Graph representation learning is of paramount importance for a variety of graph analytical tasks, ranging from node classification to community detection. Recently, graph convolutional networks (GCNs) have been successfully applied for graph representation learning. These GCNs generate node representation by aggregating features from the neighborhoods, which follows the "neighborhood aggregation" scheme. In spite of having achieved promising performance on various tasks, existing GCN-based models have difficulty in well capturing complicated non-linearity of graph data. In this paper, we first theoretically prove that coefficients of the neighborhood interacting terms are relatively small in current models, which explains why GCNs barely outperforms linear models. Then, in order to better capture the complicated non-linearity of graph data, we present a novel GraphAIR framework which models the neighborhood interaction in addition to neighborhood aggregation. Comprehensive experiments conducted on benchmark tasks including node classification and link prediction using public datasets demonstrate the effectiveness of the proposed method over the state-of-the-art methods.

Graph convolution is the core of most Graph Neural Networks (GNNs) and usually approximated by message passing between direct (one-hop) neighbors. In this work, we remove the restriction of using only the direct neighbors by introducing a powerful, yet spatially localized graph convolution: Graph diffusion convolution (GDC). GDC leverages generalized graph diffusion, examples of which are the heat kernel and personalized PageRank. It alleviates the problem of noisy and often arbitrarily defined edges in real graphs. We show that GDC is closely related to spectral-based models and thus combines the strengths of both spatial (message passing) and spectral methods. We demonstrate that replacing message passing with graph diffusion convolution consistently leads to significant performance improvements across a wide range of models on both supervised and unsupervised tasks and a variety of datasets. Furthermore, GDC is not limited to GNNs but can trivially be combined with any graph-based model or algorithm (e.g. spectral clustering) without requiring any changes to the latter or affecting its computational complexity. Our implementation is available online.

Machine learning (ML) is routinely used by countless businesses to assist with decision making. In most cases, however, the predictions and business decisions made by ML systems still require the intuition of human users to make judgment calls. In this post, I show how to combine ML with sensitivity analysis to develop a data-driven business strategy. This post focuses on customer churn (that is, the defection of customers to competitors), while covering problems that often arise when using ML-based analysis. These problems include difficulties with handling incomplete and unbalanced data, deriving strategic options, and quantitatively evaluating the potential impact of those options.

Machine learning (ML) is routinely used by countless businesses to assist with decision making. In most cases, however, the predictions and business decisions made by ML systems still require the intuition of human users to make judgment calls. In this post, I show how to combine ML with sensitivity analysis to develop a data-driven business strategy. This post focuses on customer churn (that is, the defection of customers to competitors), while covering problems that often arise when using ML-based analysis. These problems include difficulties with handling incomplete and unbalanced data, deriving strategic options, and quantitatively evaluating the potential impact of those options.

Machine learning problems can generally be divided into three types. Classification and regression, which are known as supervised learning, and unsupervised learning which in the context of machine learning applications often refers to clustering. In the following article, I am going to give a brief introduction to each of these three problems and will include a walkthrough in the popular python library scikit-learn. Before I start I'll give a brief explanation for the meaning behind the terms supervised and unsupervised learning. Supervised Learning: In supervised learning, you have a known set of inputs (features) and a known set of outputs (labels).

Machine Learning aims at automatically identifying structures and patterns in large data sets. In order to identify these patterns, algorithms often resort to standard linear algebra routines such as matrix inversion or eigenvalue decompositions. For example, support vector machines, one of the most successful traditional machine learning approaches for classification, can be cast to a linear system of equation, and then be solved using matrix inversion. Similarly, identifying the important signals in a data set can be done by identifying the leading eigenvalues and vectors of the data matrix, a method called principal component analysis. The large dimensionality of the vector spaces involved in these operations make their implementation at large scale very resource intensive, thus motivating the development of innovative methods to lower their computational cost.

Python to analyze data, create state of the art visualization and use of machine learning algorithms to facilitate decision making. Python to analyze data, create state of the art visualization and use of machine learning algorithms to facilitate decision making. Python to analyze data, create state of the art visualization and use of machine learning algorithms to facilitate decision making. Greetings, I am so excited to learn that you have started your path to becoming a Data Scientist with my course. Data Scientist is in-demand and most satisfying career, where you will solve the most interesting problems and challenges in the world.

Principal Component Analysis or PCA is a widely used technique for dimensionality reduction of the large data set. Reducing the number of components or features costs some accuracy and on the other hand, it makes the large data set simpler, easy to explore and visualize. Also, it reduces the computational complexity of the model which makes machine learning algorithms run faster. It is always a question and debatable how much accuracy it is sacrificing to get less complex and reduced dimensions data set. In this article, we will be discussing the step by step approach to achieve dimensionality reduction using PCA and then I will also show how can we do all this using python library.

Clustering tries to find structure in data by creating groupings of data with similar characteristics. The most famous clustering algorithm is likely K-means, but there are a large number of ways to cluster observations. Hierarchical clustering is an alternative class of clustering algorithms that produce 1 to n clusters, where n is the number of observations in the data set. As you go down the hierarchy from 1 cluster (contains all the data) to n clusters (each observation is its own cluster), the clusters become more and more similar (almost always). There are two types of hierarchical clustering: divisive (top-down) and agglomerative (bottom-up).

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