**Self-Attentive Neural Collaborative Filtering (SA-NCF)**

The dominant, state-of-the-art collaborative filtering (CF) methods today mainly comprises neural models. In these models, deep neural networks, e.g.., multi-layered perceptrons (MLP), are often used to model nonlinear relationships between user and item representations. As opposed to shallow models (e.g., factorization-based models), deep models generally provide a greater extent of expressiveness, albeit at the expense of impaired/restricted information flow. Consequently, the performance of most neural CF models plateaus at 3-4 layers, with performance stagnating or even degrading when increasing the model depth. As such, the question of how to train really deep networks in the context of CF remains unclear. To this end, this paper proposes a new technique that enables training neural CF models all the way up to 20 layers and beyond. Our proposed approach utilizes a new hierarchical self-attention mechanism that learns introspective intra-feature similarity across all the hidden layers of a standard MLP model. All in all, our proposed architecture, SA-NCF (Self-Attentive Neural Collaborative Filtering) is a densely connected self-matching model that can be trained up to 24 layers without plateau-ing, achieving wide performance margins against its competitors. On several popular benchmark datasets, our proposed architecture achieves up to an absolute improvement of 23%-58% and 1.3x to 2.8x fold improvement in terms of nDCG@10 and Hit Ratio (HR@10) scores over several strong neural CF baselines. … **Ternary Plot / Ternary Diagram**

A ternary plot, ternary graph, triangle plot, simplex plot, or de Finetti diagram is a barycentric plot on three variables which sum to a constant. It graphically depicts the ratios of the three variables as positions in an equilateral triangle. … **t-Distributed Stochastic Neighbor Embedding (t-SNE,TSNE)**

t-distributed stochastic neighbor embedding (t-SNE) is a machine learning algorithm for dimensionality reduction developed by Laurens van der Maaten and Geoffrey Hinton. It is a nonlinear dimensionality reduction technique that is particularly well suited for embedding high-dimensional data into a space of two or three dimensions, which can then be visualized in a scatter plot. Specifically, it models each high-dimensional object by a two- or three-dimensional point in such a way that similar objects are modeled by nearby points and dissimilar objects are modeled by distant points. The t-SNE algorithms comprises two main stages. First, t-SNE constructs a probability distribution over pairs of high-dimensional objects in such a way that similar objects have a high probability of being picked, whilst dissimilar points have an infinitesimal probability of being picked. Second, t-SNE defines a similar probability distribution over the points in the low-dimensional map, and it minimizes the Kullback-Leibler divergence between the two distributions with respect to the locations of the points in the map.

http://…buted-stochastic-neighbor-embedding-t-sne

Visualizing Data using t-SNE … **Time Oriented Language (TOL)**

TOL is the Time Oriented Language. It is a programming language dedicated to the world of statistics and focused on time series analysis and stochastic processes. It is a declarative language based on two key features: simple syntactical rules and powerful set of extensible data types and functions. TOL is callable by a small text console, but there is also a graphical interface to easily handle all language’s tools and functions, providing powerful graphical capacities. TOL is distributed under the GNU GPL license. …

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