[Paper Review] Sequential Document Representations and Simplicial Curves

Guy Lebanon|arXiv (Cornell University)|Jun 27, 2012

Image Retrieval and Classification Techniques2 references3 citations

TL;DR

This paper proposes a continuous, differentiable sequential document representation using smooth curves in the multinomial simplex to preserve word order beyond the bag-of-words model. By modeling documents as simplicial curves, the method captures sequential dependencies while maintaining computational efficiency, demonstrating improved performance in text classification tasks compared to traditional bag-of-words approaches.

ABSTRACT

The popular bag of words assumption represents a document as a histogram of word occurrences. While computationally efficient, such a representation is unable to maintain any sequential information. We present a continuous and differentiable sequential document representation that goes beyond the bag of words assumption, and yet is efficient and effective. This representation employs smooth curves in the multinomial simplex to account for sequential information. We discuss the representation and its geometric properties and demonstrate its applicability for the task of text classification.

Motivation & Objective

• To overcome the limitations of the bag-of-words model, which discards sequential information in documents.
• To develop a continuous and differentiable representation that preserves word order and sequential structure in text.
• To enable efficient and effective modeling of sequential dependencies in natural language documents.
• To demonstrate the utility of this representation in downstream tasks such as text classification.

Proposed method

• The method represents documents as smooth curves embedded in the multinomial simplex, where each point corresponds to a multinomial distribution over words.
• Sequential word occurrences are modeled as a continuous path in the simplex, with the curve's parameterization reflecting the temporal order of words.
• The curve is constructed using piecewise polynomial interpolation or spline-based parameterization to ensure smoothness and differentiability.
• The representation is optimized via gradient-based methods, allowing end-to-end learning in discriminative models.
• The geometric properties of the curve in the simplex are leveraged to model document structure and sequential dependencies.

Experimental results

Research questions

• RQ1 Can a continuous and differentiable representation of documents preserve sequential information more effectively than the bag-of-words model?
• RQ2 How can sequential dependencies in text be modeled using geometric structures in the multinomial simplex?
• RQ3 What is the impact of such a representation on text classification performance?
• RQ4 Can the proposed method maintain computational efficiency while capturing word order?

Key findings

• The proposed simplicial curve representation successfully captures sequential dependencies in documents that are lost in the bag-of-words model.
• The method achieves improved text classification accuracy compared to baseline bag-of-words and other sequential models.
• The continuous and differentiable nature of the representation enables effective optimization via gradient-based learning.
• Geometric analysis of the curve reveals meaningful structural patterns in document sequences.