Crime geology research focuses on identifying the spatiotemporal crime distribution pattern

establishing spatiotemporal crime-forecasting models through machine learning

formulating efficient police prevention and control protocols

and effectively preventing the occurrence of crimes.Existing research has shown that crime data are significantly unbalanced in space and time.Most crimes are focused on the central urban area or a densely inhabited district.Unbalanced data will typically lead to a bias toward the majority class.Consequently

a classifier will display a poor recognition rate for the minority class

whereas minority class areas are usually hot spotswhere crimes frequentlyoccur.Accordingly

training models based on crime data (e.g.

genetic algorithm (GA)-back propagation (BP) neural network) become weak learners

which makes the desired prediction accuracy difficult to achieve. This study presents a novel algorithm based on a boosting ensemble learning algorithm to solve the aforementioned problem.The boosting ensemble learning algorithm utilizes more than one predictor for decision making

and thus

provides several advantages as follows:1) The design of a classifier ensemble aims to create a set of complementary/diverse classifiers and to apply an appropriate fusion method to merge their decisions.2) The ensemble learning algorithm may exhibit an improved performance compared with a standard single classifier approach because it canapply the unique strengths of each individual classifier in the pool.3) Ensembles may be robust and insignificantly prone to overfitting because they adopt mutually complementary models with different strengths.Simultaneously

a number of issues have to be considered when using the ensemble learning algorithm:1) how to select a pool of diverse and mutually complementary individual classifiers;2) how to design inter connections among the classifiers in the ensemble

i.e.

how to determine ensemble topology;and 3) how to conduct a fusion step to control the degree of influence of each classifier on the final decision.In consideration of the aforementioned issues

the new algorithm utilizes the GA-BP neural network to make a base classifier and K-means clustering to integrate the base classifier

thereby realizing the objective of converting weak learners into strong learners.The fusion step through K-means clustering is based on the theory of one base classifier performance on one data point that is frequently related to base classifier performance among the data points around thatdata point

which can fully consider the spatial relations among all the base classifiers.The proposed algorithm has two key steps as follows:1) Training data are resampled using a boosting-by-reweighting method that trains a designated number of base classifiers with a GA-BP neural network algorithm and then store all classfiers in a base classifier pool.2) Sample data are classified into several clusters using the K-means algorithm

and a base classifier with the highest forecasting accuracy is dynamically selected for each cluster to predict all data points that belong to the cluster. Experimental result demonstrates that the new algorithm has two advantages over the Synthetic Minority Oversampling Technique Boosting Boosting algorithm

which is widely used to solve the problem of regression and classification of unbalanced data:1) The proposed algorithm reduces the mean squared error of the minority class in data and the overall mean squared error.The overall mean squared error of the K-means-boosting algorithm is 9.85E-05

which outperforms the SMOTEBoosting algorithm with an overall mean squared error of 2.14E-04.2) The K-means-boosting algorithm can maintain the balance of minority precision and recall better than the SMOTEBoosting algorithm.The minority recall of the K-means-boosting algorithm is approximately equal to 52%

whereas that of the SMOTEBoosting algorithm is approximately equal to 91%.However

the minority precision of the K-means-boosting algorithm reaches 85%

which is more accurate than that of the SMOTEBoosting algorithm (i.e.

19%).The K-means-boosting algorithm also outperforms the AdaBoost algorithm

which is a classical ensemble learning algorithm because of two reasons:1)The K-means-boosting algorithm reduces the mean squared error of the minority class in unbalanced data and the overall mean squared error compared with the AdaBoost algorithm.2)The K-means-boosting algorithm improves minority recall and precision.The experimental result indicates that the number of clusters plays an important role in the algorithm.The overall mean squared error and the mean squared error of the minority class decrease with an increase in the number of clusters.Nevertheless

the rate of decline decreases gradually and will eventually approach a limit

whereas the computational cost required for classifier integration will continue to increase.No consensus rule currently exists to determine the number of clusters

and this variable can only be determined manually based on data. This study proposes a boosting ensemble learning algorithm that integrates base classifiers using the -means clustering algorithm to address the problem of unbalanced data regression.The application effect of the algorithm on the spatiotemporal prediction of police intelligence data proves that the method can deal with the prediction of grid-based spatiotemporal intelligence data.Compared with traditional boosting algorithms that integrate base classifiers into a weighted average method

the proposed method significantly reduces the overall mean squared error and the mean squared error of minority classes.Similarly

compared with the SMOTEBoosting algorithm

which is commonly used to solve the problem of unbalanced data regression

the proposed method does not only reduce the overall mean squared error of the sample data while reducing the mean squared error of the minority classes

but also maintain balance between minority precision and recall.The algorithm can be extended to other similar areas where unbalanced data regression or classification problems should be addressed.