multi_norma

MultiNormA

Restricted Access!!

Citekey	Unpublished
Source Code	own, based on NormA from Paul and Themis
Learning type	unsupervised
Input dimensionality	multivariate

There are two parts to getting access to this algorithm:

1. You get the original NormA implementation from its original authors (see NormA).
2. You get the adaption of the algorithm to multivariate datasets from us after having received the original NormA implementation. We need the original authors' consent to share the code because we re-use significant parts of it.

After receiving the code from us, place the multinormats-folder within this folder. From the original NormA algorithm, we just require the library files. Place the original normats.lib-folder within the new multinormats-folder. The C-code and the matrix profile implementation are not required anymore because we switched to stumpy for MultiNormA.

Original Dependencies

• python==3.6
• numpy==1.15.4
• pandas==0.23.4
• scipy==1.1.0
• tqdm==4.28.1
• stumpy==1.9.2

Notes

Input Parameters

The MultiNorma takes a few input parameters that change all runs and a few that change the algorithms behavior or enable specific steps.

Hyper Parameter

• anomaly_window_size: subsequence length that is used for searching of recurrent subsequences and distance calculation to normal model. Normal Model length is set to three times this parameter. In practice with timeeval this heuristic worked well: heuristic:AnomalyLengthHeuristic(agg_type='max'). Algorithm is quite robust to different sizes passed here, only has to be high enough
• normal_model_percentage: Percentage of time series which should be used to construct normal model. In practice irrelevant, since max_motifs parameter overrides this.
• max_motifs: Maximum number of recurrent subsequences selected for normal model construction. Highly important parameter for resource consumption, if MultiNormA is taking up too much memory or taking too long, try a lower number here. Good preset: 4096
• random_state: Random seed for reproducibility.

Variants

• motif_detection: Specifies how recurrent subsequences for Normal Model construction should be selected from time series: stomp Matrix Profile based (stomp), random Random based (selects max_motifs / number dimensions in each dimension), mixed half of max_motifs selected with Matrix Profile based approach and the other half randomly selected. Experimentally, the mixed approach works best.
• sum_dims: Specifies how dimensions should be handled: True sums all dimensions up (not recommended), False handles them separately (recommended).
• normalize_join: True applies running mean join normalization after the distance calculation of the time series to the normal models before combining the joins dimension wise. False disables it. Enabling it is generally recommended.
• join_combine_method: Specifies how to combine the joins obtained for all dimensions (distances to normal models) . 0 sums them up unweighted (leads to problems in high-dimensions), 1 takes the max of all dimensions, 2 weighs the dimensions by a heuristic (1/(std*mean)rangedimensions), 3 scales up the upper 25% of values, 4 exponentiates the join by the number of channels. In our experiments, the max approach (1) worked best.

Post-Processing

The post-processing necessary for NormA is already part of the algorithm, so that for every data point, there is an anomaly score.

Copyright notice

The multinormats.lib part is provided under:

Authors: Paul Boniol, Michele Linardi, Federico Roncallo, Themis Palpanas Date: 08/07/2020 copyright retained by the authors algorithms protected by patent application FR2003946 code provided as is, and can be used only for research purposes

The rest is from:

Authors: Ben-Noah Engelhaupt, Leo Wendt Date: 26/03/2022