SAP HANA Predictive Analysis Library (PAL)

Expected Result
PAL_SILHOUETTE_RESULT_TBL:
3.1.8 K-Medians
K-medians is a clustering algorithm similar to K-means. K-medians and K-means both partition n observations
into K clusters according to their nearest cluster center. In contrast to K-means, while calculating cluster
centers, K-medians uses medians of each feature instead of means of it.
A median value is the middle value of a set of values arranged in order.
Given an initial set of K cluster centers: m1, ..., mk, the algorithm proceeds by alternating between the following
two steps and repeats until the assignments no longer change.
●
●
Assignment step: assigns each observation to the cluster with the closest center.
Update step: calculates the new median of each feature of each cluster to be the new center of that
cluster.
The K-medians implementation in PAL supports multi-threads, data normalization, different distance level
measurements, and cluster quality measurement (Silhouette). The implementation does not support
categorical data, but this can be managed through data transformation. Because median method cannot apply
to categorical data, the K-medians implementation uses the most frequent one instead. The first K and
random K starting methods are supported.
Support for Categorical Attributes
If an attribute is of category type, it will be converted to a binary vector and then be used as a numerical
attribute. For example, in the below table, "Gender" is of category type.
Table 49:
Customer ID Age Income Gender
T1 31 10,000 Female
T2 27 8,000 Male
Because "Gender" has two distinct values, it will be converted into a binary vector with two dimensions:
Table 50:
Customer ID Age Income Gender_1 Gender_2
T1 31 10,000 0 1
T2 27 8,000 1 0
Thus, the Euclidean distance between T1 and T2 is:
SAP HANA Predictive Analysis Library (PAL)
PAL Functions P U B L I C 77