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Clustering is a fundamental unsupervised learning task in both machine learning pipelines and data analysis workflows. Besides choosing a clustering technique or algorithm, another fundamental decision when designing the model is the distance (or similarity) metric used to measure proximity between data points. This choice can affect cluster shape, sensitivity to outliers, and the overall interpretability of the results.

This article is designed to guide you toward choosing the right distance metric for your clustering solution. This choice should not be taken lightly, as it depends on multiple factors, including the type of data at hand, numeric scales, and whether variables are independent, to name a few. The explanatory guide below has been written based on the following decision tree that summarizes it all:

An Explanatory Guide to Choosing the Right Distance Metric for Clustering

At the broadest level of this decision-making guide, we first consider the type of data you have. While most clustering approaches classically focus on numeric variables, this is not necessarily the case in all situations. Common variable types include the following:

• Raw text, natural language representations like embeddings, or word frequency counts (as in TF-IDF). Text-based representations are normally expressed in vector form; thus, the choice of a suitable distance metric is often straightforward: use the cosine distance (or cosine similarity). It does not take into account the magnitude of values, but rather their direction in a vector space. In simple terms, this means it is ideal for identifying vector representations derived from similar raw texts that are highly similar to each other. Curious to learn more about these text representations? Check this article out.
• Categorical or binary data: for data variables whose values are bounded to a predefined set of categories, there are two sub-cases. For binary categoricals, such as 0/1, True/False, or Yes/No, the Jaccard distance can be a simple and effective choice, especially when the goal is to focus on shared positive matches rather than shared absences. Meanwhile, for categorical data with multiple possible values, such as a person’s hair color, country of residence, or marital status, the Hamming distance can be useful because it counts the number of positions at which two data points differ across their categorical variables.
• Continuous numeric data: these require further inspection to determine the most appropriate distance metric. Let’s look more closely.

So, you have one or several numeric variables, right? The first thing to examine is the correlation between variables and their relative magnitude levels. More specifically, do your numeric variables exhibit at least one of these two traits?

1. High correlation between variables.
2. Variables that operate on very different scales from one another, such as the age of an employee versus annual salary in USD.

If either of the above is true, you might want to consider using the Mahalanobis distance. This metric evaluates distance while accounting for correlation among multiple variables, making it robust to differing scales and automatically correcting distortions otherwise caused by highly correlated variables. For large datasets, however, this may become computationally expensive, as the metric requires calculating an inverse covariance matrix.

On the other hand, if the numeric variables are independent, orthogonal, or have been previously standardized, the next thing to examine is the spatial or geometric distribution of the data. Suppose your data is high-dimensional, sparse, or contains a relatively high number of outliers (extreme values). In that case, you would lean toward the Manhattan distance (L1), which relies on absolute differences and is generally more robust to outliers than its counterpart, Euclidean distance. By contrast, if the dimensionality of your data is small to moderate, there are few or no outliers, and you want to group data points based on straightforward geometric closeness, the Euclidean distance (L2) is the most intuitive approach.

Here is the truth in practice: because some of the issues discussed above, such as correlation, outliers, or scaling, are typically addressed before applying clustering in a data cleaning and preprocessing stage, it is not unusual to end up using L2 in many scenarios involving numeric data.

One last question may arise: what if your dataset contains mixed data types, meaning variables of different types coexist? In these cases, things become slightly more complex, but there are several possible courses of action. One is to use a special distance metric called Gower distance. Another is a hybrid reformulation of the popular k-means algorithm called k-prototypes, which can accommodate mixed data. A more pragmatic alternative is to encode all variables numerically in a way that preserves as much of their original meaning as possible before applying a clustering method.

Wrapping Up

This article presented a concise yet insightful guide to choosing the right distance metric for clustering algorithms in a variety of situations, depending on the type of data, its behavior, and other key characteristics that influence this important decision.