Name
Abstract | ||
|---|---|---|
One of the most commonly used data analysis tools, principal component analysis (PCA), since is based on variance maximization, assumes a circular model, and hence cannot account for the potential noncircularity of complex data. In this paper, we introduce noncircular PCA (ncPCA), which extends the traditional PCA to the case where there can be both circular and noncircular Gaussian signals in the subspace. We study the properties of ncPCA, introduce an efficient algorithm for its computation, and demonstrate its application to model selection, i.e., the detection of both the signal subspace order and the number of circular and noncircular signals. We present numerical results to demonstrate the advantages of ncPCA over regular PCA when there are noncircular signals in the subspace. At the same time, we note that since a noncircular model has more degrees of freedom than a circular one, there are cases where a circular model might be preferred even though the underlying problem is noncircular. In particular, we show that a circular model is preferred when the signal-to-noise ratio (SNR) is low, number of samples is small, or the degree of noncircularity of the signals is low. Hence, ncPCA inherently provides guidance as to when to take noncircularity into account. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1109/TSP.2011.2160631 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
noncircular principal,noncircular pca,signal subspace order,signal processing,noncircular gaussian signal,signal subspace estimation,model selection,noncircularity,data analysis,circular model,potential noncircularity,order selection,noncircular model,variance maximization,circularity,component analysis,regular pca,propriety,principal component analysis,noncircular gaussian signals,traditional pca,noncircular signal,signal-to-noise ratio,matrix decomposition,degree of freedom,symmetric matrices,data models,complex data,signal to noise ratio,vectors,data model,noise,covariance matrix | Signal processing,Subspace topology,Pattern recognition,Model selection,Gaussian,Artificial intelligence,Covariance matrix,Signal subspace,Principal component analysis,Maximization,Mathematics | Journal |
Volume | Issue | ISSN |
59 | 10 | 1053-587X |
Citations | PageRank | References |
17 | 0.68 | 16 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xi-Lin Li | 1 | 547 | 34.85 |
| Tülay Adali | 2 | 1690 | 126.40 |
| Matthew Anderson | 3 | 263 | 14.64 |