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====== Guidelines for the homework on clustering ======


  * **Data Understanding: useful as a preliminary step to capture some data property that can help the clustering analysis (8 points)**
       * Distribution analysis and suitable transformation of variables
       * Elimination of redundant variables by correlation analysis

  * **Clustering Analysis by K-means: (15 points)**
       * Identification of the best value of k
       * Characterization of the obtained clusters by using both analysis of the k centroids and comparison of the distribution of variables within the clusters and that in the whole dataset

  * **Analysis by density-based clustering (7 points)**
       * Study of the clustering parameters
       * Characterization and interpretation of the obtained clusters

  * **Analysis by hierarchical clustering (Optional - 3 points)**
    * Analysis to be performed on a sampling of the data for scalability reasons 


====== Description of the variables ======

For each car driver we observe the following quantities, measured over a certain time window of mobile activity:  

  Length = total traveled distance (m.)
  Duration = total time spent driving (sec.)
  Count = number of different trips
  Phighway = distance traveled on highways (m.)
  Pcity = distance traveled inside cities (m.)
  Length_arc_crowded = distance traveled on 20% most crowded roads (m.)
  Pnight = distance traveled at night time (m.)
  Pover = distance traveled over speed limit (m.)
  Profile = number of systematic trips, e.g., work-home
  Radius_g = radius of gyration: sparsity of location from the center of mass of the driver (mean position)
  Radius_g_L1 = radius of gyration w.r.t. L1: sparsity of location from the driver's most frequent location (e.g., home)
  Avg_Dist_L1 = average distance from L1:  average distance from the driver's most frequent location (e.g., home)
  TimeL1L2 = % time spent at locations L1 and L2 (most and second most preferred locations)
  EntropyArc = entropy on road segment frequencies, measures the diversity of roads traveled
  EntropyLocation = entropy on location frequencies, measures the diversity of places visited
  EntropyTime = entropy on hours of the day, measures the diversity of daily patterns

Notice that there are no missing values in the dataset, hence "0"s are actual "0"s, NOT missing values.