A new method for detecting rooftops in satellite images is presented. The proposed method is based on a combination of machine learning techniques, namely, k-means clustering and support vector machines (SVM). Firstly k-means clustering is used to segment the image into a set of rooftop candidates-these are homogeneous regions in the image which are potentially associated with rooftop areas. Next, the candidates are submitted to a classification stage which determines which amongst them correspond to "true" rooftops. To achieve improved accuracy, a novel two-pass classification process is used. In the first pass, a trained SVM is used in the normal way to distinguish between rooftop and nonrooftop regions. However, this can be a challenging task, resulting in a relatively high rate of misclassification. Hence, the second pass, which we call the "histogram method, " was devised with the aim of detecting rooftops which were missed in the first pass. The performance of the model is assessed both in terms of the percentage of correctly classified candidates as well as the accuracy of the estimated rooftop area.

The framework of Integral Quadratic Constraints (IQC) introduced by Lessard et al. (2014) reduces the computation of upper bounds on the convergence rate of several optimization algorithms to semi-definite programming (SDP). In particular, this technique was applied to Nesterov's accelerated method (NAM). For quadratic functions, this SDP was explicitly solved leading to a new bound on the convergence rate of NAM, and for arbitrary strongly convex functions it was shown numerically that IQC can improve bounds from Nesterov (2004). Unfortunately, an explicit analytic solution to the SDP was not provided. In this paper, we provide such an analytical solution, obtaining a new general and explicit upper bound on the convergence rate of NAM, which we further optimize over its parameters. To the best of our knowledge, this is the best, and explicit, upper bound on the convergence rate of NAM for strongly convex functions.

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In many distributed learning problems, the heterogeneous loading of computing machines may harm the overall performance of synchronous strategies. In this paper, we propose an effective asynchronous distributed framework for the minimization of a sum of smooth functions, where each machine performs iterations in parallel on its local function and updates a shared parameter asynchronously. In this way, all machines can continuously work even though they do not have the latest version of the shared parameter. We prove the convergence of the consistency of this general distributed asynchronous method for gradient iterations then show its efficiency on the matrix factorization problem for recommender systems and on binary classification.