Computer Performance Engineering by Unknown

Author:Unknown
Language: eng
Format: epub
ISBN: 9783030444112
Publisher: Springer International Publishing

3.2 Using Robust Regression to Label Data Points

The purpose of our algorithm is to find the free flow set and the congestion set, for every day and location. More formally, we aim to find a label for each that indicates whether or . A logical first step is to determine the straight line through the origin that lies exactly between the free-flow region and the congestion region, as depicted by the black line in Fig. 2b. The slope of this line is the estimate of the critical speed of location i for each date , denoted by .

In order to obtain the critical speed and the corresponding labelling from the fundamental diagram, several methods have been studied in the literature. Examples are an iterative regression method after performing a change-point analysis [1], the use of fuzzy logic for clustering [17], and assuming a specific model for the fundamental diagram, obtaining the critical density and subsequently labelling each point [11]. However, we opt for a more intuitive and efficient method based on robust regression, to exploit the underlying structure of the fundamental diagram.

Robust regression essentially does the same as ordinary regression, yet is more robust to potential violations of the modelling assumptions (e.g. outliers), see for example [13]. To this end, each data point is assigned a weight and subsequently a linear model is fitted and a reiterative weighted least squares fit is performed (where the weights are updated each step according to the new estimate); in this way outliers have a smaller influence on the final estimates due to their lower weights and the model aims to fit the majority of the data, rather than the whole data set. We apply robust regression to the flow-density set of each location i and date j separately. Specifically, we fit the following model:

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