Given a K-Means clustering problem with 5 clusters and 100 data points, how many distances need to be calculated in each iteration?

Break Down the Problem

1. Identify the number of data points and clusters.
2. Calculate the number of distance calculations needed for each data point from each cluster center.

Relevant Concepts

• In K-Means clustering, for each data point, the distance to each cluster center must be calculated.

Analysis and Detail

1. Number of Data Points: $n = 100$
2. Number of Clusters: $k = 5$
3. Distance Calculations: Each of the $n$ data points has to calculate the distance to each of the $k$ cluster centers.

Calculation

The total number of distance calculations in each iteration can be calculated using the formula:

$\text{Total Distance Calculations} = n \times k$

Substituting the values:

$\text{Total Distance Calculations} = 100 \times 5 = 500$

Verify and Summarize

The total number of distances calculated in each iteration of the K-Means clustering process, considering that there are 100 data points and 5 clusters, is verified to be 500.

Final Answer

500 distances need to be calculated in each iteration.