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Thus, the probability, mean, and class variances for each class can be described as follows: Class C0: Background probability ω 0 = ∑ i = 1 k p i (2).
We also attempted to relax the assumption of equal within class variances, by fitting a model assuming each individual treatment has a distinct effect, but from a common class, with common class effect and a class specific variance.
The third objective function, FF, denoted the variations of miRNAs and mRNAs expression in the module, where varmi R i and varm R j were the between class variances of the ith miRNA's expression value and jth mRNA's expression value across five subtypes of MM, respectively.
Based on these matrices, we computed a class difference matrix and a squared Mahalanobis class distance matrix, that is, the squared difference between the two class element values, divided by the average of the two class variances for that particular GLEM element (Nielsen and Danielsen, 2006).
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This figure illustrates large intra class variance in each class.
In [23], minimum class variance extreme learning machine (MCVELM) was proposed for human action recognition.
However, instead of using the default average intra-class variance to define SNR, we adopt the user-specific intra-class variance to compute the user-specific SNR for each feature component to obtain an improved precision: SNR j d = ( σ d ) 2 ( σ j d ) 2 = inter - class variance intra - class variance, j ∈ { 1, 2,..., J }, d ∈ { 1, 2,..., D } (4).
The mentioned datasets are challenging for image classification because of their large intra class variance and inter class relationship.
Fig. 1 This figure illustrates that intra class variance and inter class relationship are large in real world image datasets.
Caltech 101 is a challenging dataset because of the large number of classes, intra class variance, and interclass relationship.
Based on this idea, in this work, we propose the regularized minimum class variance extreme learning machine (RMCVELM) which minimizes the empirical risk, structural risk, and intra-class variance of training data in the decision space simultaneously.
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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