Latitude: A Model for Mixed Linear-Tropical Matrix Factorization

FastSTMF: Efficient tropical matrix factorization algorithm for sparse data

Matrix factorization, one of the most popular methods in machine learning, has recently benefited from introducing non-linearity in prediction tasks using tropical semiring. The non-linearity enables a better fit to extreme values and distributions, thus discovering high-variance patterns that differ from those found by standard linear algebra. However, the optimization process of various tropical matrix factorization methods is slow. In our work, we propose a new method FastSTMF based on Sparse Tropical Matrix Factorization (STMF), which introduces a novel strategy for updating factor matrice…

热带代数与混合热带-线性代数中的矩阵分解

Matrix Factorization in Tropical and Mixed Tropical-Linear Algebras

本文研究热带代数及混合热带-线性矩阵分解，提出改进的TMF算法以规避局部最优，并引入三矩阵近似分解用于多用户效用学习，实验与推荐应用验证了有效性。

Data embedding and prediction by sparse tropical matrix factorization

Matrix factorization methods are linear models, with limited capability to model complex relations. In our work, we use tropical semiring to introduce non-linearity into matrix factorization models. We propose a method called Sparse Tropical Matrix Factorization (STMF) for the estimation of missing (unknown) values. We evaluate the efficiency of the STMF method on both synthetic data and biological data in the form of gene expression measurements downloaded from The Cancer Genome Atlas (TCGA) database. Tests on unique synthetic data showed that STMF approximation achieves a higher correlation …

热带半环上的矩阵三因子分解

Matrix tri-factorization over the tropical semiring

本文提出热带半环上的矩阵三因子分解算法triFastSTMF，用于分析多分网络，在子网络训练预测整个网络时误差比Fast-NMTF小几个数量级。

Predicting Landfall's Location and Time of a Tropical Cyclone Using Reanalysis Data

Landfall of a tropical cyclone is the event when it moves over the land after crossing the coast of the ocean. It is important to know the characteristics of the landfall in terms of location and time, well advance in time to take preventive measures timely. In this article, we develop a deep learning model based on the combination of a Convolutional Neural network and a Long Short-Term memory network to predict the landfall's location and time of a tropical cyclone in six ocean basins of the world with high accuracy. We have used high-resolution spacial reanalysis data, ERA5, maintained by Eu…

Tropical Cyclone Track Forecasting using Fused Deep Learning from Aligned Reanalysis Data

The forecast of tropical cyclone trajectories is crucial for the protection of people and property. Although forecast dynamical models can provide high-precision short-term forecasts, they are computationally demanding, and current statistical forecasting models have much room for improvement given that the database of past hurricanes is constantly growing. Machine learning methods, that can capture non-linearities and complex relations, have only been scarcely tested for this application. We propose a neural network model fusing past trajectory data and reanalysis atmospheric images (wind and…