Matrix Completion for Storm Damages Prediction

Abstract

Forecasting weather disasters is very important, but still remains a big challenge for science. Aiming to tackle this issue, our study attempts to predict storm damages by using Semantic Web data (SRBench) and techniques (matrix completion methods and Statistical Unit Node Set framework). Preliminary experiments try predicting which regions are likely to be hit by the most deadly storms like hurricane Katrina (in USA, 2005). Result shows that, even with incomplete data, the approach can determine highly threatened locations at different timesteps. It also hints the ability to forecast different storm damage scenarios.

Keywords

• matrix completion
• statistical unit node set
• storm damages prediction

1 Introduction

In 2005, hurricane Katrina hit the US, killed more than 1800 people and caused about $108 billion of property loss [ 4 ]. Unfortunately, prediction of storm's intensity and track is still a big challenge for modern meteorological models. Approaching the issue differently to such models, which often require good and sufficient data, and inspired by work in [ 6 ] and [ 2 ], we propose an alternative to estimate the likelihood that storm damages may happen to some locations, based-on Semantic Web (SW) technologies.

We consider 5 hurricanes in the US provided in the SRBench data set [ 7 ]: Charley (2004), Katrina (2005), Wilma (2005), Gustav (2008) and Ike (2008). For learning and predicting, Matrix Completion (MC) methods, used in the Statistical Unit Node Set (SUNS) framework [ 6 ], are employed as the multivariate regression approach. Usually, SW data is incomplete, but multivariate learning has shown its strength in dealing with information-missing data [ 2 ]. In [ 2, 3, 6 ], the same research group combined SPARQL with MC under SUNS framework and applied it successfully with several SW data sets (such as friend-of-a-friend and gene-disease relationships). Known triples of storms' data are trans-coded into matrices by using SUNS approach, and MC process based-on Singular Value Decomposition (SVD) technique is used for filling the missing value of unknown triples. (*) Corresponding author 2.1

Constructing data matrix from SRBench

We consider “Storm” and “Location” as the center concepts, and their relationship is the objective, of the learning and predicting processes. Under the SUNS framework, they become statistical units of interest, with relationship represented by the triple form (subject, predicate, object) of the Resource Description Framework. Hence, a triple is to indicate that storm- may “hit” location- . Considering the time-series of streaming data, the triple is extended as . Value of this extended triple is 1 if is occurring over at time , and 0 otherwise.

Fig. 1 shows an example of a grid of 6 locations hit by hurricane Katrina. At tim e , truth values of 6 hitting triples corresponding to 6 locations form the i-th row of the hitting matrix. So that, an -to-6 matrix is generated for time-steps of the storm. To perform multivariate regression, data of weather attributes in each location (winddirection, wind-speed, pressure) and attributes of the storm (latitude, longitude, pressure, wind-speed) is also used to form the columns of co-variate matrices in the same way, but filling the matrices with observed values rather than truth values.

Fig. 2 represents the data matrix aggregated from the above co-variate matrices and hitting triple matrix, with new data of observation (input data of prediction) added as new rows. For predicting the occurrence of the storm in the future, for example at next 6 hrs, hitting data of the next 6hrs will replace the matrix of current hitting triple, or it can be used to expand the aggregated matrix (column-expansion).

With a training data matrix , MC is to find a matrix model , which can be considered as a generalization of , via low-rank SVD decomposition. In [ 2 ], authors introduced Reduced-rank Penalized Regression (RRPR1) algorithm: (1) (2) 2.2

Matrix Completion

SUNS framework uses MC methods based-on SVD factorization for filling unknown entries in the aggregated matrix. Low-rank SVD decomposition is defined as formula (1), with is a data matrix, and are orthonormal matrices, and is a diagonal matrix formed from the -biggest eigenvalues: where is an approximation of , is derived from SVD factorization of and is (with is the -th eigenvalue and is the balance parameter).

In Table 1, two algorithms used in our study are presented. They are adapted from SVD-Impute algorithm [ 1 ] and SOFT-Impute algorithm [ 5 ]. In preliminary experiments, data of hurricane Katrina [ 4 ] is tested, with 6 locations in Fig. 1, and 3 attributes per location and 4 attributes of the storm (lik e in Fig. 2) over 31 6-hr time-steps (31 rows and 22 columns). However, there are just 80 observed entries of 6 locations (558 entries in total), together with 124 observed entries of the hurricane, to form a sparse co-variate matrix (density ~29.9%). It is aggregated with a 31x6 matrix of current-hitting-triple and a 31x6 matrix of next-6-hr-hitting-triple to 1 The authors used the abbreviation name “RRPP”. form a 31x34 training matrix (density ~25.8%). For testing, two observations of new locations' attributes and current hitting statements are expanded as new rows (entries of the next-6-hr-hitting-triple of each row are set to 0 (unknown)).

This data is limited, but still meaningful for testing our idea. Results show that two algorithms fill the missing entries with similar patterns of other similar training observations. Both predict (0.1, 0.7, 0.1, 0.0, 0.0, 0.0) for expected pattern (0, 1, 0, 0, 0, 0) and (0.0, -0.1, -0.2, 0.0, -0.1, 0.1) for (0, 0, 0, 0, 0, 0). This means that the pattern of hurricane Katrina is reflected well, despite of missing information. In comparing root mean square error and relative error of the training process, RRPR performs slightly better than “Naive” SVD (6.687x10-2 and 2.245x10-3 comparing to 6.697x10-2 and 2.248x10-3, respectively). However, as the data is simple, the difference is very small, and two algorithms result in the same predictions. 4

Conclusion and Discussion

Even though the tested data is limited and incomplete, the recognition of hurricane Katrina's occurrence pattern indicates strongly that MC algorithms can be used for forecasting storm damages. Moreover, using SUNS approach, other types of data in SW can be used to investigate other types of disaster damages.

So far, research on bridging SW resources and weather disasters prediction seems to be undiscovered, and we can not find other similar works. In next stage, data of 5 storms will be combined for predicting storm damage index related to population of some counties in the US, and we target to add new algorithm and heuristics for improving SUNS approach. It can be applied for forecasting damages of different disaster scenarios, which is very meaningful in the context of global climate change situation.

References

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