By Takashi Abe, Shigehiko Kanaya, Toshimichi Ikemura (auth.), José C. Príncipe, Risto Miikkulainen (eds.)
This publication constitutes the refereed court cases of the seventh foreign Workshop on Advances in Self-Organizing Maps, WSOM 2009, held in St. Augustine, Florida, in June 2009.
The forty-one revised complete papers awarded have been conscientiously reviewed and chosen from a number of submissions. The papers take care of issues within the use of SOM in lots of parts of social sciences, economics, computational biology, engineering, time sequence research, information visualization and theoretical machine science.
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Extra info for Advances in Self-Organizing Maps: 7th International Workshop, WSOM 2009, St. Augustine, FL, USA, June 8-10, 2009. Proceedings
Fig. 1. Left: the first two principal components for five engines. The data are the 7-dimensional engine variables. Right; the values of variable Y4 (HPC discharge temperature) for 4 engines. Fig. 2. Almost linear dependence between variable Y5 (EGT) and variable X10 (Total Air Temperature) The correlation between variables can be illustrated too. As an example, Figure 2 shows variable Y5 (EGT) as a function of variable X10 (Total Air Temperature) in four engines. It is obvious that both variables are strongly dependent.
A perfect binary classiﬁer ideally achieve the (0,1) coordinate at ROC space. Now, if we change the percentile Nα , the decision interval [τ − , τ + ] in Eq. (15) is modiﬁed, and a set of points in ROC space can be derived, allowing to verify the performances of the classiﬁers under diﬀerent degrees of tolerance for the quantization error. 2 A true positive is the classiﬁcation of an incoming vector x+ (t) as abnormal, when it is truly an anomalous one, and a false positive is the classiﬁcation of an incoming vector x+ (t) as abnormal when it is a normal one.
The root vertex 24 A. Argyrou represents the complete set of hierarchical data, and all other vertices are ordered in such a way that each vertex represents a sub-set of its “parent” vertex. The edges indicate the covering relation between the vertices. For example, consider a ﬁnite order set P ; x, y ∈ P ; T = (V, E, w); and vx , vy ∈ V correspond to x and y respectively. e. x ≺ y), then vx is a “child” vertex of vy . e. w : E → R+ ). Second, the graph-theoretical approach traverses the tree in a level-order manner in order to calculate the distances between the root vertex and all other vertices.