# smoteRegress: SMOTE algorithm for imbalanced regression problems In UBL: An Implementation of Re-Sampling Approaches to Utility-Based Learning for Both Classification and Regression Tasks

## Description

This function handles imbalanced regression problems using the SMOTE method. Namely, it can generate a new "SMOTEd" data set that addresses the problem of imbalanced domains.

## Usage

 ```1 2``` ```SmoteRegress(form, dat, rel = "auto", thr.rel = 0.5, C.perc = "balance", k = 5, repl = FALSE, dist = "Euclidean", p = 2) ```

## Arguments

 `form` A formula describing the prediction problem `dat` A data frame containing the original (unbalanced) data set `rel` The relevance function which can be automatically ("auto") determined (the default) or may be provided by the user through a matrix. `thr.rel` A number indicating the relevance threshold above which a case is considered as belonging to the rare "class". `C.perc` A list containing the percentage(s) of under- or/and over-sampling to apply to each "class" (bump) obtained with the threshold. The percentages should be provided in ascending order of target variable value. The percentages are applied in this order to the "classes" (bumps) obtained through the threshold. The over-sampling percentage, a number above 1, means that the examples in that bump are increased by this percentage. The under-sampling percentage, a number below 1, means that the cases in the corresponding bump are under-sampled by this percentage. If the number 1 is provided then those examples are not changed. Alternatively it may be "balance" (the default) or "extreme", cases where the sampling percentages are automatically estimated. `k` A number indicating the number of nearest neighbors to consider as the pool from where the new generated examples are generated. `repl` A boolean value controlling the possibility of having repetition of examples when performing under-sampling by selecting among the "normal" examples. `dist` A character string indicating which distance metric to use when determining the k nearest neighbors. See the details. Defaults to "Euclidean". `p` A number indicating the value of p if the "p-norm" distance is chosen. Only necessary to define if a "p-norm" is chosen in the `dist` argument. see details.

## Details

`dist` parameter:

The parameter `dist` allows the user to define the distance metric to be used in the neighbors computation. Although the default is the Euclidean distance, other metrics are available. This allows the computation of distances in data sets with, for instance, both nominal and numeric features. The options available for the distance functions are as follows:

- for data with only numeric features: "Manhattan", "Euclidean", "Canberra", "Chebyshev", "p-norm";

- for data with only nominal features: "Overlap";

- for dealing with both nominal and numeric features: "HEOM".

When the "p-norm" is selected for the `dist` parameter, it is also necessary to define the value of parameter `p`. The value of parameter `p` sets which "p-norm" will be used. For instance, if `p` is set to 1, the "1-norm" (or Manhattan distance) is used, and if `p` is set to 2, the "2-norm" (or Euclidean distance) is applied. For more details regarding the distance functions implemented in UBL package please see the package vignettes.

SmoteR algorithm:

Imbalanced domains cause problems to many learning algorithms. These problems are characterized by the uneven proportion of cases that are available for certain ranges of the target variable which are the most important to the user.

SMOTE (Chawla et. al. 2002) is a well-known algorithm for classification tasks to fight this problem. The general idea of this method is to artificially generate new examples of the minority class using the nearest neighbors of these cases. Furthermore, the majority class examples are also under-sampled, leading to a more balanced data set. SmoteR is a variant of SMOTE algorithm proposed by Torgo et al. (2013) to address the problem of imbalanced domains in regression tasks. This function uses the parameters `rel` and `thr.rel`, a relevance function and a relevance threshold for distinguishing between the normal and rare cases.

The parameter `C.perc` controls the amount of over-sampling and under-sampling applied and can be automatically estimated either to balance or invert the distribution of examples across the different bumps. The parameter `k` controls the number of neighbors used to generate new synthetic examples.

## Value

The function returns a data frame with the new data set resulting from the application of the smoteR algorithm.

## Author(s)

Paula Branco [email protected], Rita Ribeiro [email protected] and Luis Torgo [email protected]

## References

Chawla, N. V., Bowyer, K. W., Hall, L. O., and Kegelmeyer, W. P. (2002). Smote: Synthetic minority over-sampling technique. Journal of Artificial Intelligence Research, 16:321-357.

Torgo, Luis and Ribeiro, Rita P and Pfahringer, Bernhard and Branco, Paula (2013). SMOTE for Regression. Progress in Artificial Intelligence, Springer,378-389.

`RandUnderRegress, RandOverRegress`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ``` ir <- iris[-c(95:130), ] mysmote1.iris <- SmoteRegress(Sepal.Width~., ir, dist = "HEOM", C.perc=list(0.5,2.5)) mysmote2.iris <- SmoteRegress(Sepal.Width~., ir, dist = "HEOM", C.perc = list(0.2, 4), thr.rel = 0.8) smoteBalan.iris <- SmoteRegress(Sepal.Width~., ir, dist = "HEOM", C.perc = "balance") smoteExtre.iris <- SmoteRegress(Sepal.Width~., ir, dist = "HEOM", C.perc = "extreme") # checking visually the results plot(sort(ir\$Sepal.Width)) plot(sort(smoteExtre.iris\$Sepal.Width)) # using a relevance function provided by the user rel <- matrix(0, ncol = 3, nrow = 0) rel <- rbind(rel, c(2, 1, 0)) rel <- rbind(rel, c(3, 0, 0)) rel <- rbind(rel, c(4, 1, 0)) sP.ir <- SmoteRegress(Sepal.Width~., ir, rel = rel, dist = "HEOM", C.perc = list(4, 0.5, 4)) ```