Machine learningLesson 1 of 3 in the course Unsupervised learning

K-Means Clustering: Objective, Algorithm, Evaluation, and Applications

5 flashcards · 5 quiz questions · 5 match pairs · 3 fill-in sentences · English

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Summary

This lesson introduces k-means, an unsupervised learning method for grouping observations by similarity. It explains the role of cluster centers and the objective the method optimizes.

K-means partitions nn observations into kk groups, where kk is chosen in advance and k≤nk \leq n. Each observation is represented as a vector of numerical features. The method assigns every observation to exactly one cluster.

All flashcards

What is k-means clustering?
An unsupervised method that partitions numerical observations into a chosen number, k, of groups by assigning points to nearby means and minimizing within-cluster squared distances.
What is a centroid?
The feature-wise arithmetic mean of the observations in a cluster. It represents the cluster but does not have to be an observed data point.
What does WCSS measure?
Within-cluster sum of squares: the sum, over all observations, of squared Euclidean distances from each observation to its assigned cluster centroid.
Why are distances squared in the standard objective?
Squared Euclidean distances define the standard k-means objective, which is minimized by arithmetic means and penalizes large deviations more heavily than small ones.
What are Voronoi cells in k-means?
The regions of space formed by nearest-centroid assignment. Each cell contains points closer to its centroid than to any other centroid.

Quiz questions

  1. What does the parameter k specify in k-means?Answer: The number of clusters into which the observations are partitioned.
  2. What is a cluster centroid in standard k-means?Answer: The feature-wise mean of the observations assigned to that cluster.
  3. Which quantity does standard k-means seek to minimize?Answer: The sum of squared Euclidean distances from observations to their assigned centroids.
  4. Why does standard k-means use a mean rather than a geometric median as its center?Answer: The mean minimizes the sum of squared Euclidean distances within a cluster.
  5. What geometric regions result when points are assigned to their nearest centroid?Answer: Voronoi cells, with each region containing points nearest to one centroid.

Based on the Wikipedia article K-means clustering, licensed CC BY-SA 4.0. Adapted into a summary, flashcards and quizzes.

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