6 Conclusion

In this work, we have made a revision of classical methods for dimensionality reduction and clustering. After seeing the disadvantages of these approaches, we conclude that the main problem is that they do not consider the explicit form of the differential manifold structure in which our data probably lie. With the purpose of solving this problem, we have focused this work in the study of advanced methods for dimensionality reduction and clustering, specifically Laplacian Eigenmaps (LE) and Spectral Clustering algorithms. The main advantages of these techniques are that they reduced the dimension of our original data, preserving the local geometric information of the points. The embedding of the points corresponds to the subjacent manifold to which the original data belongs.