The kernel density estimation is a way to approximate the probability density function of a random variable in a non-parametric way. In the case of the spotify data-set the fitted GMM is a multivariate normal distribution due to the number of features in the date-set. The fitted GMM is then evaluated on the songs in order to calculate their individual density scores. An outlier in this model would then have a low density score, meaning the probability that a song fits into any of the clusters made by the GMM is low. The then lowest density score sogns are illustrated in a bar chart plot below.
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The k-neighbor estimation detects which objects deviate from normal behavior. First, the inverse distance density estimation is calculated through the following expression,