# Which Clustering Algorithm Works Well for Mixed Type Data Categorical and Numerical?

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Angela Bailey

Which Clustering Algorithm Works Well for Mixed Type Data Categorical and Numerical?

Clustering is an essential tool in data analysis and machine learning that allows us to discover patterns and relationships within a dataset. While clustering algorithms are typically designed to work with homogeneous data types, such as numerical or categorical data separately, there is often a need to cluster mixed type data that contains both categorical and numerical variables. In this article, we will explore some clustering algorithms that are well-suited for handling such mixed type data.

## K-means Clustering

K-means is one of the most popular clustering algorithms due to its simplicity and efficiency. However, it is primarily designed for numerical data.

When dealing with mixed type data, we can use a technique called binary encoding, where categorical variables are transformed into binary features before applying K-means. This technique encodes each category of a variable as a binary feature (0 or 1) and allows us to incorporate categorical information into the algorithm. However, it is worth noting that K-means may still struggle with high-dimensional mixed type data due to the curse of dimensionality.

## K-prototype Clustering

K-prototype is an extension of K-means specifically designed for clustering mixed type data by combining the advantages of K-means and K-modes. While K-means handles numerical variables, K-modes works well with categorical variables.

The K-prototype algorithm assigns cluster centroids based on both numerical distances (using Euclidean distance) and categorical similarity (using simple matching dissimilarity). By considering both types of variables simultaneously, the K-prototype algorithm provides more accurate clustering results for mixed type datasets.

## Hierarchical Clustering

Hierarchical clustering is another versatile approach that can handle mixed type data. This algorithm builds a hierarchy of clusters by iteratively merging or splitting clusters based on a chosen distance metric.

In the case of mixed type data, we can use a combination of distance metrics suitable for numerical and categorical variables, such as Euclidean distance for numerical variables and Jaccard or Hamming distance for categorical variables. Hierarchical clustering allows us to visualize the clustering structure through dendrograms, making it easier to interpret and analyze the results.

## DBSCAN

DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a density-based clustering algorithm that can handle mixed type data effectively. It groups together data points that are close to each other in terms of both numerical proximity and categorical similarity.

DBSCAN does not require specifying the number of clusters in advance, making it suitable for datasets where the number of clusters is unknown. However, determining appropriate values for the epsilon (numerical proximity threshold) and minimum points parameters can be challenging, especially when dealing with mixed type data.

## GMM (Gaussian Mixture Model)

GMM is a probabilistic model that assumes data points are generated from a mixture of Gaussian distributions. It can handle both numerical and categorical variables by modeling them as continuous or discrete components within the mixture model.

GMM estimates the parameters of these components using an iterative expectation-maximization algorithm. While GMM provides more flexibility in modeling mixed type data compared to other algorithms, it may be computationally intensive and sensitive to the choice of initialization.

### Conclusion

When working with mixed type data containing both categorical and numerical variables, it’s important to choose a clustering algorithm that can effectively handle this type of data. In this article, we explored several clustering algorithms, including K-means with binary encoding, K-prototype clustering, hierarchical clustering with appropriate distance metrics, DBSCAN, and GMM. Each algorithm has its strengths and weaknesses, so it is essential to consider the specific characteristics of your dataset and the desired outcome when selecting an appropriate clustering algorithm.