Coresets-Methods and History: A Theoreticians Design Pattern for Approximation and Streaming Algorithms

We present a technical survey on the state of the art approaches in data reduction and the coreset framework. These include geometric decompositions, gradient methods, random sampling, sketching and random projections. We further outline their importance for the design of streaming algorithms and give a brief overview on lower bounding techniques

Multi-GCN: Graph Convolutional Networks for Multi-View Networks, with Applications to Global Poverty

With the rapid expansion of mobile phone networks in developing countries, large-scale graph machine learning has gained sudden relevance in the study of global poverty. Recent applications range from humanitarian response and poverty estimation to urban planning and epidemic containment. Yet the vast majority of computational tools and algorithms used in these applications do not account for the multi-view nature of social networks: people are related in myriad ways, but most graph learning models treat relations as binary. In this paper, we develop a graph-based convolutional network for learning on multi-view networks. We show that this method outperforms state-of-the-art semi-supervised learning algorithms on three different prediction tasks using mobile phone datasets from three different developing countries. We also show that, while designed specifically for use in poverty research, the algorithm also outperforms existing benchmarks on a broader set of learning tasks on multi-view networks, including node labelling in citation networks

Dimensionality Reduction for k-Means Clustering and Low Rank Approximation

We show how to approximate a data matrix $\mathbf{A}$ with a much smaller sketch $\mathbf{\tilde A}$ that can be used to solve a general class of constrained k-rank approximation problems to within $(1+\epsilon)$ error. Importantly, this class of problems includes $k$-means clustering and unconstrained low rank approximation (i.e. principal component analysis). By reducing data points to just $O(k)$ dimensions, our methods generically accelerate any exact, approximate, or heuristic algorithm for these ubiquitous problems. For $k$-means dimensionality reduction, we provide $(1+\epsilon)$ relative error results for many common sketching techniques, including random row projection, column selection, and approximate SVD. For approximate principal component analysis, we give a simple alternative to known algorithms that has applications in the streaming setting. Additionally, we extend recent work on column-based matrix reconstruction, giving column subsets that not only `cover' a good subspace for \bv{A}, but can be used directly to compute this subspace. Finally, for $k$-means clustering, we show how to achieve a $(9+\epsilon)$ approximation by Johnson-Lindenstrauss projecting data points to just $O(\log k/\epsilon^2)$ dimensions. This gives the first result that leverages the specific structure of $k$-means to achieve dimension independent of input size and sublinear in $k$