Identifying Multi-Dimensional Co-Clusters in Tensors Based on Hyperplane Detection in Singular Vector Spaces.

Area of Science:

• Data Mining and Machine Learning
• Bioinformatics
• Computational Biology

Background:

• Co-clustering, or biclustering, is vital for analyzing high-dimensional data like gene expression and text.
• Multi-dimensional arrays (tensors) are increasingly common, necessitating advanced co-clustering methods.
• Detecting coherent patterns across all data modes is crucial for robust analysis.

Purpose of the Study:

• To propose a novel co-clustering method, HDSVS, for multi-dimensional data analysis.
• To develop a technique capable of identifying coherent patterns in tensors.
• To validate the proposed method's performance on synthetic and real-world biological data.

Main Methods:

• Higher-Order Singular Value Decomposition (HOSVD) to decompose tensors into core and singular vector matrices.
• Linear Grouping Algorithm (LGA) for clustering row vectors of singular vector matrices.
• Hyperplane detection in singular vector spaces for identifying multi-dimensional co-clusters.

Main Results:

• HDSVS demonstrated favorable performance on synthetic noisy and overlapped data.
• Experiments with gene expression and embryonic cell lineage data confirmed HDSVS's reliability.
• Detected co-clusters showed strong consistency with genetic pathways and gene ontology annotations.

Conclusions:

• HDSVS is a robust and stable co-clustering method for multi-dimensional data.
• The method effectively identifies biologically relevant patterns in complex datasets.
• HDSVS outperforms state-of-the-art methods in detecting multi-dimensional co-clusters.