The article introduces new methods for analyzing data called LMS and LTS-type PCA, which are alternatives to traditional PCA. These methods aim to find the best linear subspace for organizing multidimensional data points by minimizing different types of distances. The researchers used a data-driven optimization algorithm to develop these new approaches, making them both easy to understand and practical to use. The key findings show that these new methods can be effective in handling complex data sets and provide more accurate results compared to classical PCA.