**6. Experimental results**

10 Will-be-set-by-IN-TECH

deemed anomalous. However, it is likely that it may still fall in the normality region of the second closest but less dense pattern having larger normality range. The hardness of LMC-ES based classification algorithm will result in the misclassification of such samples. However, MMC-GFS based classification and anomaly detection algorithm does not give a hard decision and checks for the membership of test trajectories w.r.t. different patterns until it is identified as a valid member of some pattern or it has been identified as anomalous w.r.t. *k* nearest medoids. This relatively softer approach enables the MMC-GFS based classification algorithm to adapt to the multimodal distribution of samples within different patterns. This phenomena is highlighted in Fig. 2. The samples, represented by 'x' marker, will be classified to blue pattern but is marked as anomalous using LMC-ES classifier as it falls outside the normality range of dense medoids belonging to the closest pattern. On the other hand, soft classification technique as proposed in MMC-GFS frameworks will correctly classify the sample as normal members of green pattern. Another benefit of MMC-GFS framework is that it can be applied to any feature space representation of trajectories with a given distance function. On the other

hand, LMC-ES can only operate in feature spaces with a computable mean.

Fig. 2. Scenario for evaluating the adaptation of classification algorithms as proposed in

Algorithms to generate *m*-Medoids model, as proposed in LMC-ES framework, is efficient and scalable to large datasets. On the other hand, the modeling algorithm of MMC-GFS is not scalable to very large datasets due to the requirement of affinity matrix computation. The space and time complexity is quadratic which is problematic for patterns with large number of training sample. However, this problem can be easily catered by splitting the training sample into subsets and selecting candidate medoids in each subset using algorithm as specified in section 3.1. The final selection of medoids can be done by applying the same algorithm again but now using the candidate medoids instead of all the training sample belonging to a given pattern. The classification algorithm of MMC-GFS framework is more efficient as compared to LMC-ES framework. This efficiency gain is due to the non-iterative unmerged anomaly detection with respect to a given medoid. The anomaly detection is done by applying a single

On the other hand, LMC-ES implements iterative merged anomaly detection, which is more accurate but time consuming as compared to the modeling algorithm proposed in MMC-GFS framework. The time complexity of merged anomaly detection is *O*(*m* ∗ *log*(*m*) − *τ* ∗ *log*(*τ*)).

*th* closest medoid as specified in eq. (13).

different *m*-Medoids based frameworks.

threshold to the distance of the test sample from its *ı*

In this section, we present some results to analyze the performance of the proposed multimodal *m*-Medoids based modeling, classification and anomaly detection as compared to competitive techniques.
