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For a baseline set with mean and covariance matrix, the Mahalanobis distance of data from it is defined as.
To determine if a data point belongs to multiple clusters, we consider the distance of data points to each cluster center.
We prove that if the energy consumed by data transmission is proportional to dα+c, where d is the distance of data transmission and α and c are some constants, then for a circular area of interest with radius R, the optimal number of annuli that maximizes the network lifetime is m="R((α−1)/c)1/α for an arbitrary sensor density function.
When the fault rupture lasts a long time, the epicen-tral distance of data should be great enough to get a T S −T P exceeding the rupture duration, where T p and T S are the travel times of P and S waves.
Here, again, the most robust result (0 steps away) was by NJ analysis using Euclidean distance of data linearly normalized by the linear ratio of means.
However, vocal gap deviation (the orthogonal distance of data points to the lower-bound regression) was significantly smaller when singing reactively than when singing spontaneously, indicating that skylarks performed closer to the performance limit when challenged.
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Besides the distances of data examples to SVMs hyperplanes, the type-2 fuzzy SVMs fusion system also considers the accuracy information of individual SVMs.
Direct application of a clustering method for the automatic selection of representative clusters would take into account the inter-distances of data points resulting in biased large surface clusters that spread towards the centre of the feature space.
To take the structure of the data into account, an additional term is introduced in the likelihood, which encourages the preservation of small distances of data points from the same developmental stage (i.e. 2-cell stage, 4-cell stage,..., 64-cell stage).
The Fisher Discriminant Ratio is employed to determine a boundary between the clustered and scattered data points in one cluster, which is computed based on the distance densities of data points to the cluster centroid.
If the condition is ideal, then all the distance calculation of data points is evenly distributed to each machine and in parallel execution, so the time complexity is reduced to O nk2/m) * (numofiterations).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com