Fusion Engineering and Design 85 (2010) 423–424 Contents lists available at ScienceDirect Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes Empirically derived basis functions for unsupervised classiﬁcation of radial proﬁle data D.G. Pretty a,∗ , J. Vega b , M.A. Ochando b , F.L. Tabarés b a Plasma Physics Laboratory, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200, Australia b Asociatión EURATOM/CIEMAT para Fusión, Avda Complutense 22, 28040 Madrid, Spain article info Article history: Available online 16 February 2010 Keywords: Proﬁle classiﬁcation SVD Support vector machine abstract We present an analysis of empirically derived basis vectors for feature detection in radial proﬁle data. Our aim is to classify broad and peaked proﬁles using unsupervised techniques. Radial data often con- tains a continuum of proﬁle shapes from broad to peaked, as such clustering methods may be unreliable. Previously, ad hoc heuristic measures had been used for classiﬁcation of proﬁles from raw data (without tomographic reconstruction), which required signiﬁcant manual inspection of the data. Here, we apply a singular value decomposition (SVD) to a training data matrix consisting of a concatenation of multichan- nel bolometry time series data from 103 TJ-II plasma discharges with good representation of the range of proﬁles. The second largest spatial basis vector (topo) has radial roots either side of the plasma centre, and can intuitively be interpreted as a peakedness perturbation. The inverted topo matrix can be used to process new data for automated proﬁle classiﬁcation. Finally, we show an application of this method using support vector machines to locate other signals related to the radiation proﬁle. © 2010 Elsevier B.V. All rights reserved. 1. Empirical spatial basis vectors Distinct “bell” and “dome” shaped proﬁles are observed in TJ-II bolometry (CBOL) proﬁle data. In order to allow rapid or real- time classiﬁcation of the proﬁles, it is desirable to use raw data, and tomographically reconstruct data only for speciﬁc shots of interest. Previously, an ad hoc comparison of outer bolometry chan- nels  b = CBOL13/CBOL14 was used to detect changes in proﬁle shape from raw data. A transition of  b from constant low value (1   b  4) to higher values with increased ﬂuctuation was found to correspond with a bell to dome transition. However, as the  b parameterisation is not suitable for quantitative or unsupervised use we instead use basis vectors, empirically derived using a singu- lar value decomposition (SVD) of a data matrix selected to describe the proﬁle features we wish to classify. The SVD is deﬁned as S = UAV ∗ [1] where, in the context of this paper, the rows of S are the separate bolometry timeseries channels, the columns of U and V contain the spatial (topo) and temporal (chrono) orthonormal singular vectors respectively, V ∗ denotes the conjugate transpose of V , and the diagonal matrix A contains the non-negative singular values. The SVD is closely related to principle component analysis (PCA); if the channels means are subtracted from S, the topos U correspond to the principle components of SS T . ∗ Corresponding author at: Plasma Physics Laboratory, Research School of Physical Sciences, Australian National University, Canberra, Australia. Tel.: +61 402 305 212. E-mail address: david.pretty@anu.edu.au (D.G. Pretty). Both SVD and PCA methods are widely used with fusion data, e.g. for interferometry proﬁle inversions [2] tokomak q-proﬁle con- trol [3] and ﬂuctuation mode analysis [4,5]. While these methods are generally used for feature extraction (dimensionality reduc- tion) and noise removal, here our goal is proﬁle classiﬁcation with respect to a predetermined feature, namely the peakedness of the proﬁle. As described below, when the desired feature is expressed as a singular vector we beneﬁt from the quantiﬁcation of classiﬁ- cation uncertainty. To generate the basis vectors, we construct an N c × N s data matrix S by concatenating the N c = 16 bolometry channels of 103 TJ-II discharges, where N s = number of shots × samples per shot, with pre- and post-shot noise removed. The 103 discharges selected represent a wide range of typical TJ-II plasmas in which bell and dome proﬁles have been observed. The dominant topos (columns of U with largest correspond- ing singular values) are shown in Fig. 1; the largest topo (topo 0) gives the general radial proﬁle, and the topo 1 is the perturbation which deﬁnes a peaked (ﬂattened) proﬁle when the corresponding chrono vector is positive (negative). Tomographic reconstruction of timeseries generated from these two largest topos show this inter- pretation from the raw data corresponds to the observed bell and dome shaped proﬁles. The occurrence of topo 1 as a measure of peakedness is not guaranteed by the SVD but is a consequence of the training set S being selected from shots in which the bell–dome modiﬁcation is the proﬁle perturbation with greatest signal energy. The conﬁdence in topo 1 as a reliable direct parameterisation of the basic proﬁle shape can be quantiﬁed as: p n1 = a 2 1 c 1 / ∑ i=1,2,...,15 a 2 i c i 0920-3796/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2010.01.020