Related papers: Hierarchization for the Sparse Grid Combination Te…

In this paper, we consider large-scale ranking problems where one is given a set of (possibly non-redundant) pairwise comparisons and the underlying ranking explained by those comparisons is desired. We show that stochastic gradient descent…

The parallel linear equations solver capable of effectively using 1000+ processors becomes the bottleneck of large-scale implicit engineering simulations. In this paper, we present a new hierarchical parallel master-slave-structural…

We propose a novel approach to the problem of clustering hierarchically aggregated time-series data, which has remained an understudied problem though it has several commercial applications. We first group time series at each aggregated…

Computing high-quality independent sets quickly is an important problem in combinatorial optimization. Several recent algorithms have shown that kernelization techniques can be used to find exact maximum independent sets in medium-sized…

Subspace clustering refers to the problem of clustering high-dimensional data that lie in a union of low-dimensional subspaces. State-of-the-art subspace clustering methods are based on the idea of expressing each data point as a linear…

Localization in a pre-built map is a basic technique for robot autonomous navigation. Existing mapping and localization methods commonly work well in small-scale environments. As a map grows larger, however, more memory is required and…

Algebraic multigrid (AMG) is an $\mathcal{O}(n)$ solution process for many large sparse linear systems. A hierarchy of progressively coarser grids is constructed that utilize complementary relaxation and interpolation operators. High-energy…

Hierarchical clustering is a class of algorithms that seeks to build a hierarchy of clusters. It has been the dominant approach to constructing embedded classification schemes since it outputs dendrograms, which capture the hierarchical…

Modern hardware systems are heavily underutilized when running large-scale graph applications. While many in-memory graph frameworks have made substantial progress in optimizing these applications, we show that it is still possible to…

Several learning applications require solving high-dimensional regression problems where the relevant features belong to a small number of (overlapping) groups. For very large datasets and under standard sparsity constraints, hard…

Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…

The sparse, hierarchical, and modular processing of natural signals is related to the ability of humans to recognize objects with high accuracy. In this study, we report a sparse feature processing and encoding method, which improved the…

Neural networks have seen limited use in prediction for high-dimensional data with small sample sizes, because they tend to overfit and require tuning many more hyperparameters than existing off-the-shelf machine learning methods. With…

With the rapid advancement of next-generation satellite networks, addressing clustering tasks, user grouping, and efficient link management has become increasingly critical to optimize network performance and reduce interference. In this…

Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while…

Optimizing with group sparsity is significant in enhancing model interpretability in machining learning applications, e.g., feature selection, compressed sensing and model compression. However, for large-scale stochastic training problems,…

A multiscale optimization framework for problems over a space of Lipschitz continuous functions is developed. The method solves a coarse-grid discretization followed by linear interpolation to warm-start project gradient descent on…

Sparse graphs built by sparse representation has been demonstrated to be effective in clustering high-dimensional data. Albeit the compelling empirical performance, the vanilla sparse graph ignores the geometric information of the data by…

Spectral clustering and its extensions usually consist of two steps: (1) constructing a graph and computing the relaxed solution; (2) discretizing relaxed solutions. Although the former has been extensively investigated, the discretization…

We propose a new tensor factorization method, called the Sparse Hierarchical-Tucker (Sparse H-Tucker), for sparse and high-order data tensors. Sparse H-Tucker is inspired by its namesake, the classical Hierarchical Tucker method, which aims…