Machine Learning (Cluster & principal component analysis (PCA)

The aim of this TASK is the clustering of real estate with the interpretation of the resulting clusters

and dimension reduction of features. Implement all the required methods by yourself. Use a small development dataset (which you

build yourself) to show that your implementation is working properly before applying your

algorithm to the entire dataset.

All plots need proper labels and titles. Start your discussion with a short description of the plots.


1) (10 points) Cluster the real estate by looking for suitable features and normalizing them, if

necessary. Create an elbow plot for 2 ≤ k ≤ 20 and choose a suitable number of clusters k.

Do a clustering for the chosen k, visualize the resulting clusters with suitable representations

and try to characterize the clusters (which properties of the buildings in each cluster).

Tip 1: One way to characterize a cluster is to examine which features have the smallest

relative variance (i.e. are most similar).

Tip 2: In addition to the elbow method, there are other variants ("that you should know") to

determine a suitable cluster number:

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2) (15 points) Apply a principal component analysis (PCA) on the features selected in 1) and

cluster the real estate on the first 3 principal components. Again, create an elbow plot for 2 ≤

k ≤ 20 and determine the most appropriate number of clusters. Cluster with the found k and

again, characterize the resulting clusters.

 Discuss the difference between the clusters of tasks 1) and 2).

 Visualize the first 3 principal components and discuss properties that could negatively

impact clustering.

 Is it enough to use only the first 3 principal components?

Evner: Algoritme, Machine Learning (ML), Matlab and Mathematica

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