In this paper we propose a novel method for learning a Mahalanobis distance measure to be used in the KNN classification algorithm. The algorithm directly maximizes a stochastic variant of the leave-one-out KNN score on the training set. It can also learn a low-dimensional linear embedding of labeled data that can be used for data visualization and fast classification. Unlike other methods, our classification model is non-parametric, making no assumptions about the shape of the class distributions or the boundaries between them. The performance of the method is demonstrated on several data sets, both for metric learning and linear dimensionality reduction. 1

We present a novel approach to the aesthetic drawing of undirected graphs. The method has two phases: first embed the graph in a very high dimension and then project it into the 2-D plane using PCA. Experiments we have carried out show the ability of the method to draw graphs of 10 nodes in few seconds. The new method appears to have several advantages over classical methods, including a significantly better running time, a useful inherent capability to exhibit the graph in various dimensions, and an effective means for interactive exploration of large graphs.

Abstract. The spectral approach for graph visualization computes the layout of a graph using certain eigenvectors of related matrices. Some important advantages of this approach are an ability to compute optimal layouts (according to specific requirements) and a very rapid computation time. In this paper we explore spectral visualization techniques and study their properties from different points of view. We also suggest a novel algorithm for calculating spectral layouts resulting in an extremely fast computation by optimizing the layout within a small vector space.

In many physical statistical, biological and other investigations it is desirable to approximate a system of points by objects of lower dimension and/or complexity. For this purpose, Karl Pearson invented principal component analysis in 1901 and found ‘lines and planes of closest fit to system of points’. The famous k-means algorithm solves the approximation problem too, but by finite sets instead of lines and planes. This chapter gives a brief practical introduction into the methods of construction of general principal objects, i.e. objects embedded in the ‘middle ’ of the multidimensional data set. As a basis, the unifying framework of mean squared distance approximation of finite datasets is selected. Principal graphs and manifolds are constructed as generalisations of principal components and k-means principal points. For this purpose, the family of expectation/maximisation algorithms with nearest generalisations is presented. Construction of principal graphs with controlled complexity is based on the graph grammar approach.

The major goal of our work was to develop an efficient defect-oriented parametric test method for analog & mixed-signal integrated circuits based on Artificial Neural Network (ANN) classification of a selected circuit’s parameter using different methods of signal preprocessing. Thus, ANN has been used for detecting catastrophic defects in an experimental mixedsignal CMOS circuits by sensing the abnormalities in the analyzed circuit’s response and by their consequent classification into a proper category, representing either good or defective circuit. To reduce the complexity of neural network, Wavelet Decomposition (WD) is used to perform preprocessing of the analyzed parameter. This brings significant enhancement in the correct classification, and makes the neural network-based test method very efficient and versatile for detecting hard-detectable catastrophic defects. Moreover, investigation of the possibility to utilize this approach also in detection of parametric faults in analog circuits was the subject of our research as well. Therefore, a new methodology for neural network based detection of parametric defects using Principal Component Analysis (PCA) of the analyzed circuit’s response has been proposed. Since the training set selection plays a crucial role in achieving desirable classification results, we also propose a new approach to this selection employing Convex hull (qhull) graphics algorithm. As it is shown in the experiments performed, well trained neural network is not only able to detect the faulty devices but also identify the particular parameter deviation in the respective circuit element. K e y w o r d s: testing analog IC, defect detection, artificial neural networks, wavelet decomposition, principal component analysis, convex hull algorithm

Tensorial data are frequently encountered in various machine learning tasks today and dimensionality reduction is one of their most important applications. This paper extends the classical principal component analysis (PCA) to its multilinear version by proposing a novel unsupervised dimensionality reduction algorithm for tensorial data, named as uncorrelated multilinear PCA (UMPCA). UMPCA seeks a tensor-to-vector projection that captures most of the variation in the original tensorial input while producing uncorrelated features through successive variance maximization. We evaluate the UMPCA on a second-order tensorial problem, face recognition, and the experimental results show its superiority, especially in lowdimensional spaces, through the comparison with three other PCA-based algorithms. 1.

consistency

The availability of large geospatial data from different sources has dramatically increased, but for the usage of such data in geo-mashup or contextaware systems, a data fusion component is necessary. To solve the integration issue classifiers are obtained by supervised training, with feature vectors derived from textual and geospatial attributes. In an application example, a coherent part of Germany was annotated by humans and used for supervised learning. Annotation by humans is not free of errors, which decreases the performance of the classifier. We show how visual analytics techniques can be used to efficiently detect such false annotations. Especially the textual features introduce high-dimensional feature vectors, where visual analytics becomes important and helps to understand and improve the trained classifiers. Particular technical components used in our systems are scatterplots, multiple coordinated views, and interactive data drill-down. 1

In this paper, we perform gender classification based on 2.5D facial surface normals (facial needle-maps), and present two novel principal geodesic analysis (PGA) methods, weighted PGA and supervised PGA, to parameterize the facial needle-maps, and compare their performances with PGA for gender classification. Experimental results demonstrate the feasibility of gender classification based on facial needle-maps, and show that incorporating weights or pairwise relationships of labeled data into PGA improves the gender discriminating powers in the leading eigenvectors and the gender classification accuracy. 1.