GMM-based Imbalanced Fractional Whale Particle Filter for Multiple Object Tracking in Surveillance Videos

The imbalanced surveillance video dataset consists of majority and minority classes as normal and anomalous instances in the nonlinear and non-Gaussian framework. The normal and anomalous instances cause majority and minority samples or particles associated with high and low probable regions when considering the standard particle filter. The minority particles tend to be at high risk of being suppressed by the majority particles, as the proposal probability density function (pdf) encourages the highly probable regions of the input data space to remain a biased distribution. The standard particle filter-based tracker afflicts with sample degeneration and sample impoverishment due to the biased proposal pdf ignoring the minority particles. The difficulty in designing the correct proposal pdf prevents particle filter-based tracking in the imbalanced video data. The existing methods do not discuss the imbalanced nature of particle filter-based tracking. To alleviate this problem and tracking challenges, this paper proposes a novel fractional whale particle filter (FWPF) that fuses the fractional calculus-based whale optimization algorithm (FWOA) and the standard particle filter under weighted sum rule fusion. Integrating the FWPF with an iterative Gaussian mixture model (GMM) with unbiased sample variance and sample mean allows the proposal pdf to be adaptive to the imbalanced video data. The adaptive proposal pdf leads the FWPF to a minimum variance unbiased estimator for effectively detecting and tracking multiple objects in the imbalanced video data. The fractional calculus up to the first four terms makes the FWOA a local and global search operator with inherent memory property. The fractional calculus in the FWOA oversamples minority particles to be diversified with multiple imputations to eliminate data distortion with low bias and low variance. The proposed FWPF presents a novel imbalance evaluation metric, tracking distance correlation for the imbalanced tracking over UCSD surveillance video data and shows greater efficacy in mitigating the effects of the imbalanced nature of video data compared to other existing methods. The proposed method also outshines the existing methods regarding precision and accuracy in tracking multiple objects. The consistent tracking distance correlation near zero values provides efficient imbalance reduction through bias-variance correction compared to the existing methods.