paper, we propose a new approach to predict the proline cis/trans isomerization in proteins using support vector machine (SVM). The preliminary results indicated that using Radial Basis Function (RBF) kernels could lead to better prediction performance than that of polynomial and linear kernel functions. We used single sequence information of different local window sizes, amino acid compositions of different local sequences, multiple sequence alignment obtained from PSI-BLAST and the secondary structure information predicted by PSIPRED. We explored these different sequence encoding schemes in order to investigate their effects on the prediction performance. The training and testing of this approach was performed on a newly enlarged dataset of 2424 non-homologous proteins determined by X-Ray diffraction method using 5-fold cross-validation. Selecting the window size 11 provided the best performance for determining the proline cis/trans isomerization based on the single amino acid sequence. It was found that using multiple sequence alignments in the form of PSI-BLAST profiles could significantly improve the prediction performance, the prediction accuracy increased from 62.8% with single sequence to 69.8% and Matthews Correlation Coefficient (MCC) improved from 0.26 with single local sequence to 0.40. Furthermore, if coupled with the predicted secondary structure information by PSIPRED, our method yielded a prediction accuracy of 71.5% and MCC of 0.43, 9% and 0.17 higher than the accuracy achieved based on the singe sequence information, respectively. Conclusion A new method has been developed to predict the proline cis/trans isomerization in proteins based on support vector machine, which used the single amino acid sequence with different local window sizes, the amino acid compositions of local sequence flanking centered proline residues, the position-specific scoring matrices (PSSMs) extracted by PSI-BLAST and the predicted secondary structures generated by PSIPRED. The successful application of SVM approach in this study reinforced that SVM is a powerful tool in predicting proline cis/trans isomerization in proteins and biological sequence analysis.
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The majority of distribution utilities do not have accurate information on the constituents of their loads. This information is very useful in managing and planning the network, adequately and economically. Customer loads are normally categorized in three main sectors: 1) residential; 2) industrial; and 3) commercial. In this paper, penalized least-squares regression and Euclidean distance methods are developed for this application to identify and quantify the makeup of a feeder load with unknown sectors/subsectors. This process is done on a monthly basis to account for seasonal and other load changes. The error between the actual and estimated load profiles are used as a benchmark of accuracy. This approach has shown to be accurate in identifying customer types in unknown load profiles, and is used in cross-validation of the results and initial assumptions.
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Body composition of 292 males aged between 18 and 65 years was measured using the deuterium oxide dilution technique. Participants were divided into development (n=146) and cross-validation (n=146) groups. Stature, body weight, skinfold thickness at eight sites, girth at five sites, and bone breadth at four sites were measured and body mass index (BMI), waist-to-hip ratio (WHR), and waist-to-stature ratio (WSR) calculated. Equations were developed using multiple regression analyses with skinfolds, breadth and girth measures, BMI, and other indices as independent variables and percentage body fat (%BF) determined from deuterium dilution technique as the reference. All equations were then tested in the cross-validation group. Results from the reference method were also compared with existing prediction equations by Durnin and Womersley (1974), Davidson et al (2011), and Gurrici et al (1998). The proposed prediction equations were valid in our cross-validation samples with r=0.77- 0.86, bias 0.2-0.5%, and pure error 2.8-3.6%. The strongest was generated from skinfolds with r=0.83, SEE 3.7%, and AIC 377.2. The Durnin and Womersley (1974) and Davidson et al (2011) equations significantly (p<0.001) underestimated %BF by 1.0 and 6.9% respectively, whereas the Gurrici et al (1998) equation significantly (p<0.001) overestimated %BF by 3.3% in our cross-validation samples compared to the reference. Results suggest that the proposed prediction equations are useful in the estimation of %BF in Indonesian men.
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Spatially-explicit modelling of grassland classes is important to site-specific planning for improving grassland and environmental management over large areas. In this study, a climate-based grassland classification model, the Comprehensive and Sequential Classification System (CSCS) was integrated with spatially interpolated climate data to classify grassland in Gansu province, China. The study area is characterized by complex topographic features imposed by plateaus, high mountains, basins and deserts. To improve the quality of the interpolated climate data and the quality of the spatial classification over this complex topography, three linear regression methods, namely an analytic method based on multiple regression and residues (AMMRR), a modification of the AMMRR method through adding the effect of slope and aspect to the interpolation analysis (M-AMMRR) and a method which replaces the IDW approach for residue interpolation in M-AMMRR with an ordinary kriging approach (I-AMMRR), for interpolating climate variables were evaluated. The interpolation outcomes from the best interpolation method were then used in the CSCS model to classify the grassland in the study area. Climate variables interpolated included the annual cumulative temperature and annual total precipitation. The results indicated that the AMMRR and M-AMMRR methods generated acceptable climate surfaces but the best model fit and cross validation result were achieved by the I-AMMRR method. Twenty-six grassland classes were classified for the study area. The four grassland vegetation classes that covered more than half of the total study area were "cool temperate-arid temperate zonal semi-desert", "cool temperate-humid forest steppe and deciduous broad-leaved forest", "temperate-extra-arid temperate zonal desert", and "frigid per-humid rain tundra and alpine meadow". The vegetation classification map generated in this study provides spatial information on the locations and extents of the different grassland classes. This information can be used to facilitate government agencies' decision-making in land-use planning and environmental management, and for vegetation and biodiversity conservation. The information can also be used to assist land managers in the estimation of safe carrying capacities which will help to prevent overgrazing and land degradation.
