Linear Discriminant Analysis

The Linear Discriminant Analysis (LDA) is a classification algorithm, used in machine learning and pattern detection. For linearly classifiable data, it classifies the data faster than the Support Vector Machine. It also allows for dimensionality reduction, if required. It is used if two or more features convey the same information; for optimizing, the redundant features are not used in deciding the classification criteria. Basically, the LDA maximizes the ratio of the between-class variance to the within-class variance.

For practical purposes, the LDA seems to be used more often than the SVM. So we tried this classification method on our data. We obtained the following results for a Single Sensor LDA.

LDA classification results

Picking on Quiet Data too!

The idea of running the KSigma algorithm on the filtered data seemed promising after seeing the plots in the previous blog. But, what we did not realize all this while was that, if the algorithm was picking better in the quake time, it would pick better on the quiet time too. We were basically enhancing the frequencies that distinguish the quiet time from the quake time, that seemed like the reason why there were more picks in the quiet time.

Below is a plot showing this effect. The top sub plot is the original data from the SAC file. The two blue lines are the TauP estimations of the P and S wave arrival times, the first is for the P wave and the second is for the S wave.

Quiet time picking