Localized Supervised Metric Learning on ... - Researcher - IBM

which confirms the importance of leveraging label information
into the distance metric. We also observe that
Wavelet features improve the performance significantly
for LSML, where the classification error drops by half
(from about 15% to less than 7%.)
Table 1. Classification error comparison
Expert PCA LSML
Statistic features 0.2295 0.2131 0.1475
Wavelet features NA 0.2295 0.0656
Table 2. Precision@10 retrieval results
Expert PCA LSML
Statistic features 0.6120 0.5355 0.6557
Wavelet features NA 0.5410 0.7869
Sensitivity Analysis There are two parameters in the
study: 1) the number of neighbors k in the k-NN classifier
and 2) the dimensionality d of the resulting lowdimensional
space (after PCA and LSML). Figure 3
shows the reuslts of sentivity analysis on these two parameters.
Figure 3(a) plots classification error vs. k for
all methods. Small k leads to lower classification error,
which confirms the need for a localized distance metric.
Figure 3(b) plots classification error vs. dimensionality
d for all methods except Expert, which confirms the
stability of LSML w.r.t. to different d.
6. Conclusion and Discussion
We have presented a method for deriving semantically
sound similarity measures for retrieving patients
represented by multi-dimensional time series. Our
method uses both statistical and wavelet based features
to capture the characteristics of patients, and leverages
localized supervised metric learning to incorporate
physicians’ expert domain knowledge. Experiments using
the MIMIC II database demonstrates the efficacy of
this appraoch. In future work we plan to explore ways
to explicitly incorporate temporal characteristics of the
data to further improve metric learning in this particular
context.
References
[1] MIMIC II Database.
http://physionet.org/physiobank/database/mimic2db/.
[2] X. Chen, D. Xu, G. Zhang, and R. Mukkamala. Forecasting
acute hypotensive episodes in intensive care
patients based on a peripheral arterial blood pressure
waveform. Computers in Cardiology, 36, 2000.
[3] I. Daubechies. Ten Lectures on Wavelets. SIAM,
Philadelphia, 1992.
(a) Stable with different k
(b) Stable with different d
Figure 3. LSML is stable with different parameter
values.
[4] K. Fukunaga. Introduction to Statistical Pattern Recognition.
Academic Press, San Diego, California, 1990.
[5] J. Goldberger, S. Roweis, G. Hinton, and R. Salakhutdinov.
Neighborhood component analysis. In NIPS, 2005.
[6] Y. Jia, F. Nie, and C. Zhang. Trace ratio problem revisited.
IEEE Transactions on Neural Networks, 2009.
[7] M. Saeed and R. Mark. A novel method for the efficient
retrieval of similar multiparameter physiologic time series
using wavelet-based symbolic representations. In
American Medical Informatics Association, 2006.
[8] M. Sugiyama. Dimensionality reduction of multimodal
labeled data by local fisher discriminant analysis. J.
Mach. Learn. Res., 8, 2007.
[9] F. Wang, J. Sun, T. Li, and N. Anerousis. Two heads
better than one: <strong>Metric</strong>+active learning and its applications
for it service classification. In ICDM, 2009.
[10] F. Wang and C. Zhang. Feature extraction by maximizing
the neighborhood margin. In CVPR, 2007.
[11] E. P. Xing, A. Y. Ng, M. I. Jordan, and S. Russell.
Distance metric learning, with application to clustering
with side-information. In NIPS, 2002.
[12] L. Yang. Distance metric learning: A comprehensive
survey. Technical report, Michgan State University,
2006.