Spectral embedding finds meaningful (relevant) structure in image and microarray data

BMC Bioinformatics

Table 2 LOO-CV classification error rates for six DR methods and three classifiers (fibroblast data)

		PCA (cor)	PCA (cov)	Nonmetric MDS	kernel PCA^†	Spectral Ng *et al*.^‡	Spectral Lafon
*KNN ( k = 2)	Pan paniscus	27.27%–41.02%	0%–13.71%	0%–13.69%	0%–9.13%	0%–9.02%	0%
	Gorilla gorilla	8.33%–29.39%	8.33%–12.61%	8.33%–12.42%	8.33%–12.49%	8.33%–29.33%	0%
	Homo sapiens	4.55%	0%–2.28%	0%–2.22%	0%–2.26%	0%–4.66%	0%
	Total	20.09%	2.22%–7.83%	2.22%–7.74%	2.22%–6.79%	2.22%–13.93%	0%
*KNN ( k = 3)	Pan paniscus	27.27%	18.18%	18.18%	9.09%	9.09%	0%
	Gorilla gorilla	8.33%	16.67%	16.67%	16.67%	25%	0%
	Homo sapiens	4.55%	4.55%	4.55%	0%	0%–3.04%	0%
	Total	11.11%	11.11%	11.11%	8.56%	8.88%–13.79%	0%
QDA	Pan paniscus	72.73%	9.09%	9.09%	0%	0%	0%
	Gorilla gorilla	16.67%	8.33%	8.33%	0%	8.33%	0%
	Homo sapiens	4.55%	0%	0%	0%	0%	0%
	Total	24.44%	4.44%	4.44%	0%	2.22%	0%
LDA	Pan paniscus	18.18%	9.09%	9.09%	0%	0%	**9.09%
	Gorilla gorilla	25%	8.33%	8.33%	8.33%	41.67%	0%
	Homo sapiens	0%	0%	0%	0%	9.09%	0%
	Total	11.11%	4.44%	4.44%	2.22%	15.56%	**2.22%

*The k-nearest neighbors (KNN) classifier was calculated over 1,000 independent trials for the mean error rates to be determined. Range of error values indicate that one or more trials provided a smaller error rate, though the average was computed.
† KNN k = 2: ε = 174,000; KNN k = 3: ε = 57,000; QDA: ε = 67,000; LDA: ε = 73,000
^‡ KNN k = 2: ε = 21,000; KNN k = 3: ε = 21,000; QDA: ε = 20,000; LDA: ε = 20,000
**The 9.09% error rate corresponds to a single Pan paniscus sample that is misclassified by LOO-CV using LDA as a classifier.

ISSN: 1471-2105