---
id: K-Modes
aliases:
  - K-Modes: Clustering Categorical Data (Youtube)
tags: []
---

## K-Modes: Clustering Categorical Data [(Youtube)](https://www.youtube.com/watch?v=b39_vipRkUo)

- _K-Means_ cannot directly handle non-numerical (categorical) data - ==how to
  calculate the mean? What do they mean?==
  - Mapping categorical value to 0/1 cannot generate quality clusters (in
    high-dimensional space)
- _**K-Modes**_: An extension to _K-Means_ by replacing means of clusters with
  _**modes**_
  - Mode: The value that appears the most often in a **set** of data values
- <u>Dissimilarity</u> measure between object X and the center of a cluster
  $Z_l$
  - $\Phi(x_j, z_j) = 1 - n_j^{\dfrac{r}{n_l}}$ when $x_j = z_j = r$; 1 when
    $x_j \ne z_j$
    - where $z_j$ is the categorical value of attribute j in $Z_l$, $n_l$ is the
      number of objects in cluster $l$, and $n_j^r$ is the number of objects
      whose attribute value is r
- This dissimilarity measure (distance function) is _**frequency-based**_
- Algorithm is still based on iterative _object_ cluster assignment and
  _centroid_ update
- A mixture of categorical and numerical data: Using a _**K-Prototype**_ method