TY - JOUR
T1 - Locally multidimensional scaling by creating neighborhoods in diffusion maps
AU - Lancewicki, Tomer
AU - Aladjem, Mayer
N1 - Funding Information:
The authors would like to thank the associate editor and reviewers for their critical reading of the manuscript and helpful comments. This work was supported in part by the METRO450 Consortium, Office of the Chief scientist in Israel׳s Ministry of Economy, as well as by Applied Materials.
PY - 2014/9/2
Y1 - 2014/9/2
N2 - This paper analyzes and improves an advanced multidimensional scaling method, known as locally multidimensional scaling, which assumes that high-dimensional data lie on a low-dimensional manifold. The method preserves local distances in the manifold by using classical scaling on a set of clusters in the high-dimensional data. These clusters are called neighborhoods, and the success of the method depends on the proper selection of these neighborhoods. At present, a neighborhood set is difficult to tune, and even if done well, the method may not function properly in dealing with noisy data. Our proposal utilizes clustering in a diffusion map, and thereby improves the original method in two ways. First, neighborhood selection is easier to tune, and second, the neighborhoods chosen enable the improved method to work under noisy data conditions. Our experiments demonstrate better tuning and robustness-to-noise results compared with the original method and some other existing multidimensional scaling methods on synthetic and real data sets.
AB - This paper analyzes and improves an advanced multidimensional scaling method, known as locally multidimensional scaling, which assumes that high-dimensional data lie on a low-dimensional manifold. The method preserves local distances in the manifold by using classical scaling on a set of clusters in the high-dimensional data. These clusters are called neighborhoods, and the success of the method depends on the proper selection of these neighborhoods. At present, a neighborhood set is difficult to tune, and even if done well, the method may not function properly in dealing with noisy data. Our proposal utilizes clustering in a diffusion map, and thereby improves the original method in two ways. First, neighborhood selection is easier to tune, and second, the neighborhoods chosen enable the improved method to work under noisy data conditions. Our experiments demonstrate better tuning and robustness-to-noise results compared with the original method and some other existing multidimensional scaling methods on synthetic and real data sets.
KW - Diffusion map
KW - Dimensionality reduction
KW - Multidimensional scaling
UR - http://www.scopus.com/inward/record.url?scp=84900988430&partnerID=8YFLogxK
U2 - 10.1016/j.neucom.2014.02.019
DO - 10.1016/j.neucom.2014.02.019
M3 - Article
AN - SCOPUS:84900988430
SN - 0925-2312
VL - 139
SP - 382
EP - 396
JO - Neurocomputing
JF - Neurocomputing
ER -