Example fpca.inverse_transform to detect outliers

[Clej]

I propose an example of using inverse_transform in FPCA to detect outliers from the reconstruction error (RE) between the input and the recovered input from the eigenspace. In other words, given a fitted fpca, a threshold and a test sample x the decision rule is:

x_hat  = fpca.inverse_transform(fpca.transform(x))
RE = lp_distance(x, x_hat, p=2) / lp_norm(x, p=2)
if RE>= threshold:
   print('x is an outlier')

In the example, we use synthetic data generated from centered gaussian processes. The nonoutliers are generated with a Gaussian kernel and the outliers are generated with an exponential kernel. There are only nontouliers in the training dataset (used to fit the FPCA and set the threshold). There are both outliers and nonoutliers in the test samples.

I tried to make my explanations as concise and intuitive as possible.

The script generates two figures: (i) the dataset and (ii) the distribution of the REs. (i)

(ii)

Finally, we output the truely detected outliers and nonoutliers.

[codecov[bot]]

Codecov Report

Merging #389 (546ea84) into develop (a4e7b04) will not change coverage. The diff coverage is n/a.

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