In this paper, we propose a new approach to identify anomalous behaviour based on heterogeneous data and a new data fusion technique. There are four types of data sets applied in this study including credit card, loyalty card, GPS, and image data. The first step of the complete framework in this proposed study is to identify the best features for every data set. Then, the new anomaly detection technique which is recently introduced and known as Empirical Data Analytics (EDA) is applied to detect the abnormal behaviour based on the data sets. Standardised eccentricity (a newly introduced within EDA measure offering a new simplified form of the well-known Chebyshev Inequality) can be applied to any data distribution. Image data is processed using pre-trained deep learning network, and classification is done by using support vector machine (SVM). At the final stage of the proposed method is combining anomaly result and image recognition using new data fusion technique. From the experiment results, this proposed technique may simplify the tedious job in the real complex cases of forensic investigation. The proposed techniques can assist the human expert in processing huge amount of heterogeneous data to detect anomalies. In future research, text data can also be used as a part of heterogeneous data mixture, and the new data fusion technique may be applied to other data sets.