Most research in human activity recognition is supervised, while non-supervised approaches are not completely unsupervised. Moreover, These methods cannot be used in real-time applications due to high calculations. In this paper, we provide a novel flexible multi-objective particle swarm optimization clustering method based on game theory (FMOPG) to discover human activities fully unsupervised. Unlike conventional clustering methods that estimate the number of clusters and are very time-consuming and inaccurate, an incremental technique is introduced which makes the proposed method flexible in dealing with the number of clusters and improves the speed of clustering. By adopting this technique, clusters with a better connectedness and good separation from other clusters are gradually selected. Updating of particles’ velocity is modified by adopting the concept of mean-shift vector to improve the convergence speed of PSO in achieving the best solution and dealing with non-spherical shape clusters. Multi-objective optimization problem is mapped to game theory by adopting Nash equilibrium to select the optimal solution on the pareto front. Gaussian mutation is also employed on the pareto front to generate diverse solutions and create a balance between exploitation and exploration. Moreover, A smart grid-based method is proposed to initialize the population to generate diverse solutions and reduce the variance between the worst and best clustering results. The proposed method is compared with state-of-the-art methods on seven challenging datasets. FMOPG has improved clustering accuracy by 3.65 % compared to other automated methods. Moreover, the incremental technique has improved the clustering time by 71.18 %.

Most deep clustering methods despite providing complex networks to learn better from data, use a shallow clustering method. These methods have difficulty in finding good clusters due to the lack of ability to handle between local search and global search to prevent premature convergence. In other words, they do not consider different aspects of the search and it causes them to get stuck in the local optimum. In addition, the majority of existing deep clustering approaches perform clustering with the knowledge of the number of clusters, which is not practical in most real scenarios where such information is not available. To address these problems, this paper presents a novel automatic deep sparse clustering approach based on an evolutionary algorithm called Multi-Trial Vectorbased Differential Evolution (MTDE). Sparse auto-encoder is first applied to extract embedded features. Manifold learning is then adopted to obtain representation and extract the spatial structure of features. Afterward, MTDE clustering is performed without prior information on the number of clusters to find the optimal clustering solution. The proposed approach was evaluated on various datasets, including images and time-series. The results demonstrate that the proposed method improved MTDE by 18.94% on average and compared to the most recent deep clustering algorithms, is consistently among the top three in the majority of datasets. Source code is available on Github: https://github.com/parhamhadikhani/ADSMTDE_Clustering.

Many algorithms have been proposed to solve the clustering problem. However, most of them lack a proper strategy to maintain a good balance between exploration and exploitation to prevent premature convergence. Multi-Trial Vector-based Differential Evolution (MTDE) is an improved differential evolution (DE) algorithm that is done by combining three strategies and distributing the population between these strategies to avoid getting stuck at a local optimum. In addition, it records inferior solutions to share information about visited regions with solutions of the next generations. In this paper, an Improved version of the Multi-Trial Vector-based Differential Evolution (IMTDE) algorithm is proposed and adapted for clustering data. The purpose here is to enhance the balance between the exploration and exploitation mechanisms in MTDE by employing Gaussian crossover and modifying the sub-population distribution between the strategies. To evaluate the performance of the proposed clustering, 19 datasets with different dimensions, shapes, and sizes were employed. The obtained results of IMTDE demonstrate improvement in MTDE performance by an average of 12%. Our comparative study with state-of-the-art algorithms demonstrates the superiority of IMTDE in most of these datasets because of the effective search strategies and the sharing of previous experiences in generating more promising solutions. Source code is available on Github: https://github.com/parhamhadikhani/IMTDE-Clustering.

Despite many advances in human activity recognition, most existing works are conducted with supervision. Supervised methods rely on labeled training data. However, obtaining labeled data is difficult, costly, and time-consuming. In this paper, we introduce an automatic multi-objective particle swarm optimization clustering based on Gaussian mutation and game theory (MOPGMGT) to tackle the problem of human activity discovery fully unsupervised and map the multi-objective clustering problem to game theory to get the best optimal solution. The proposed algorithm does not require any prior knowledge of the number of activities to be discovered and can find the optimal number. Multi-objective optimization problems typically cannot have a single optimal solution. To solve this issue, Nash Equilibrium (NE) is applied to the pareto front to choose the best solution. NE does not just look for the best solution, but tries to optimize the final solution by considering the effect of choosing each of the solutions as the best solution on the other solutions and one with the best impact is chosen. Moreover, a Gaussian mutation is applied on the pareto front to avoid premature convergence. Experiments on five challenging datasets demonstrate that the proposed approach is the most efficient to achieve better accuracy in human activity discovery and also can determine the optimal number of clusters.