Understand
Data visualization is one of the major applications of nonlinear dimensionality reduction.
- From the information retrieval perspective, the quality of a visualization can be evaluated by considering the extent that the neighborhood relation of each data point is maintained while the number of unrelated points that are retrieved is minimized.
- This property can be quantified as a trade-off between the mean precision and mean recall of the visualization.
- While there have been some approaches to formulate the visualization objective directly as a weighted sum of the precision and recall, there is no systematic way to determine the optimal trade-off between these two nor a clear interpretation of the optimal value.
Built on
A nonlinear mapping for data structure analysis
Sammon, J.W.: · 1969
Earlier work this paper cites.
A global geometric framework for nonlinear dimensionality reduction
Tenenbaum, J.B., de Silva, V., Langford, J.C.: · 2000
Earlier work this paper cites.
Nonlinear dimensionality reduction by locally linear embedding
Roweis, S.T., Saul, L.K.: · 2000
Earlier work this paper cites.
Laplacian eigenmaps and spectral techniques for embedding and clustering
Belkin, M., Niyogi, P.: · 2001
Earlier work this paper cites.
Similar
Stochastic neighbor embedding
Hinton, G., Roweis, S.: · 2003
Cited alongside, same era.
Learning a kernel matrix for nonlinear dimensionality reduction
Weinberger, K.Q., Sha, F., Saul, L.K.: · 2004
Cited alongside, same era.
Estimation of non-normalized statistical models by score matching
Hyvärinen, A.: · 2005
Cited alongside, same era.
Then
Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation
Cichocki, A., Zdunek, R., Phan, A.H., Amari, S.i.: · 2009
Later among the works it cites.
Information retrieval perspective to nonlinear dimensionality reduction for data visualization
Venna, J., Peltonen, J., Nybo, K., Aidos, H., Kaski, S.: · 2010
Later among the works it cites.
Learning the information divergence
Dikmen, O., Yang, Z., Oja, E.: · 2014
Later among the works it cites.
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