Constructing fast approximate eigenspaces with application to the fast graph Fourier transforms

Distributed Estimation for Principal Component Analysis: an Enlarged Eigenspace Analysis

The growing size of modern data sets brings many challenges to the existing statistical estimation approaches, which calls for new distributed methodologies. This paper studies distributed estimation for a fundamental statistical machine learning problem, principal component analysis (PCA). Despite the massive literature on top eigenvector estimation, much less is presented for the top-$L$-dim ($L>1$) eigenspace estimation, especially in a distributed manner. We propose a novel multi-round algorithm for constructing top-$L$-dim eigenspace for distributed data. Our algorithm takes advantage of …

Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network

Recent work by Cohen \emph{et al.} has achieved state-of-the-art results for learning spherical images in a rotation invariant way by using ideas from group representation theory and noncommutative harmonic analysis. In this paper we propose a generalization of this work that generally exhibits improved performace, but from an implementation point of view is actually simpler. An unusual feature of the proposed architecture is that it uses the Clebsch--Gordan transform as its only source of nonlinearity, thus avoiding repeated forward and backward Fourier transforms. The underlying ideas of the…

通过分箱谱损失在非结构化网格上进行混沌动力学的尺度感知学习

Scale-Aware Learning of Chaotic Dynamics on Unstructured Meshes via Binned Spectral Losses

研究针对非结构化网格上混沌动力系统代理建模问题，通过用图拉普拉斯频带取代傅里叶频带，提供可扩展近似及引入GLEAM，扩展分箱谱功率损失，提高了长期预测保真度并保留统计不变量。

Facial Emotion Characterization and Detection using Fourier Transform and Machine Learning

We present a Fourier-based machine learning technique that characterizes and detects facial emotions. The main challenging task in the development of machine learning (ML) models for classifying facial emotions is the detection of accurate emotional features from a set of training samples, and the generation of feature vectors for constructing a meaningful feature space and building ML models. In this paper, we hypothesis that the emotional features are hidden in the frequency domain; hence, they can be captured by leveraging the frequency domain and masking techniques. We also make use of the…

Complex Hyperbolic Knowledge Graph Embeddings with Fast Fourier Transform

The choice of geometric space for knowledge graph (KG) embeddings can have significant effects on the performance of KG completion tasks. The hyperbolic geometry has been shown to capture the hierarchical patterns due to its tree-like metrics, which addressed the limitations of the Euclidean embedding models. Recent explorations of the complex hyperbolic geometry further improved the hyperbolic embeddings for capturing a variety of hierarchical structures. However, the performance of the hyperbolic KG embedding models for non-transitive relations is still unpromising, while the complex hyperbo…