I started with loading all the libraries and dependencies. The columns in the dataset are customer id, gender, age, income and spending score. I dropped the id column as that does not seem relevant to the context. Also I plotted the age frequency of customers. Next I made a box plot of spending score and annual income to better visualize the distribution range. The range of spending score is clearly more than the annual income range.

Check out my new paper entitled "Support Vector Machines, Wasserstein's distance and gradient-penalty GANs are connected"! In this paper, we explain how one can derive SVMs and gradient penalized GANs (or those with Lipschitz-1 discriminator) from the same framework! We also show new gradient penalties that lead to better GANs. This paper may completely change your perspective on the Wasserstein's distance, Wasserstein GAN (WGAN), Hinge GAN (HingeGAN), and the use of gradient penalties in GANs. At least, it did for me!

I have been recently confronted to the issue of finding similarities among time-series and though about using k-means to cluster them. To illustrate the method, I'll be using data from the Penn World Tables, readily available in R (inside the {pwt9} package): First, of all, let's only select the needed columns: The goal here is to cluster the different countries by looking at how similar they are on the avh variable. Let's do some further cleaning. The k-means implementation in R expects a wide data frame (currently my data frame is in the long format) and no missing values. These could potentially be imputed, but I can't be bothered: To convert my data frame from long to wide, I use the fresh pivot_wider() function, instead of the less intuitive spread() function.

We will first import libraries as NumPy, matplotlib, pyplot and derivative function. Then with a NumPy function – linspace() we define our variable \(w \) domain between 1.0 and 5.0 and 100 points. Also we define alpha which will represent learning rate. Next, we will define our \(y \) ( in our case \(J(w) \)) and plot to see a convex function, we will use \((w-3) 2 \). So we can see that we plotted our convex function as an example.

Dimensionality reduction is a technique for reducing the number of variables of data samples and has been successfully applied in many fields to make machine learning algorithms faster and more accurate, including the pathological diagnoses of gene expression data [26], the analysis of chemical sensor data [16], the community detection in social networks [27], the analyses of neural spike sorting [1], and others [22]. Due to their dependence on label information, dimensionality reduction methods can be divided into supervised and unsupervised methods. Typical unsupervised dimensionality reduction methods are the principal component analysis (PCA) [12, 15], the classical multidimensional scaling (MDS) [4], the locality preserving projections (LPP) [11], and the t-distributed stochastic neighbor embedding (t-SNE) [28]. To make use of prior knowledge on the labels, we focus on supervised dimensionality reduction methods. Supervised dimensionality reduction methods map data samples into an optimal low-dimensional space for satisfactory classification while incorporating the label information. One of the most popular supervised dimensionality reduction methods is the linear discriminant analysis (LDA) [3], which maximizes the between-class scatter and reduces the within-class scatter in a low-dimensional space.

A recent Forbes article [41] states that "Machine learning algorithms are very dependent on accurate, clean, and well-labeled training data to learn from so that they can produce accurate results" and "According to a recent report from AI research and advisory firm Cognilytica, over 80% of the time spent in AI projects are spent dealing with and wrangling data." While some abnormal samples, or outliers, can be detected and filtered during the preprocessing steps, others are more difficult to detect: for instance, a sophisticated adversary might try to "poison" data to force a desired outcome [33]. Other seemingly abnormal observations could be inherent to the underlying data-generating process. An "ideal" learning method should not discard informative samples, while limiting the effect of individual observation on the output of the learning algorithm at the same time. We are interested in robust methods that are model-free, and require minimal assumptions on the underlying distribution. We study two types of robustness: robustness to heavy tails expressed in terms of the moment requirements, as well as robustness to adversarial contamination. Heavy tails can be used to model variation and randomness naturally occurring in the sample, while adversarial contamination is a convenient way to model outliers of unknown nature. The statistical framework used throughout the paper is defined as follows. Let p S, S q be a measurable space, and let X P S be a random variable with distribution P .

In this paper, we propose a gamification approach as a novel framework for smart building infrastructure with the goal of motivating human occupants to reconsider personal energy usage and to have positive effects on their environment. Human interaction in the context of cyber-physical systems is a core component and consideration in the implementation of any smart building technology. Research has shown that the adoption of human-centric building services and amenities leads to improvements in the operational efficiency of these cyber-physical systems directed towards controlling building energy usage. We introduce a strategy in form of a game-theoretic framework that incorporates humans-in-the-loop modeling by creating an interface to allow building managers to interact with occupants and potentially incentivize energy efficient behavior. Prior works on game theoretic analysis typically rely on the assumption that the utility function of each individual agent is known a priori. Instead, we propose novel utility learning framework for benchmarking that employs robust estimations of occupant actions towards energy efficiency. To improve forecasting performance, we extend the utility learning scheme by leveraging deep bi-directional recurrent neural networks. Using the proposed methods on data gathered from occupant actions for resources such as room lighting, we forecast patterns of energy resource usage to demonstrate the prediction performance of the methods. The results of our study show that we can achieve a highly accurate representation of the ground truth for occupant energy resource usage. We also demonstrate the explainable nature on human decision making towards energy usage inherent in the dataset using graphical lasso and granger causality algorithms. Finally, we open source the de-identified, high-dimensional data pertaining to the energy game-theoretic framework.

Many irregular domains such as social networks, financial transactions, neuron connections, and natural language structures are represented as graphs. In recent years, a variety of graph neural networks (GNNs) have been successfully applied for representation learning and prediction on such graphs. However, in many of the applications, the underlying graph changes over time and existing GNNs are inadequate for handling such dynamic graphs. In this paper we propose a novel technique for learning embeddings of dynamic graphs based on a tensor algebra framework. Our method extends the popular graph convolutional network (GCN) for learning representations of dynamic graphs using the recently proposed tensor M-product technique. Theoretical results that establish the connection between the proposed tensor approach and spectral convolution of tensors are developed. Numerical experiments on real datasets demonstrate the usefulness of the proposed method for an edge classification task on dynamic graphs.

We introduce a novel end-to-end approach for learning to cluster in the absence of labeled examples. Our clustering objective is based on optimizing normalized cuts, a criterion which measures both intra-cluster similarity as well as inter-cluster dissimilarity. We define a differentiable loss function equivalent to the expected normalized cuts. Unlike much of the work in unsupervised deep learning, our trained model directly outputs final cluster assignments, rather than embeddings that need further processing to be usable. Our approach generalizes to unseen datasets across a wide variety of domains, including text, and image. Specifically, we achieve state-of-the-art results on popular unsupervised clustering benchmarks (e.g., MNIST, Reuters, CIFAR-10, and CIFAR-100), outperforming the strongest baselines by up to 10.9%. Our generalization results are superior (by up to 21.9%) to the recent top-performing clustering approach with the ability to generalize.

Graph Neural Networks (GNNs) for prediction tasks like node classification or edge prediction have received increasing attention in recent machine learning from graphically structured data. However, a large quantity of labeled graphs is difficult to obtain, which significantly limits the true success of GNNs. Although active learning has been widely studied for addressing label-sparse issues with other data types like text, images, etc., how to make it effective over graphs is an open question for research. In this paper, we present an investigation on active learning with GNNs for node classification tasks. Specifically, we propose a new method, which uses node feature propagation followed by K-Medoids clustering of the nodes for instance selection in active learning. With a theoretical bound analysis we justify the design choice of our approach. In our experiments on four benchmark datasets, the proposed method outperforms other representative baseline methods consistently and significantly.