What's the appropriate choice between Cosine Similarity and Euclidean Distance for measuring similarity in my dataset?

I have a dataset with numerical features, and I want to calculate the similarity between data points. Should I use Euclidean distance or cosine similarity for this task? Here’s an example of my data and how I’m calculating the similarity:

Which similarity measure (Euclidean distance or cosine similarity) is more appropriate for my dataset, and why?


  1. Cosine similarity is a suitable choice for your dataset when you want to measure similarity between data points based on the direction of the vectors in a high-dimensional space, regardless of their magnitude. This is particularly useful when dealing with text data or any data where the feature values represent magnitudes.

In the case of cosine similarity, values close to 1 indicate high similarity (data points are in similar directions), while values close to 0 indicate dissimilarity (data points are orthogonal) and negative values indicate dissimilarity with opposite directions.

Here’s an example using a dataset of text documents where cosine similarity would be appropriate:

Cosine similarity is well-suited for scenarios like document similarity, collaborative filtering, and other cases where you want to capture the similarity in orientation of the feature vectors rather than their magnitudes.

  1. Euclidean distance is a suitable choice for your dataset when you want to measure similarity based on the overall ‘closeness’ of data points in the feature space. It considers both the direction and magnitude of the vectors, making it a good option when feature magnitudes are relevant to your analysis.

In the case of Euclidean distance, smaller values indicate higher similarity (data points are close in the feature space), and larger values indicate greater dissimilarity.

Here’s an example using a dataset of numerical measurements where Euclidean distance would be appropriate:

Euclidean distance is commonly used for clustering, anomaly detection, and cases where both the direction and magnitude of feature values are important factors for determining similarity. It’s worth noting that Euclidean distance is sensitive to feature scale, so standardizing or normalizing your data might be necessary depending on your specific use case.