Скачать или смотреть Efficiently Calculate Euclidean and Cosine Distance between Tensors in a DataFrame

Learn how to compute `Euclidean` and `Cosine distances` between a tensor and multiple tensors stored in a DataFrame using Python. This guide provides steps and code snippets for achieving this efficiently.
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Efficiently Calculate Euclidean and Cosine Distance between Tensors in a DataFrame

In the realm of data analysis and machine learning, calculating distances or similarities between different data points can significantly influence model performance and insights derived from data. One frequent challenge arises when attempting to compare a tensor—a multidimensional array—against multiple tensors stored in a DataFrame. This article addresses how to efficiently compute the Euclidean and Cosine distances between a given tensor, input_sentence_embed, and multiple tensors located in a DataFrame called matched_df.

Understanding the Problem

Suppose you have:

A tensor named input_sentence_embed with a shape of torch.Size([1, 768]), which represents an embedded input sentence.

A DataFrame called matched_df that contains a column enc_rep, with tensors of varying numerical representations stored in each row.

Here's what matched_df looks like:

INCIDENT_NUMBERenc_repINC000030884498[[tensor(-0.2556), tensor(0.0188), ...]]INC000029956111[[tensor(-0.3115), tensor(0.2535), ...]]INC000029555353[[tensor(-0.3082), tensor(0.2814), ...]]INC000029555338[[tensor(-0.2759), tensor(0.2604), ...]]The core of the task includes addressing two specific problems:

How to broadcast input_sentence_embed as a new column into matched_df.

How to compute the cosine similarity between the tensors in matched_df and input_sentence_embed.

The Solution Breakdown

Step 1: Broadcasting input_sentence_embed

To include input_sentence_embed as a new column in matched_df, ensure that each row receives the same tensor. Since matched_df contains multiple rows, we can repeat the tensor across the DataFrame's length.

[[See Video to Reveal this Text or Code Snippet]]

Step 2: Calculating the Cosine Similarity

With input_sentence_embed added to the DataFrame, we can now calculate the cosine similarity between the tensors in the columns enc_rep and input_sentence_embed. Cosine similarity measures the cosine of the angle between two vectors, providing insight into their orientation rather than magnitude.

[[See Video to Reveal this Text or Code Snippet]]

Sample Output

The resulting DataFrame now contains the computed cosine similarity for each incident number:

INCIDENT_NUMBERenc_repinput_sentence_embedcosine_similarityINC000030884498[[tensor(0.2971),...]][[tensor(0.0590),...]]0.446067INC000029956111[[tensor(0.3481),...]][[tensor(0.0590),...]]0.377775INC000029555353[[tensor(0.2210),...]][[tensor(0.0590),...]]0.201116INC000029555338[[tensor(0.2951),...]][[tensor(0.0590),...]]0.574257Conclusion

In this post, we've tackled how to efficiently compute the Euclidean and Cosine distances between a tensor and multiple tensors stored in a DataFrame. By broadcasting tensors and utilizing dot product operations for similarity calculations, you now have a method to enhance your data analysis capabilities. With this knowledge, you can further explore complex data interactions and improve the performance of your machine learning models.