Machine Learning Line Bundle Cohomologies of Hypersurfaces in Toric Varieties

Different techniques from machine learning are applied to the problem of computing line bundle cohomologies of (hypersurfaces in) toric varieties. While a naive approach of training a neural network to reproduce the cohomologies fails in the general case, by inspecting the underlying functional form of the data we propose a second approach. The cohomologies depend in a piecewise polynomial way on the line bundle charges. We use unsupervised learning to separate the different polynomial phases. The result is an analytic formula for the cohomologies. This can be turned into an algorithm for computing analytic expressions for arbitrary (hypersurfaces in) toric varieties.Comment: 8 pages, 6 figures, 5 tables; typos corrected, reference added, clarifications adde

Artificial Neural Network Approach to the Analytic Continuation Problem

Inverse problems are encountered in many domains of physics, with analytic continuation of the imaginary Green's function into the real frequency domain being a particularly important example. However, the analytic continuation problem is ill defined and currently no analytic transformation for solving it is known. We present a general framework for building an artificial neural network (ANN) that solves this task with a supervised learning approach. Application of the ANN approach to quantum Monte Carlo calculations and simulated Green's function data demonstrates its high accuracy. By comparing with the commonly used maximum entropy approach, we show that our method can reach the same level of accuracy for low-noise input data, while performing significantly better when the noise strength increases. The computational cost of the proposed neural network approach is reduced by almost three orders of magnitude compared to the maximum entropy methodComment: 6 pages, 4 figures, supplementary material available as ancillary fil

BL-MNE: Emerging Heterogeneous Social Network Embedding through Broad Learning with Aligned Autoencoder

Network embedding aims at projecting the network data into a low-dimensional feature space, where the nodes are represented as a unique feature vector and network structure can be effectively preserved. In recent years, more and more online application service sites can be represented as massive and complex networks, which are extremely challenging for traditional machine learning algorithms to deal with. Effective embedding of the complex network data into low-dimension feature representation can both save data storage space and enable traditional machine learning algorithms applicable to handle the network data. Network embedding performance will degrade greatly if the networks are of a sparse structure, like the emerging networks with few connections. In this paper, we propose to learn the embedding representation for a target emerging network based on the broad learning setting, where the emerging network is aligned with other external mature networks at the same time. To solve the problem, a new embedding framework, namely "Deep alIgned autoencoder based eMbEdding" (DIME), is introduced in this paper. DIME handles the diverse link and attribute in a unified analytic based on broad learning, and introduces the multiple aligned attributed heterogeneous social network concept to model the network structure. A set of meta paths are introduced in the paper, which define various kinds of connections among users via the heterogeneous link and attribute information. The closeness among users in the networks are defined as the meta proximity scores, which will be fed into DIME to learn the embedding vectors of users in the emerging network. Extensive experiments have been done on real-world aligned social networks, which have demonstrated the effectiveness of DIME in learning the emerging network embedding vectors.Comment: 10 pages, 9 figures, 4 tables. Full paper is accepted by ICDM 2017, In: Proceedings of the 2017 IEEE International Conference on Data Mining

Investigating the generalizability of EEG-based Cognitive Load Estimation Across Visualizations

We examine if EEG-based cognitive load (CL) estimation is generalizable across the character, spatial pattern, bar graph and pie chart-based visualizations for the nback~task. CL is estimated via two recent approaches: (a) Deep convolutional neural network, and (b) Proximal support vector machines. Experiments reveal that CL estimation suffers across visualizations motivating the need for effective machine learning techniques to benchmark visual interface usability for a given analytic task

Stacking-based Deep Neural Network: Deep Analytic Network on Convolutional Spectral Histogram Features

Stacking-based deep neural network (S-DNN), in general, denotes a deep neural network (DNN) resemblance in terms of its very deep, feedforward network architecture. The typical S-DNN aggregates a variable number of individually learnable modules in series to assemble a DNN-alike alternative to the targeted object recognition tasks. This work likewise devises an S-DNN instantiation, dubbed deep analytic network (DAN), on top of the spectral histogram (SH) features. The DAN learning principle relies on ridge regression, and some key DNN constituents, specifically, rectified linear unit, fine-tuning, and normalization. The DAN aptitude is scrutinized on three repositories of varying domains, including FERET (faces), MNIST (handwritten digits), and CIFAR10 (natural objects). The empirical results unveil that DAN escalates the SH baseline performance over a sufficiently deep layer.Comment: 5 page