Data stream mining extracts information from large quantities of data flowing fast and continuously (data streams). They are usually affected by changes in the data distribution, giving rise to a phenomenon referred to as concept drift. Thus, learning models must detect and adapt to such changes, so as to exhibit a good predictive performance after a drift has occurred. In this regard, the development of effective drift detection algorithms becomes a key factor in data stream mining. In this work we propose CURIE, a drift detector relying on cellular automata. Specifically, in CURIE the distribution of the data stream is represented in the grid of a cellular automata, whose neighborhood rule can then be utilized to detect possible distribution changes over the stream. Computer simulations are presented and discussed to show that CURIE, when hybridized with other base learners, renders a competitive behavior in terms of detection metrics and classification accuracy. CURIE is compared with well-established drift detectors over synthetic datasets with varying drift characteristics.

The original results are given in O_R_1.xlsx and O_R_2.xlsx, which correspond to the original results for the order functions F1 and F2 respectively. At the beginning of these resources, a complete table compiles the results of the experiments. Each detector is hybridized with the base learners and tested over 20 datasets (10 in O_R_1.xlsx and 10 in O_R_2.xlsx). The whole set of metrics is presented: prequential accuracy (pACC), RAM−Hours, true positives (TP), false positives (FP), true negatives (TN), false negatives(FN), distance to the drift (μD), precision, recall, MCC, and non-detection rate (ND). The ranking of pACC, RAM−Hours, μD , MCC, and ND is provided for every experiment. At the end of the resources, 6 summarizing tables are shown. On the left, the “F global rank” shows the mean rank of detectors, while “F global results” shows the mean and standard deviation of the metrics. On the right, these tables (“F abrupt rank”, “F gradual rank”, “F abrupt results”, and “F gradual results”) detail the mean ranks and metrics for abrupt and gradualdatasets. Finally, the O_R_3.xlsx shows the means results.

All datasets have been uploaded to Harvard Dataverse repository: https://dataverse.harvard.edu/dataset.xhtml?persistentId=doi:10.7910/DVN/5OWRGB.

The scikit-multiflow framework, as one of the most commonly accepted libraries in stream learning, allows generating a wide variety of synthetic data in order to simulate a realistic occurrence of drifts. Here, and in Section 5.1 of the manuscript, the detail of the datasets:

• With "Sine" generator: it is ruled by a sequence of classification functions. "Sine_A" refers to abrupt cases and "SineG" to gradual ones. In the case of "Sine_F1", the order of the functions is SINE1, reversed SINE1, SINE2, and reversed SINE2. For "Sine_F2" the order is namely, reversed SINE2, SINE2, reversed SINE1, and SINE1. Therefore, "Sine" stream generator provides 4 different datasets: Sine_A_F1, Sine_A_F2, Sine_G_F1, and Sine_G_F2. They consist of 2 numerical features without noise, and a balanced binary class.
• With "Random Tree" generator: it is ruled by a sequence of tree random state functions, i.e. the seed for the random generation of trees. We have chosen 4 seeds (9856, 2563, 8873, 7896), and we have altered their order to produce 4 different datasets. "RT_A" refers to abrupt cases and "RT_G" to gradual ones; then theyare: RT_A_F1,RT_A_F2,RT_G_F1, and RT_G_F2. The parameters max_tree_depth, min_leaf_depth, and fraction_leaves_per_level were set to 6, 3, and 0.15 respectively. They consist of 2 numerical features without noise, and balanced binary class.
• With "Mixed" generator: it is ruled by a sequence of classification functions. "Mixed_A" refers to abrupt cases and "Mixed_G" to gradual ones. In the case of "Mixed_F1", the order of the functions is 0-1-0-1. For "Mixed_F2" the order is reversed 1-0-1-0. Therefore, "Mixed" stream generator provides 4 different datasets: Mixed_A_F1, Mixed_A_F2, Mixed_G_F1, and Mixed_G_F2. They consist of 4 numerical features without noise, and a balanced binary class.
• With "Sea" generator: it is ruled by a sequence of classification functions. "Sea_A" refers to abrupt cases and "Sea_G" to gradual ones. In the case of "Sea_F1", the order of the functions is 0-1-2-3. For "Sea_F2" the order is reversed 3-2-1-0. Therefore, "Sea" stream generator provides 4 different datasets: "Sea_A_F1", "Sea_A_F2", "Sea_G_F1",and "Sea_G_F2". They consist of 3 numerical features, a balanced binary class, andwith the probability that noise will happen in the generation of 0.2 (probability range between 0 and 1).
• With "Stagger" generator: it is ruled by a sequence of classification functions. "Stagger_A" refers to abrupt cases and "Stagger_G" to gradual ones. In the case of "Stagger_F1", the order of the functions is 0-1-2-0. For "Stagger_F2" the order is reversed 2-1-0-2. Therefore, "Stagger" stream generator provides 4 different datasets: "Stagger_A_F1", "Stagger_A_F2", "Stagger_G_F1", and "Stagger_G_F2". They consist of 3 numerical features without noise, and a balanced binary class.

All the experiments can be performed with the file "curie_def.py". Here, we can select:

• Datasets and types with the variables "datasets" and "tipos" respectively.
• CURIE parameters: bins_margin,mutation_period,num_mutantneighs_fordetection,preparatory_size,sliding_window_size,radius, and n_bins.
• The path to save results in variable "path_saving_results".
• The path to read the datasets in variable "path".
• The functions order in "functions_order" variable to launch the experiments of F1 or F2 as explained in the paper.
• The variable "curie" for the CURIE detector.
• The variable "detectores_ref" for all the detectors.
• The variable "learners_ref" for all the base learners.
• The results are stored in different variables for scores (prequential accuracy), times and rams for calculating RAM-Hours metric, and detections.
• These results are then stored in a "temp.csv"
• Finally, Friedman and Nemenyi tests can be performed with the corresponding results for each metric (prequential accuracy, RAM-Hours, distance to the drift, MCC, and ND).

The source code for CURIE can be found in the file "CA_VonNeumann_estimator.py".

Please, if you use these resources, make a citation of this work:

@article{lobo2021curie, title={Curie: a cellular automaton for concept drift detection}, author={Lobo, Jesus L and Del Ser, Javier and Osaba, Eneko and Bifet, Albert and Herrera, Francisco}, journal={Data Mining and Knowledge Discovery}, pages={1--24}, year={2021}, publisher={Springer} }

And for the dataset citation:

@data{DVN/5OWRGB_2020, author = {López Lobo, Jesús}, publisher = {Harvard Dataverse}, title = {{Synthetic datasets for concept drift detection purposes}}, UNF = {UNF:6:VVTBgRNMEV+B/GmoE3Myng==}, year = {2020}, version = {V1}, doi = {10.7910/DVN/5OWRGB}, url = {https://doi.org/10.7910/DVN/5OWRGB} }