In this paper we explore different regression models based on Clusterwise Linear Regression (CLR). CLR aims to find the partition of the data into @math clusters, such that linear regressions fitted to each of the clusters minimize overall mean squared error on the whole data. The main obstacle preventing to use found regression models for prediction on the unseen test points is the absence of a reasonable way to obtain CLR cluster labels when the values of target variable are unknown. In this paper we propose two novel approaches on how to solve this problem. The first approach, predictive CLR builds a separate classification model to predict test CLR labels. The second approach, constrained CLR utilizes a set of user-specified constraints that enforce certain points to go to the same clusters. Assuming the constraint values are known for the test points, they can be directly used to assign CLR labels. We evaluate these two approaches on three UCI ML datasets as well as on a large corpus of health insurance claims. We show that both of the proposed algorithms significantly improve over the known CLR-based regression methods. Moreover, predictive CLR consistently outperforms linear regression and random forest, and shows comparable performance to support vector regression on UCI ML datasets. The constrained CLR approach achieves the best performance on the health insurance dataset, while enjoying only @math times increased computational time over linear regression.
applies a modification of CLR @cite_2 to prediction of monthly rainfall in Australia, taking weighted average of different models based on the cluster sizes @cite_15 . However, since the cluster weights do not depend on the features of the new object, the final model is always linear which limits its representational power.
@cite_15 @cite_2
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Abstract This paper develops the Clusterwise Linear Regression (CLR) technique for prediction of monthly rainfall. The CLR is a combination of clustering and regression techniques. It is formulated as an optimization problem and an incremental algorithm is designed to solve it. The algorithm is applied to predict monthly rainfall in Victoria, Australia using rainfall data with five input meteorological variables over the period of 1889–2014 from eight geographically diverse weather stations. The prediction performance of the CLR method is evaluated by comparing observed and predicted rainfall values using four measures of forecast accuracy. The proposed method is also compared with the CLR using the maximum likelihood framework by the expectation-maximization algorithm, multiple linear regression, artificial neural networks and the support vector machines for regression models using computational results. The results demonstrate that the proposed algorithm outperforms other methods in most locations. Heavy precipitation for several days and weeks always leads to some extreme nature disasters. Long-lead term precipitation forecasting plays an important role on the prevision of such calamities. Most works focus on the generation of training labels with allocation of the proper corresponding spatio-temporal information. In this paper, we will provide a different path by performing regression analysis using the precipitation amounts at particular locations. This method is called Hierarchical Clustering based Bayesian Structural Vector Autoregression (HC-BSVAR). The approach for HC-BSVAR is divided into two steps. First, we apply a hierarchical clustering algorithm to identify the Elite locations and then transfer the 3-dimensional data space into a new traditional 2-dimensional data space. Every column of the new data frame is a hydro-meteorological feature of the original data and each row represents a time point (day) in the original space. Secondly, an economic-based multivariate time series model called Bayesian-based Structural Vector Autoregression (BSVAR) is exploited to perform the final prediction result. The prediction quality will be vary for different cut of tree structure which generated by hierarchical clustering. The coefficient for determination of each location by each level of cut is applied to quantize the quality of prediction. The relationship between the cut level of clustering geographic locations and the regression model performance are also discussed, based on the result of prediction quality. Abstract Short-term high-resolution precipitation forecasting has important implications for navigation, flood forecasting, and other hydrological and meteorological concerns. This article introduces a pixel-based algorithm for Short-term Quantitative Precipitation Forecasting (SQPF) using radar-based rainfall data. The proposed algorithm called Pixel- Based Nowcasting (PBN) tracks severe storms with a hierarchical mesh-tracking algorithm to capture storm advection in space and time at high resolution from radar imagers. The extracted advection field is then extended to nowcast the rainfall field in the next 3 hr based on a pixel-based Lagrangian dynamic model. The proposed algorithm is compared with two other nowcasting algorithms (WCN: Watershed-Clustering Nowcasting and PER: PERsistency) for ten thunderstorm events over the conterminous United States. Object-based verification metric and traditional statistics have been used to evaluate the performance of the proposed algorithm. It is shown that the proposed algorithm is superior over comparison algorithms and is effective in tracking and predicting severe storm events for the next few hours. The primary accomplishment of this research has been demonstrating the power of the deconvolution technique developed by Neuman and de Marsily (1976) in dealing with noisy rainfallrunoff records of short duration. Such records are encountered in arid environments where rainfall often occurs in short isolated bursts and the data are measured with a considerable margin of error. Our research work consisted of superimposing known noise on synthetic rainfallrunoff data and examining the ability of the Neuman -de Marsily deconvolution method to estimate the correct impulse response of the system when the data include only a single storm event. Approximately 50 Monte Carlo simulation runs were performed for each of three different noise models considered in our work. The results clearly demonstrated that the deconvolution model leads to reliable estimates and can be used with confidence in the presence of realistic noise levels. In addition to the Monte Carlo simulation tests and their analysis, certain improvements were introduced into the original deconvolution technique. In particular, the original version of the technique required that the hydrologist exercise subjective judgement in choosing the "best" solution for the deconvolution problem from a large number of admissible solutions. Our new method of selecting the "best" result is based on a comparative analysis of residuals and is more reliable than the earlier subjective approach. The improved method has been applied to real as well as synthetic rainfall runoff data.