DeepMoD
We introduce DeepMoD, a deep learning based model discovery algorithm which seeks the partial differential equation underlying a spatio-temporal data set. DeepMoD employs sparse regression on a library of basis functions and their corresponding spatial derivatives. A feed-forward neural network approximates the data set and automatic differentiation is used to construct this function library and perform regression within the neural network. This construction makes it extremely robust to noise and applicable to small data sets and, contrary to other deep learning methods, does not require a training set and is impervious to overfitting. We illustrate this approach on several physical problems, such as the Burgers’, Korteweg-de Vries, advection-diffusion and Keller-Segel equations, and find that it requires as few as O(10^2) samples and works at noise levels up to 75%. This resilience to noise and high performance at very few samples highlights the potential of this method to be applied on experimental data. Code and examples available at https://…/DeePyMoD. …

Simultaneous Perturbation Stochastic Approximation (SPSA)
This manuscript presents the following: (1) an improved version of the Binary Simultaneous Perturbation Stochastic Approximation (SPSA) Method for feature selection in machine learning (Aksakalli and Malekipirbazari, Pattern Recognition Letters, Vol. 75, 2016) based on non-monotone iteration gains computed via the Barzilai and Borwein (BB) method, (2) its adaptation for feature ranking, and (3) comparison against popular methods on public benchmark datasets. The improved method, which we call SPSA-FSR, dramatically reduces the number of iterations required for convergence without impacting solution quality. SPSA-FSR can be used for feature ranking and feature selection both for classification and regression problems. After a review of the current state-of-the-art, we discuss our improvements in detail and present three sets of computational experiments: (1) comparison of SPSA-FS as a (wrapper) feature selection method against sequential methods as well as genetic algorithms, (2) comparison of SPSA-FS as a feature ranking method in a classification setting against random forest importance, chi-squared, and information main methods, and (3) comparison of SPSA-FS as a feature ranking method in a regression setting against minimum redundancy maximum relevance (MRMR), RELIEF, and linear correlation methods. The number of features in the datasets we use range from a few dozens to a few thousands. Our results indicate that SPSA-FS converges to a good feature set in no more than 100 iterations and therefore it is quite fast for a wrapper method. SPSA-FS also outperforms popular feature selection as well as feature ranking methods in majority of test cases, sometimes by a large margin, and it stands as a promising new feature selection and ranking method. …

Keyhole Markup Language (KML)
Keyhole Markup Language (KML) is an XML notation for expressing geographic annotation and visualization within Internet-based, two-dimensional maps and three-dimensional Earth browsers. KML was developed for use with Google Earth, which was originally named Keyhole Earth Viewer. It was created by Keyhole, Inc, which was acquired by Google in 2004. KML became an international standard of the Open Geospatial Consortium in 2008. Google Earth was the first program able to view and graphically edit KML files. Other projects such as Marble have also started to develop KML support.
https://…/shapeFileToKML
http://…/9781482234817 …

Latent Convex Hull (LCH)
Providing unexpected recommendations is an important task for recommender systems. To do this, we need to start from the expectations of users and deviate from these expectations when recommending items. Previously proposed approaches model user expectations in the feature space, making them limited to the items that the user has visited or expected by the deduction of associated rules, without including the items that the user could also expect from the latent, complex and heterogeneous interactions between users, items and entities. In this paper, we define unexpectedness in the latent space rather than in the feature space and develop a novel Latent Convex Hull (LCH) method to provide unexpected recommendations. Extensive experiments on two real-world datasets demonstrate the effectiveness of the proposed model that significantly outperforms alternative state-of-the-art unexpected recommendation methods in terms of unexpectedness measures while achieving the same level of accuracy. …