3 Optimizations for cover
In the CoverTest.R, you can see that if the number of interval is fixed, you might get a bad result as shown below because intervals are not enough for the whole data points (Figure 1). Moreover, even you use (domain_max - domain_min) / num_intervals to get the best width size, stride cover won’t give you best data calculated from center of data points (Figure 2).
To solve the problem, you can choose only interval_width instead of intervals, and the equation is define as :
- \(stride: w\Big(1-\frac{p}{100}\Big), \text{cover_span}=(n-1)\cdot \text{stride} + w\)
- \(extension:\text {centre}\pm\tfrac{w}{2}\tfrac{p}{100}, \text{cover_span}=n\cdot w + w\frac{p}{100} = w\Big(n+\frac{p}{100}\Big)\)
To get the best n, you then get the equation below :
\(Stride:{\;n \;\ge\; \Big\lceil \frac{L - w}{\,w(1-\frac{p}{100})\,}\Big\rceil + 1\;}\)
\(Extention :{\;n \;\ge\; \Big\lceil \frac{L}{w} - \frac{p}{100}\Big\rceil\;}\)
Finally, a uniformed intervals for your data points are constructed.
