犯罪时间序列的混沌特征分析与短期预测

现有犯罪时间序列预测方法侧重于捕捉序列自相关性来构建预测模型,但缺少对犯罪时间序列所反映的社会治安系统非线性和复杂性特征的考虑。 针对这一不足,提出了一种基于混沌分析的长短期记忆(long short-term memory, LSTM)LSTM 预测方法(Chaos-LSTM)。 首先将犯罪时间序列进行相空间重构得到其重构参数以及高维特征,然后计算犯罪时间序列的 Lyapunov 指数判断其混沌特性,最后对符合混沌特征的犯罪时间序列利用重构参数进行序列重建,输入 LSTM 模型进行时序预测。 以北方某特大城市 2007—2014 年的抢劫、入室盗窃、抢夺、诈骗类犯罪的日序列数据进行了实验验证,结果表明:4类案件的时序数据均表现出明显的混沌特征。 Chaos-LSTM 模型在预测精度上较 LSTM 模型有明显提升,平均绝对百分误差(mean absolute percentage error, MAPE)提 升 度 最 高 可 达 19. 7% ,百 分 比 均 方 根 误 差 (percentage root mean square error,PRMSE)提升度最高为 4. 19% ,其中对稀疏性数据序列的提升效果更为明显,显示出该方法对稀疏犯罪时间序列具有更好的适应性。

Chaos Characteristic Analysis and Short-Term Prediction of Crime Time Series

Existing crime time series prediction methods focus on capturing the autocorrelation of sequence to build prediction mod-els, but they lack consideration of the nonlinearity and complexity of the social security system reflected by crime time series. Aiming at this deficiency, an long short-term memory ( LSTM) prediction method was proposed based on chaos analysis ( Chaos-LSTM) . First-ly, the crime time series was reconstructed in phase space to obtain its reconstruction parameters and high-dimensional features, and then the Lyapunov exponent of the crime time series was calculated to judge its chaotic characteristics. Finally using the reconstructionparameters to reconstruct the crime time series conforming to chaotic characteristics, and input to the LSTM model for time series pre-diction. The daily serial data of robbery, burglary, snatch and fraud in a northern megacity from 2007 to 2014 were used for experimen-tal verification. The results show these as follows. The time series data of the four types of cases all showed obvious chaotic characteris-tics. The Chaos-LSTM model demonstrates a significant improvement in predictive accuracy compared to the LSTM model. The maxi-mum increase of mean absolute percentage error( MAPE) is 19. 7% , and the highest improvement of percentage root mean square error( PRMSE) is 4. 19% . The improvement effect on sparse data series is more obvious, indicating that the method has better adaptability to sparse crime time series.