Although the analysis of data is a task that has gained the interest of the statistical community in recent years and whose familiarity with the statistical computing environment, they encourage the current statistical community (to students and teachers of the area) to complete statistical analysis reproducible by means of the tool R. However for years there has been a gap between the calculation of matrices on a large scale and the term "big data", in this work the Normalized Cut algorithm for images is applied. Despite the expected, the R environment to do image analysis is poorly, in comparison with other computing platforms such as the Python language or with specialized software such as OpenCV.
Being well known the absence of such function, in this work we share an implementation of the Normalized Cut algorithm in the R environment with extensions to programs and processes performed in C ++, to provide the user with a friendly interface in R to segment images. The article concludes by evaluating the current implementation and looking for ways to generalize the implementation for a large scale context and reuse the developed code.
Key words: Normaliced Cut, image segmentation, Lanczos algorithm, eigenvalues and eigenvectors, graphs, similarity matrix, R (the statistical computing environment), open source, large scale and big data.
Vamos a demostrar el notable teorema que dice que, dadas dos matrices cuadradras \(A\) y \(B\) del mismo tamaño, si \(AB=I\), donde \(I\) es la matriz identidad del mismo tamaño que la matrices \(A\) y \(B\), entonces \(A\) es invertible y \(B^{-1}=A\). La prueba será directa y sólo usaremos el hecho de que si \(|A|\ne0\) entonces \(A\) es invertible. La pregunta es si puedes tú, estimado estudiante, ofrecer otra prueba de la que aquí se sugiere. Sirva además este texto como un ejemplo de escritura con LaTeX.
Under a partly linear model we study a family of robust estimates for the regression parameter and the regression function when some of the predictors take values on a Riemannian manifold. We obtain the consistency and the asymptotic normality of the proposed estimators. Simulations and an application to a real dataset show the good performance of our proposal under small samples and contamination.