Clustering Data Using Techniques of Image Processing Erode and Dilate to Avoid the Use of Euclidean Distance

Clustering is one of the most popular methods of machine learning. The process of clustering involves the division of a set of abstract objects into a certain number of groups which integrated with objects of similar characteristics. Therefore, a cluster integrates objects which are similar to them, but dissimilar to the elements that belong to the rest of the clusters. Several clustering methods have proposed in the literature with different performance levels. All these techniques use as similarity criterion the Euclidean distance among cluster elements. However, there exist diverse scenarios where the Euclidean distance cannot be utilized appropriately to separate the elements in groups. Under such conditions, traditional cluster methods cannot directly apply. On the other hand, the operations of dilate and erode are a set of non-linear operators that modify the shape of a data group in the feature space, to obtain a monolithic object. Although morphological operations have demonstrated its importance in several engineering fields as image processing, its use as a clustering technique has been practically overlooked. In this work, an alternative clustering algorithm is proposed to group elements without considering the distance as a similarity criterion. In our approach, the data were separated into different groups by considering morphological operations. Under this scheme, the procedure allows the integration of data points, which present a spatial connection. Since the proposed algorithm does not use the distance in its functioning, it solves complex clustering problems which traditional clustering algorithms cannot.