A Graph Signal Processing Approach to Noise Reduction in Concept Maps

Concept maps (CMs) are graphical representations of knowledge widely used across multiple disciplines, in which concepts are represented as nodes and semantic relationships between concepts are modeled as labeled, directed edges. When concepts and relations are embedded in a metric space, signals can be naturally defined over the nodes and edges of the concept graph. In this paper, we introduce a novel approach to the study of CMs based on Graph Signal Processing (GSP) techniques for analyzing and processing signals over CMs. We address the problem of reducing the noise in word representations caused by misconceptions and semantic inaccuracies. A novel framework for filtering noisy graph signals in CMs is developed by formulating a convex optimization problem that jointly minimizes data fitting error, semantic misalignment within concept–relation–concept triplets representing sentences, and smoothness of word signals with respect to the directed graph topology. Numerical experiments demonstrate the effectiveness of the proposed approach in reducing semantic noise in CMs.