7,998 research outputs found
Ultra-Scalable Spectral Clustering and Ensemble Clustering
This paper focuses on scalability and robustness of spectral clustering for
extremely large-scale datasets with limited resources. Two novel algorithms are
proposed, namely, ultra-scalable spectral clustering (U-SPEC) and
ultra-scalable ensemble clustering (U-SENC). In U-SPEC, a hybrid representative
selection strategy and a fast approximation method for K-nearest
representatives are proposed for the construction of a sparse affinity
sub-matrix. By interpreting the sparse sub-matrix as a bipartite graph, the
transfer cut is then utilized to efficiently partition the graph and obtain the
clustering result. In U-SENC, multiple U-SPEC clusterers are further integrated
into an ensemble clustering framework to enhance the robustness of U-SPEC while
maintaining high efficiency. Based on the ensemble generation via multiple
U-SEPC's, a new bipartite graph is constructed between objects and base
clusters and then efficiently partitioned to achieve the consensus clustering
result. It is noteworthy that both U-SPEC and U-SENC have nearly linear time
and space complexity, and are capable of robustly and efficiently partitioning
ten-million-level nonlinearly-separable datasets on a PC with 64GB memory.
Experiments on various large-scale datasets have demonstrated the scalability
and robustness of our algorithms. The MATLAB code and experimental data are
available at https://www.researchgate.net/publication/330760669.Comment: To appear in IEEE Transactions on Knowledge and Data Engineering,
201
Application of the exact regularized point particle method (ERPP) to particle laden turbulent shear flows in the two-way coupling regime
The Exact Regularized Point Particle method (ERPP), which is a new inter-phase momentum coupling ap- proach, is extensively used for the first time to explore the response of homogeneous shear turbulence in presence of different particle populations. Particle suspensions with different Stokes number and/or mass loading are considered. Particles with Kolmogorov Stokes number of order one suppress turbulent kinetic energy when the mass loading is increased. In contrast, heavier particles leave this observable almost un- changed with respect to the reference uncoupled case. Turbulence modulation is found to be anisotropic, leaving the streamwise velocity fluctuations less affected by unitary Stokes number particles whilst it is increased by heavier particles. The analysis of the energy spectra shows that the turbulence modulation occurs throughout the entire range of resolved scales leading to non-trivial augmentation/depletion of the energy content among the different velocity components at different length-scales. In this regard, the ERPP approach is able to provide convergent statistics up to the smallest dissipative scales of the flow, giving the opportunity to trust the ensuing results. Indeed, a substantial modification of the turbu- lent fluctuations at the smallest-scales, i.e. at the level of the velocity gradients, is observed due to the particle backreaction. Small scale anisotropies are enhanced and fluctuations show a greater level of in- termittency as measured by the probability distribution function of the longitudinal velocity increments and by the corresponding flatness
Persistent Homology and String Vacua
We use methods from topological data analysis to study the topological
features of certain distributions of string vacua. Topological data analysis is
a multi-scale approach used to analyze the topological features of a dataset by
identifying which homological characteristics persist over a long range of
scales. We apply these techniques in several contexts. We analyze N=2 vacua by
focusing on certain distributions of Calabi-Yau varieties and Landau-Ginzburg
models. We then turn to flux compactifications and discuss how we can use
topological data analysis to extract physical informations. Finally we apply
these techniques to certain phenomenologically realistic heterotic models. We
discuss the possibility of characterizing string vacua using the topological
properties of their distributions.Comment: 32 pages, 12 pdf figure
- …