When using an unsupervised alogirthm, what is the "learning" part since it belong to machine learning field?
You said:


  and based on my personal understanding, this "adaptation" is only possible with "supervised algorithm"


However, it is not true. Let's consider a clustering method as an unsupervised algorithm like K-means. Each iteration in K-means algorithm is a basis for the next iteration of the K-means up to the convergence of the algorithm. Hence, it means we are learning the structure of the data in each iteration up to reaching a specific target value. Although it is unsupervised, we are learning the structure of the data in each iteration. Indeed, it is a kind of (unsupervised) learning at all.