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The concentrations of Na, K, Ca, Mg, Ba, Sr, Fe, Al, Mn, Zn, Pb, Cu, Ni, Cr, Co, Se, U and Ti were determined in the osteoderms and/or flesh of estuarine crocodiles (Crocodylus porosus) captured in three adjacent catchments within the Alligator Rivers Region (ARR) of northern Australia. Results from multivariate analysis of variance showed that when all metals were considered simultaneously, catchment effects were significant (P≤0.05). Despite considerable within-catchment variability, linear discriminant analysis (LDA) showed that differences in elemental signatures in the osteoderms and/or flesh of C. porosus amongst the catchments were sufficient to classify individuals accurately to their catchment of occurrence. Using cross-validation, the accuracy of classifying a crocodile to its catchment of occurrence was 76% for osteoderms and 60% for flesh. These data suggest that osteoderms provide better predictive accuracy than flesh for discriminating crocodiles amongst catchments. There was no advantage in combining the osteoderm and flesh results to increase the accuracy of classification (i.e. 67%). Based on the discriminant function coefficients for the osteoderm data, Ca, Co, Mg and U were the most important elements for discriminating amongst the three catchments. For flesh data, Ca, K, Mg, Na, Ni and Pb were the most important metals for discriminating amongst the catchments. Reasons for differences in the elemental signatures of crocodiles between catchments are generally not interpretable, due to limited data on surface water and sediment chemistry of the catchments or chemical composition of dietary items of C. porosus. From a wildlife management perspective, the provenance or source catchment(s) of 'problem' crocodiles captured at settlements or recreational areas along the ARR coastline may be established using catchment-specific elemental signatures. If the incidence of problem crocodiles can be reduced in settled or recreational areas by effective management at their source, then public safety concerns about these predators may be moderated, as well as the cost of their capture and removal. Copyright © 2002 Elsevier Science B.V.
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Existing crowd counting algorithms rely on holistic, local or histogram based features to capture crowd properties. Regression is then employed to estimate the crowd size. Insufficient testing across multiple datasets has made it difficult to compare and contrast different methodologies. This paper presents an evaluation across multiple datasets to compare holistic, local and histogram based methods, and to compare various image features and regression models. A K-fold cross validation protocol is followed to evaluate the performance across five public datasets: UCSD, PETS 2009, Fudan, Mall and Grand Central datasets. Image features are categorised into five types: size, shape, edges, keypoints and textures. The regression models evaluated are: Gaussian process regression (GPR), linear regression, K nearest neighbours (KNN) and neural networks (NN). The results demonstrate that local features outperform equivalent holistic and histogram based features; optimal performance is observed using all image features except for textures; and that GPR outperforms linear, KNN and NN regression
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Stormwater pollution is linked to stream ecosystem degradation. In predicting stormwater pollution, various types of modelling techniques are adopted. The accuracy of predictions provided by these models depends on the data quality, appropriate estimation of model parameters, and the validation undertaken. It is well understood that available water quality datasets in urban areas span only relatively short time scales unlike water quantity data, which limits the applicability of the developed models in engineering and ecological assessment of urban waterways. This paper presents the application of leave-one-out (LOO) and Monte Carlo cross validation (MCCV) procedures in a Monte Carlo framework for the validation and estimation of uncertainty associated with pollutant wash-off when models are developed using a limited dataset. It was found that the application of MCCV is likely to result in a more realistic measure of model coefficients than LOO. Most importantly, MCCV and LOO were found to be effective in model validation when dealing with a small sample size which hinders detailed model validation and can undermine the effectiveness of stormwater quality management strategies.
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Research problem: Overfitting and collinearity problems commonly exist in current construction cost estimation applications and obstruct researchers and practitioners in achieving better modelling results. Research objective and method: A hybrid approach of Akaike information criterion (AIC) stepwise regression and principal component regression (PCR) is proposed to help solve overfitting and collinearity problems. Utilization of this approach in linear regression is validated by comparing it with other commonly used approaches. The mean square error obtained by leave-one-out cross validation (MSELOOCV) is used in model selection in deciding predictive variables.