Robust locally linear embedding using penalty functions

• Main Authors: Winlaw, M., Samimi Dehkordy, Leila, Ghodsi, A.
• Format: Conference Proceeding
• Language: eng ; jpn
• Subjects: Irrigation
• ISSN: 2161-4393; 2161-4407
• DOI: 10.1109/IJCNN.2011.6033516

We introduce a modified version of locally linear embedding (LLE) which is more robust to noise. This is accomplished by adding a regularization term to the reconstruction weight cost function. We propose two alternative regularization terms, the ℓ 2 -norm and the elastic-net function; a weighted average of the ℓ 2 - and ℓ 1 -norm. Adding the ℓ 2 -norm to the cost function produces more uniform weights. With noise in the data, a more uniform weight structure provides a better representation of the linear patch surrounding each data point. In the case of the elastic-net function, the addition of the ℓ 1 -norm produces sparse weights; eliminating possible outliers from the reconstruction. We use several examples to show that these methods are able to outperform LLE and are comparable to other dimensionality reduction algorithms.