Usage of Multiple RTL Features for Earthquakes Prediction

Abstract

We construct a classification model, that predicts if an earthquake with the magnitude above a threshold will take place at a given location in a time range 30–180 days from now. A common approach is to use expert-generated features like Region-Time-Length (RTL) features as an input to the model. The proposed approach aggregates of multiple generated RTL features to take into account effects at various scales and to improve the quality of a machine learning model. For our data on Japan earthquakes 1992–2005 and predictions at locations given in this database, the best model provides precision as high as 0.95 and recall as high as 0.98.

Supported by Skoltech.

A Quality Metrics for Classification Problem

Introduce necessary definitions: Classification problem can be formulated as whether this object belongs to the target class or not.

• True Positive—if the object belongs to the target class and we predict that it belongs.

• True Negative—if the object doesn’t belong to the target class and we predict that it doesn’t.

• False Positive—if the object doesn’t belong to the target class but we predict that it does.

• False Negative—if the object belongs to the target class but we predict that it doesn’t.

The precision score quantifies the ability of a classifier to not label a negative example as positive. The is the probability that a positive prediction made by the classifier is positive. The score is in the range [0, 1] with 0 is the worst, and 1 is perfect. The precision score can be defined as:

$$\mathbf{Precision} = \frac{True Positive}{True Positive + False Positive}$$

The recall score quantifies the ability of the classifier to find all the positive samples. It defines what part of positive samples have been chosen by classifier as positive. The score is in the range [0, 1] with 0 is the worst, and 1 is perfect.

$$\mathbf{Recall} = \frac{True Positive}{True Positive + False Negative}$$

The F1-score is a single metric that combines both precision and recall via their harmonic mean. It measures the test accuracy and reaches its best value at 1 (perfect precision and recall) and worst at 0.

$$\mathbf{F1} = 2 \frac{Precision Recall}{Precision + Recall}$$

ROC AUC score counts the curve area under the Roc_curve. Roc_curve is the plot True Positive rate from the False Positive rate, which defines as

$$True Positive Rate = \frac{True Positive}{True Positive + False Negative}$$

$$False Positive Rate = \frac{False Positive}{False Positive + True Negative}$$

ROC AUC score measures the quality of binary classifier. The best value is 1, value 0.5 is equal to random classification.

PR AUC score counts the curve area under the Precision_Recall_curve: Precision from Recall. Precision-Recall is a useful measure of success of prediction when the classes are very imbalanced. The perfect classifier curve ends in (1.0, 1.0) and has area under it that equals 1.