This paper studies the utility of using data analytics and machine learning techniques for identifying, classifying, and characterizing the dynamics of large-scale parallel (MPI) programs. To this end, we run microbenchmarks and realistic proxy applications with the regular compute-communicate structure on two different supercomputing platforms and choose the per-process performance and MPI time per time step as relevant observables. Using principal component analysis, clustering techniques, correlation functions, and a new "phase space plot," we show how desynchronization patterns (or lack thereof) can be readily identified from a data set that is much smaller than a full MPI trace. Our methods also lead the way towards a more general classification of parallel program dynamics.

Clustering is an unsupervised algorithm that is used for determining the intrinsic groups present in unlabelled data. For instance, a B2C business might be interested in finding segments in its customer base. Clustering is hence used commonly for different use-cases like customer segmentation, market segmentation, pattern recognition, search result clustering etc. Some standard clustering techniques are K-means, DBSCAN, Hierarchical clustering amongst other methods. Clusters created using techniques like Kmeans are often not easy to decipher because it is difficult to determine why a particular row of data is classified in a particular bucket.

Abstract: Two important nonparametric approaches to clustering emerged in the 1970's: clustering by level sets or cluster tree as proposed by Hartigan, and clustering by gradient lines or gradient flow as proposed by Fukunaga and Hosteler. In a recent paper, we argue the thesis that these two approaches are fundamentally the same by showing that the gradient flow provides a way to move along the cluster tree. In making a stronger case, we are confronted with the fact the cluster tree does not define a partition of the entire support of the underlying density, while the gradient flow does. Abstract: Mean shift is a simple interactive procedure that gradually shifts data points towards the mode which denotes the highest density of data points in the region. Mean shift algorithms have been effectively used for data denoising, mode seeking, and finding the number of clusters in a dataset in an automated fashion.

Clustering of large-scale data is key to implementing segmentation-based algorithms. Segmentation can include identifying customer groups to facilitate targeted marketing, identifying prescriber groups to allow health care players to reach out to them with the right messaging, and identifying patterns or abnormal values in the data. K-Means is the most popular clustering algorithm adopted across different problem areas, mostly owing to its computational efficiency and ease of understanding the algorithm. K-Means relies on identifying cluster centers from the data. It alternates between assigning points to these cluster centers using the Euclidean distance metric and recomputes the cluster centers till a convergence criterion is achieved.

Unsupervised learning algorithms are "unsupervised" because you let them run without direct supervision. You feed the data into the algorithm, and the algorithm figures out the patterns. The following picture shows the differences between three of the most popular unsupervised learning algorithms: Principal Component Analysis, k-Means clustering and Hierarchical clustering. The three are closely related, because data clustering is a type of data reduction; PCA can be viewed as a continuous counterpart of K-Means (see Ding & He, 2004).

While gravitational microlensing by planetary systems provides unique vistas on the properties of exoplanets, observations of a given 2-body microlensing event can often be interpreted with multiple distinct physical configurations. Such ambiguities are typically attributed to the close-wide and inner-outer types of degeneracies that arise from transformation invariances and symmetries of microlensing caustics. However, there remain unexplained inconsistencies between aforementioned theories and observations. Here, leveraging a fast machine learning inference framework, we present the discovery of the offset degeneracy, which concerns a magnification-matching behaviour on the lens-axis and is formulated independent of caustics. This offset degeneracy unifies the close-wide and inner-outer degeneracies, generalises to resonant topologies, and upon reanalysis, not only appears ubiquitous in previously published planetary events with 2-fold degenerate solutions, but also resolves prior inconsistencies. Our analysis demonstrates that degenerate caustics do not strictly result in degenerate magnifications and that the commonly invoked close-wide degeneracy essentially never arises in actual events. Moreover, it is shown that parameters in offset degenerate configurations are related by a simple expression. This suggests the existence of a deeper symmetry in the equations governing 2-body lenses than previously recognised.

Learning from a continuous stream of non-stationary data in an unsupervised manner is arguably one of the most common and most challenging settings facing intelligent agents. Here, we attack learning under all three conditions (unsupervised, streaming, non-stationary) in the context of clustering, also known as mixture modeling. We introduce a novel clustering algorithm that endows mixture models with the ability to create new clusters online, as demanded by the data, in a probabilistic, time-varying, and principled manner. To achieve this, we first define a novel stochastic process called the Dynamical Chinese Restaurant Process (Dynamical CRP), which is a non-exchangeable distribution over partitions of a set; next, we show that the Dynamical CRP provides a non-stationary prior over cluster assignments and yields an efficient streaming variational inference algorithm. We conclude with experiments showing that the Dynamical CRP can be applied on diverse synthetic and real data with Gaussian and non-Gaussian likelihoods.

The Adversarially Learned Mixture Model (AMM) is a generative model for unsupervised or semi-supervised data clustering. The AMM is the first adversarially optimized method to model the conditional dependence between inferred continuous and categorical latent variables. Experiments on the MNIST and SVHN datasets show that the AMM allows for semantic separation of complex data when little or no labeled data is available. The AMM achieves a state-of-the-art unsupervised clustering error rate of 2.86% on the MNIST dataset. A semi-supervised extension of the AMM yields competitive results on the SVHN dataset.

The ubiquitous interrelations between algebraic geometry and physics has for centuries flourished fruitful phenomena in both fields. With connections made as far back as Archimedes whose work on conic sections aided development of concepts surrounding the motion under gravity, physical understanding has largely relied upon the mathematical tools available. In the modern era, these two fields are still heavily intertwined, with particular relevance in addressing one of the most significant problems of our time - quantising gravity. String theory as a candidate for this theory of everything, relies heavily on algebraic geometry constructions to define its spacetime and to interpret its matter. However, where new mathematical tools arise their implementation is not always simple.

We introduce an unsupervised clustering algorithm to improve training efficiency and accuracy in predicting energies using molecular-orbital-based machine learning (MOB-ML). This work determines clusters via the Gaussian mixture model (GMM) in an entirely automatic manner and simplifies an earlier supervised clustering approach [J. Chem. Theory Comput., 15, 6668 (2019)] by eliminating both the necessity for user-specified parameters and the training of an additional classifier. Unsupervised clustering results from GMM have the advantage of accurately reproducing chemically intuitive groupings of frontier molecular orbitals and having improved performance with an increasing number of training examples. The resulting clusters from supervised or unsupervised clustering is further combined with scalable Gaussian process regression (GPR) or linear regression (LR) to learn molecular energies accurately by generating a local regression model in each cluster. Among all four combinations of regressors and clustering methods, GMM combined with scalable exact Gaussian process regression (GMM/GPR) is the most efficient training protocol for MOB-ML. The numerical tests of molecular energy learning on thermalized datasets of drug-like molecules demonstrate the improved accuracy, transferability, and learning efficiency of GMM/GPR over not only other training protocols for MOB-ML, i.e., supervised regression-clustering combined with GPR(RC/GPR) and GPR without clustering. GMM/GPR also provide the best molecular energy predictions compared with the ones from literature on the same benchmark datasets. With a lower scaling, GMM/GPR has a 10.4-fold speedup in wall-clock training time compared with scalable exact GPR with a training size of 6500 QM7b-T molecules.