Cosine similarity, while popular for comparing vectors, can be misleading when vector magnitudes carry significant meaning. The blog post demonstrates how cosine similarity focuses solely on the angle between vectors, ignoring their lengths. This can lead to counterintuitive results, particularly in scenarios like recommendation systems where a small, highly relevant vector might be ranked lower than a large, less relevant one simply due to magnitude differences. The author advocates for considering alternatives like dot product or Euclidean distance, especially when vector magnitude represents important information like purchase count or user engagement. Ultimately, the choice of similarity metric should depend on the specific application and the meaning encoded within the vector data.
The blog post "Don't use cosine similarity carelessly" cautions against the naive application of cosine similarity, particularly in machine learning and recommendation systems, without a thorough understanding of its implications and potential pitfalls. The author meticulously illustrates how cosine similarity, while effective in certain scenarios, can produce misleading or undesirable results when the underlying data possesses specific characteristics.
The core argument revolves around the fact that cosine similarity solely focuses on the angle between vectors, effectively disregarding the magnitude or scale of those vectors. This can be problematic when comparing items with drastically different scales of interaction or activity. For instance, in a movie recommendation system, a user who consistently rates movies highly will appear similar to another user who rates movies highly, even if their taste in genres is vastly different. This is because the large magnitude of their ratings dominates the cosine similarity calculation, obscuring the nuanced differences in their preferences. The author underscores this with an example of book recommendations, where a voracious reader may appear similar to other avid readers regardless of their preferred genres simply due to the high volume of their reading activity.
The author further elaborates this point by demonstrating how cosine similarity can be sensitive to "bursts" of activity. A sudden surge in interaction with certain items, perhaps due to a promotional campaign or temporary trend, can disproportionately influence the similarity calculations, potentially leading to recommendations that are not truly reflective of long-term preferences.
The post provides a concrete example using a movie rating dataset. It showcases how users with different underlying preferences can appear deceptively similar based on cosine similarity if one user has rated many more movies overall. The author emphasizes that this issue becomes particularly pronounced in sparsely populated datasets, common in real-world recommendation systems.
The post concludes by suggesting alternative approaches that consider both the direction and magnitude of the vectors, such as Euclidean distance or Manhattan distance. These metrics, unlike cosine similarity, are sensitive to differences in scale and are therefore less susceptible to the pitfalls described earlier. The author also encourages practitioners to critically evaluate the characteristics of their data before blindly applying cosine similarity and to consider alternative metrics when magnitude plays a crucial role in determining true similarity. The overall message is that while cosine similarity is a valuable tool, its limitations must be recognized and accounted for to ensure accurate and meaningful results.
Summary of Comments ( 70 )
https://news.ycombinator.com/item?id=42704078
Hacker News users generally agreed with the article's premise, cautioning against blindly applying cosine similarity. Several commenters pointed out that the effectiveness of cosine similarity depends heavily on the specific use case and data distribution. Some highlighted the importance of normalization and feature scaling, noting that cosine similarity is sensitive to these factors. Others offered alternative methods, such as Euclidean distance or Manhattan distance, suggesting they might be more appropriate in certain situations. One compelling comment underscored the importance of understanding the underlying data and problem before choosing a similarity metric, emphasizing that no single metric is universally superior. Another emphasized how important preprocessing is, highlighting TF-IDF and BM25 as helpful techniques for text analysis before using cosine similarity. A few users provided concrete examples where cosine similarity produced misleading results, further reinforcing the author's warning.
The Hacker News post "Don't use cosine similarity carelessly" (https://news.ycombinator.com/item?id=42704078) sparked a discussion with several insightful comments regarding the article's points about the pitfalls of cosine similarity.
Several commenters agreed with the author's premise, emphasizing the importance of understanding the implications of using cosine similarity. One commenter highlighted the issue of scale invariance, pointing out that two vectors can have a high cosine similarity even if their magnitudes are vastly different, which can be problematic in certain applications. They used the example of comparing customer purchase behavior where one customer buys small quantities frequently and another buys large quantities infrequently. Cosine similarity might suggest they're similar, ignoring the significant difference in total spending.
Another commenter pointed out that the article's focus on document comparison and TF-IDF overlooks common scenarios like comparing embeddings from large language models (LLMs). They argue that in these cases, magnitude does often carry significant semantic meaning, and normalization can be detrimental. They specifically mentioned the example of sentence embeddings, where longer sentences tend to have larger magnitudes and often carry more information. Normalizing these embeddings would lose this information. This commenter suggested that the article's advice is too general and doesn't account for the nuances of various applications.
Expanding on this, another user added that even within TF-IDF, the magnitude can be a meaningful signal, suggesting that document length could be a relevant factor for certain types of comparisons. They suggested that blindly applying cosine similarity without considering such factors can be problematic.
One commenter offered a concise summary of the issue, stating that cosine similarity measures the angle between vectors, discarding information about their magnitudes. They emphasized the need to consider whether magnitude is important in the specific context.
Finally, a commenter shared a personal anecdote about a machine learning competition where using cosine similarity instead of Euclidean distance drastically improved their results. They attributed this to the inherent sparsity of the data, highlighting that the appropriateness of a similarity metric heavily depends on the nature of the data.
In essence, the comments generally support the article's caution against blindly using cosine similarity. They emphasize the importance of considering the specific context, understanding the implications of scale invariance, and recognizing that magnitude can often carry significant meaning depending on the application and data.