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This objective function is called sum-of-squared errors (SSE), which corresponds to minimizing within-cluster variances.
In this way, our MKDA-based ordinal regression tries to estimate the projection w minimizing within-class distance with the constraint of ordinal information.
For instance, by regarding each sub-histogram as a class, Menotti et al. [3] developed a local-adaptive method that first partitions the overall histogram into multiple sub-histograms by minimizing within-class variance and then applies HE to each sub-histogram separately.
The cluster analysis reduces n original estuaries into g groups such that 1<g<n with the general goal of <span class="lh">minimizing within-group variation and maximizing between-group variation.
Accurate stand delineation has the goal of maximizing between-stand variance while minimizing within-stand variance.
At the same time, trees aim to discriminate disjunctive homogeneous subsets by minimizing within-variance and maximizing between-variance.
For each pair of species, it computes the factor that maximizes the inter-species variance while minimizing within-species variance and therefore represents the direction along which both species are the most differentially distributed.
Unlike traditional clustering (e.g., k means or fuzzy clustering approaches) that typically involves minimizing within- and maximizing between-cluster variance, cluster identification using LCA employs a model-based approach in which the 'probabilities' of class membership are estimated from model parameters and individuals' observed scores[ 12].
For the CTree, nodes are split to minimize within-node impurity.
dCluster analysis classifies individuals on the basis of similarities of some characteristics seeking to minimize within-group variance and maximize between-group variance.
On the other hand, discriminant analysis-based methods maximize between-class variance and minimize within-class variance to separate neighboring categories with maintenance of their ordinal scales.
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