# An Improved Evolutionary Multi-Objective Clustering Algorithm Based on Autoencoder
###### Abstract  
Evolutionary multi-objective clustering (EMOC) algorithms have gained popularity recently, as they can obtain a set of clustering solutions in a single run by optimizing multiple objectives. Particularly, in one type of EMOC algorithm, the number of clusters \(k\) is taken as one of the multiple objectives to obtain a set of clustering solutions with different \(k\). However, the numbers of clusters \(k\) and other objectives are not always in conflict, so it is impossible to obtain the clustering solutions with all different \(k\) in a single run. Therefore, evolutionary multi-objective k-clustering (EMO-KC) has recently been proposed to ensure this conflict. However, EMO-KC could not obtain good clustering accuracy on high-dimensional datasets. Moreover, EMOC-KC's validity is not ensured as one of its objectives (SSD\({}_{\text{exp}}\), which is transformed from the sum of squared distances (SSD)) could not be effectively optimized and it could not avoid invalid solutions in its initialization. In this paper, an improved evolutionary multi-objective clustering algorithm based on autoencoder (AE-IEMOKC) is proposed to improve the accuracy and ensure the validity of EMO-KC. The proposed AE-IEMOKC is established by combining an autoencoder with an improved version of EMO-KC (IEMO-KC) for better accuracy, where IEMO-KC is improved based on EMO-KC by proposing a scaling factor to help effectively optimize the objective of SSD\({}_{\text{exp}}\) and introducing a valid initialization to avoid the invalid solutions. Experimental results on several datasets demonstrate the accuracy and validity of AE-IEMOKC. The results of this paper may provide some useful information for other EMOC algorithms to improve accuracy and convergence. multi-objective clustering; autoencoder; deep learning; high-dimensional datasets +
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An Improved Evolutionary Multi-Objective Clustering Algorithm Based on AutoencoderM. [PERSON], [PERSON], [PERSON], [PERSON], M. An Improved Evolutionary Multi-Objective Clustering Algorithm Based on AutoencoderM. [PERSON], [PERSON], [PERSON], [PERSON], M. An Improved Evolutionary Multi-Objective Clustering Algorithm Based on AutoencoderM. [PERSON], [PERSON], [PERSON], [PERSON], M. An Improved Evolutionary Multi-Objective Clustering Algorithm Based on AutoencoderM. [PERSON], [PERSON], [PERSON], [PERSON], M. An Improved Evolutionary Multi-Objective Clustering Algorithm Based on AutoencoderM. [PERSON], [PERSON], [PERSON], [PERSON], M. An Improved Evolutionary Multi-Objective Clustering Algorithm Based on AutoencoderM. [PERSON], M. An Improved Evolutionary Multi-Objective Clustering Algorithm Based on AutoencoderM. clusters \(k\) is taken as one of the multiple objectives to obtain a set of clustering solutions with different \(k\). However, the numbers of clusters \(k\) and other objectives are not always in conflict, so clustering solutions with all different \(k\) cannot be obtained in a single run [6]. In this case, evolutionary multi-objective k-clustering (EMO-KC) has been proposed recently, which has an effective bi-objective model to ensure this conflict [7]. In this model, the number of clusters \(k\) and \(\text{SSD}_{\text{exp}}\) (see Equation (5)), which is transformed from the sum of squared distances (SSD), are taken as two objectives to ensure the conflict. The advantages of EMO-KC have been demonstrated in CCDG-K [8]. However, there are still several limitations of EMO-KC in its accuracy and validity. EMO-KC usually has a large number of decision variables, which increases with the dimensionality of the datasets, resulting in a large search space [9]. It is difficult for EMO-KC to converge to the global optimal solutions in such a large search space. As a result, the clustering accuracy of EMO-KC on high-dimensional datasets is limited. Furthermore, one of the two objectives of EMO-KC, \(\text{SSD}_{\text{exp}}\), could not be effectively optimized.