## 3 Literature Survey
### Frameworks for Data Reduction
The method for evaluating the vector of \(p\)-values is to control the false discovery rate (FDR) using the Benjamini-Hochberg procedure [96]. A case study using data from the UCI Machine Learning Repository [97] reduced an initial set of 4764 features to 623 [98]. For instance reduction, [PERSON] et al. (2016) employ a framework based on two clustering algorithms, affinity propagation (AP) and k-nearest neighbor (k-NN), to extract \"exemplars\", or representations of some number of actual data points [99]. A clustering algorithm is employed to cluster the data instances into similar groups; an exemplar is then defined to represent the group. The context is in network security, specifically anomaly detection. The idea is that records for http traffic and network data under normal circumstances can be grouped or aggregated into representations of those conditions, which can produce cost savings in data storage. The technique is potentially extendable to other areas of manufacturing, although for mature processes there may not be the desire to perform aggregation of records because the \"easy\" relationships have already been discovered. Rather, a large number of records may be necessary to identify hidden structures or correlations in subgroups that might otherwise, in smaller sample sizes, be considered outliers [100; 101]. A second instance reduction [PERSON], [PERSON], and [PERSON] (2010) develop an instance reduction framework that draws a distinction between instances close to class boundaries and instances farther away from class boundaries [102]. The reasoning is that instances farther away from class boundaries are less critical to the classification process and are therefore more \"expendable\" from an instance reduction standpoint. The four-step framework first uses a filtering component such as ENN to smooth class boundaries and then classifies instances as \"border\" and \"non-border\". Following a pruning step for the border instances, the non-border instances are clustered using mean shift clustering (MSC). As previously indicated, the reviewed articles from the Section 3.3, summarized in Table 4, cover reductions in the number of samples required to obtain a satisfactory result, techniques to reduce the number of instances or records, and techniques to reduce the number of features or attributes. Of greatest interest to this review is the second category, feature selection, and two approaches seen in this section merit further discussion in relation to each other. The first approach, the TSFRESH approach, generates a list of up to 794 features from a single time series and, using statistical independence as the test, reduces the feature set by eliminating the features that do not exhibit a significant statistical dependence with the response. Using this approach, a model with N time series  
Figure 2: High-level TSFRESH process  
inputs would have 794 N features extracted by TSFRESH. Even if TSFRESH then filters out 50% of the features, there still could remain many hundreds of features in the model. This could be an excessive number of features that strains the capacity of the analyst to truly grasp what is going on or pinpoint the critical relationship(s) of interest. Extending the approach to include subsequent filter(s) could be a step in remedying this challenge. The second approach of interest is the use of optimization heuristics to obtain a near-optimal subset of features for the problem at hand. It might be a reasonable extension to TSFRESH to incorporate a second filter that seeks to better optimize the feature set with respect to the objective function, possibly using a heuristic such as simulated annealing. This would also add the dimension of feature interaction, which is currently not present in the TSFRESH statistical independence filter.