You are performing a K-means clustering algorithm on a set of data. The data has been initialized randomly with 3 clusters as follows:
| Cluster | Data Point |
|---|---|
| A | (2, –1) |
| A | (–1, 2) |
| A | (–2, 1) |
| A | (1, 2) |
| B | (4, 0) |
| B | (4, –1) |
| B | (0, –2) |
| B | (0, –5) |
| C | (–1, 0) |
| C | (3, 8) |
| C | (–2, 0) |
| C | (0, 0) |
A single iteration of the algorithm is performed using the Euclidian distance between points and the cluster containing the fewest number of data points is identified.
Calculate the number of data points in this cluster.
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Key:D
The cluster centers are A: (0, 1), B: (2, –2), and C: (0, 2). The new assignments are:
| Cluster | Data Point | New Cluster |
|---|---|---|
| A | (2, –1) | B |
| A | (–1, 2) | C |
| A | (–2, 1) | A |
| A | (1, 2) | C |
| B | (4, 0) | B |
| B | (4, –1) | B |
| B | (0, –2) | B |
| B | (0, –5) | B |
| C | (–1, 0) | A |
| C | (3, 8) | C |
| C | (–2, 0) | A |
| C | (0, 0) | A |
Cluster C has the fewest points with three.
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.