One of the most popular exploratory approaches to reduce dimensionality and more easily describe the main sources of variation is principal component analysis. Despite the interesting advantages of this method, its application sometimes presents some difficulties. The presence of outliers in the data set has a detrimental effect on the results of this approach, which suggests that a type of principal components that are robust is beneficial for obtaining reliable results. In addition, the presence of intermediate loadings in some linear combinations makes it difficult to interpret the components, in which case a type of component thinning can be considered. In this paper, an efficient hybrid approach is presented to obtain both robust and sparse principal components simultaneously, and then statistical simulation is used to evaluate and compare it with the proposed approaches. Finally, the tools mentioned are used in the analysis of a real example related to the crime dataset in the United States.