Hypergraph based semi-supervised learning algorithms applied to speech recognition problem: a novel approach

Most network-based speech recognition methods are based on the assumption that the labels of two adjacent speech samples in the network are likely to be the same. However, assuming the pairwise relationship between speech samples is not complete. The information a group of speech samples that show very similar patterns and tend to have similar labels is missed. The natural way overcoming the information loss of the above assumption is to represent the feature data of speech samples as the hypergraph. Thus, in this paper, the three un-normalized, random walk, and symmetric normalized hypergraph Laplacian based semi-supervised learning methods applied to hypergraph constructed from the feature data of speech samples in order to predict the labels of speech samples are introduced. Experiment results show that the sensitivity performance measures of these three hypergraph Laplacian based semi-supervised learning methods are greater than the sensitivity performance measures of the Hidden Markov Model method (the current state of the art method applied to speech recognition problem) and graph based semi-supervised learning methods (i.e. the current state of the art network-based method for classification problems) applied to network created from the feature data of speech samples.

💡 Research Summary

The paper proposes a novel approach to speech‑recognition that leverages hypergraph‑based semi‑supervised learning. Traditional network‑based speech recognizers rely on the assumption that two adjacent samples in a graph are likely to share the same label. This pairwise assumption ignores higher‑order relationships: groups of samples that are mutually similar but not directly connected can convey important label information. To capture such relationships, the authors model the set of speech feature vectors as a hypergraph G = (V, E), where vertices V represent individual speech samples and hyper‑edges E connect more than two vertices simultaneously.

Construction of the hypergraph is performed by applying k‑means clustering to the feature vectors (the exact feature extraction pipeline is not detailed). Each cluster becomes a hyper‑edge; its weight is derived from intra‑cluster distances or cluster size. This yields a richer connectivity structure than a simple graph.

Three hypergraph Laplacians are defined:

1. Un‑normalized Laplacian L_un = D_v − H W Hᵀ, where D_v is the vertex degree matrix, H the incidence matrix, and W the diagonal hyper‑edge weight matrix.
2. Random‑walk Laplacian L_rw = I − D_v⁻¹ H W Hᵀ, which corresponds to a stochastic transition matrix.
3. Symmetric‑normalized Laplacian L_sym = I − D_v⁻¹ᐟ² H W Hᵀ D_v⁻¹ᐟ², preserving symmetry and ensuring eigenvalues lie in