An EM-Based Piecewise Linear Regression Algorithm

Nusser, Sebastian; Otte, Clemens; Hauptmann, Werner

doi:10.1007/978-3-540-87656-4_58

Cited by 2 publications

(5 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…trends in natural phenomena in medical or biomedical fields of research) and not used for predictions. Second, in common piecewise regression approaches, it is only the information about the input space that is used for partitioning the data (identifying the split points) (Nusser et al, 2008). Nusser et al (2008) for the first time, did the partitioning using the target variable.…”

Section: Related Workmentioning

confidence: 99%

“…Second, in common piecewise regression approaches, it is only the information about the input space that is used for partitioning the data (identifying the split points) (Nusser et al, 2008). Nusser et al (2008) for the first time, did the partitioning using the target variable. The authors in that paper suggest that ignoring the target variable and clustering the input data for partitioning the space is an insufficient strategy in two cases: (a) "where the data points cannot be distinguished within the input space"; (b) in regions of high data density in real-world application problems.…”

Section: Related Workmentioning

confidence: 99%

“…In this paper, we incorporate the information about the target variable into the process of split (break) point identification in piecewise linear regression modeling and then use the PLR for longterm forecasting of time series. An important factor in many fields of application where transparency and understandability are highly required in order to evaluate the proposed solutions by the experts of that field is the interpretability of the solution (Nusser et al, 2008). Using moving average, our proposed solution is very easy to be understood and interpreted by the experts of other fields where little mathematical knowledge is required.…”

Section: Related Workmentioning

confidence: 99%

See 2 more Smart Citations

Comparative Analysis of Three Techniques for Predictions in Time Series Having Repetitive Patterns

Niknafs¹,

Sun²,

Richter

et al. 2011

Proceedings of the 13th International Conference on Enterprise Information Systems

View full text Add to dashboard Cite

Modelling nonlinear patterns is possible through using regression (curve fitting) methods. However, they can be modelled by linear regression (LR) methods, too. This kind of modelling is usually used to depict and study trends and it is not used for prediction purposes. Our goal is to study the applicability and accuracy of piecewise linear regression in predicting a target variable in different time spans (where a pattern is being repeated). Using moving average, we identified the split points and then tested our approach on a real world case study. The dataset of the amount of recycling material in Blue Carts in Calgary (including more than 31,000 records) was taken as a case study for evaluating the performance of the proposed approach. Root mean square error (RMSE) and Spearman rho were used to evaluate and prove the applicability of this prediction approach and evaluate its performance. A comparison between the performances of Support Vector Machine (SVM), Neural Networks (NN), and the proposed LR-based prediction approach is also presented. The results show that the proposed approach works very well for such prediction purposes. It outperforms SVM and is a powerful competitor for NN.

show abstract

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Comparative Analysis of Three Techniques for Predictions in Time Series Having Repetitive Patterns

Niknafs¹,

Sun²,

Richter

et al. 2011

Proceedings of the 13th International Conference on Enterprise Information Systems

View full text Add to dashboard Cite

show abstract

“…To attain high prediction performance with interpretability, previous works have proposed some extensions of linear regression model (e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14]). In stratified regression [1], the data are stratified based on design variables, and at each level, a linear regression model is defined using explanatory variables and response variables.…”

Section: Introductionmentioning

confidence: 99%

“…The gating function, which receives the same input as experts, weights each output of experts, so that we can finally get a single output. Piecewise Linear Regression Model (e.g., [9,10]) is also an extension of linear regression model. It divides the input space, and has different linear regression model in each subspace.…”

Section: Introductionmentioning

confidence: 99%

Cluster’s Number Free Bayes Prediction of General Framework on Mixture of Regression Models

et al. 2021

View full text Add to dashboard Cite

Prediction based on a single linear regression model is one of the most common way in various field of studies. It enables us to understand the structure of data, but might not be suitable to express the data whose structure is complex. To express the structure of data more accurately, we make assumption that the data can be divided in clusters, and has a linear regression model in each cluster. In this case, we can assume that each explanatory variable has their own role; explaining the assignment to the clusters, explaining the regression to the target variable, or being both of them. Introducing probabilistic structure to the data generating process, we derive the optimal prediction under Bayes criterion and the algorithm which calculates it sub-optimally with variational inference method. One of the advantages of our algorithm is that it automatically weights the probabilities of being each number of clusters in the process of the algorithm, therefore it solves the concern about selection of the number of clusters. Some experiments are performed on both synthetic and real data to demonstrate the above advantages and to discover some behaviors and tendencies of the algorithm.

show abstract

An EM-Based Piecewise Linear Regression Algorithm

Cited by 2 publications

References 4 publications

Comparative Analysis of Three Techniques for Predictions in Time Series Having Repetitive Patterns

Comparative Analysis of Three Techniques for Predictions in Time Series Having Repetitive Patterns

Cluster’s Number Free Bayes Prediction of General Framework on Mixture of Regression Models

Contact Info

Product

Resources

About