Guided Locally Linear Embedding

• Published in: Pattern recognition letters 2011-05, Vol.32 (7), p.1029-1035
• Main Authors: Alipanahi, Babak, Ghodsi, Ali
• Format: Article
• Language: English
• Subjects: Applied sciences; Classification; Exact sciences and technology; Image processing; Information, signal and communications theory; Locally Linear Embedding; Pattern recognition; Signal and communications theory; Signal processing; Signal representation. Spectral analysis; Signal, noise; Supervised dimensionality reduction; Telecommunications and information theory
• ISSN: 0167-8655; 1872-7344
• DOI: 10.1016/j.patrec.2011.02.002

Visualizations of the embeddings acquired by GLLE on the USPS handwritten digits dataset. [Display omitted] ► Locally Linear Embedding (LLE) is an unsupervised algorithm. ► It is not possible to guide LLE toward modes of variability that may be of particular interest. ► We have proposed a novel, supervised extension to Locally Linear Embedding that we call GLLE. ► We have demonstrated the effectiveness of GLLE in classification and data visualization tasks. Nonlinear dimensionality reduction is the problem of retrieving a low-dimensional representation of a manifold that is embedded in a high-dimensional observation space. Locally Linear Embedding (LLE), a prominent dimensionality reduction technique is an unsupervised algorithm; as such, it is not possible to guide it toward modes of variability that may be of particular interest. This paper proposes a supervised variation of LLE. Similar to LLE, it retrieves a low-dimensional global coordinate system that faithfully represents the embedded manifold. Unlike LLE, however, it produces an embedding in which predefined modes of variation are preserved. This can improve several supervised learning tasks including pattern recognition, regression, and data visualization.