Background: Spatially resolved transcriptomics (ST) measures gene expression along with the spatial coordinates of measurements. The analysis ST data involves significant computation complexity. In this work, we propose a dimensionality reduction algorithm that retains structure. Methods: We combine wavelet transformation matrix factorization to select spatially-varying ge...

Abstract—What matrix factorization methods do is reduce the dimensionality of data without losing any important information. In this work, we present Non-negative Matrix Factorization (NMF) method, focusing on its advantages concerning other factorization. We discuss main optimization algorithms, used to solve NMF problem, and their convergence. The paper also contains a comparative study betwe...

• Clusters of dimensionality reduction results are interpreted using Shapley values. Summary visualizations convey the decisions processes. values can reveal ubiquitous information medical datasets. Dimensionality (DR) techniques have been consistently supporting high-dimensional data analysis in various applications. Besides patterns uncovered by these techniques, interpretation DR based on ea...

Article history: Received 15 December 2008 Received in revised form 4 June 2009 Accepted 16 June 2009 Available online 24 June 2009

Analysis of Molecular Motion using Non-Linear Dimensionality