Network traffic arises from the superposition of Origin-Destination (OD) flows. Hence, a thorough understanding of OD flows is essential for modeling network traffic, and for addressing a wide variety of problems including traffic engineering, traffic matrix estimation, capacity planning, forecasting and anomaly detection. However, to date, OD flows have not been closely studied, and there is very little known about their properties. We present

Source separation arises in a surprising number of signal processing applications, from speech recognition to EEG analysis. In the square linear blind source separation problem without time delays, one must find an unmixing matrix which can detangle the result of mixing n unknown independent sources through an unknown n \Theta n mixing matrix. The recently introduced ICA blind source separation algorithm (Baram and Roth 1994; Bell and Sejnowski 1995) is a powerful and surprisingly simple technique for solving this problem. ICA is all the more remarkable for performing so well despite making absolutely no use of the temporal structure of its input! This paper presents a new algorithm, contextual ICA, which derives from a maximum likelihood density estimation formulation of the problem. cICA can incorporate arbitrarily complex adaptive history-sensitive source models, and thereby make use of the temporal structure of its input. This allows it to separate in a number of situations where s...

With Islands of Music we present a system which facilitates exploration of music libraries without requiring manual genre classification. Given pieces of music in raw audio format we estimate their perceived sound similarities based on psychoacoustic models. Subsequently, the pieces are organized on a 2-dimensional map so that similar pieces are located close to each other. A visualization using a metaphor of geographic maps provides an intuitive interface where islands resemble genres or styles of music. We demonstrate the approach using a collection of 359 pieces of music.

There has been much publicity about the ability of artificial neural networks to learn and generalize. In fact, the most commonly used artificial neural networks, called multilayer perceptrons, are nothing more than nonlinear regression and discriminant models that can be implemented with standard statistical software. This paper explains what neural networks are, translates neural network jargon into statistical jargon, and shows the relationships between neural networks and statistical models such as generalized linear models, maximum redundancy analysis, projection pursuit, and cluster analysis.

Complex data types—such as images, documents, DNA sequences, etc.—are becoming increasingly important in modern database applications. A typical query in many of these applications seeks to find objects that are similar to some target object, where (dis)similarity is defined by some distance function. Often, the cost of evaluating the distance between two objects is very high. Thus, the number of distance evaluations should be kept at a minimum, while (ideally) maintaining the quality of the result. One way to approach this goal is to embed the data objects in a vector space so that the distances of the embedded objects approximates the actual distances. Thus, queries can be performed (for the most part) on the embedded objects. In this paper, we are especially interested in examining the issue of whether or not the embedding methods will ensure that no relevant objects are left out (i.e., there are no false dismissals and, hence, the correct result is reported). Particular attention is paid to the SparseMap, FastMap, and MetricMap embedding methods. SparseMap is a variant of Lipschitz embeddings, while FastMap and MetricMap are inspired by dimension reduction methods for Euclidean spaces (using KLT or the related PCA and SVD). We show that, in general, none of these embedding methods guarantee that queries on the embedded objects have no false dismissals, while also demonstrating the limited cases in which the guarantee does hold. Moreover, we describe a variant of SparseMap that allows queries with no false dismissals. In addition, we show that with FastMap and MetricMap, the distances of the embedded objects can be much greater than the actual distances. This makes it impossible (or at least impractical) to modify FastMap and MetricMap to guarantee no false dismissals.

This paper surveys the contributions of five mathematicians --- Eugenio Beltrami (1835--1899), Camille Jordan (1838--1921), James Joseph Sylvester (1814--1897), Erhard Schmidt (1876--1959), and Hermann Weyl (1885--1955) --- who were responsible for establishing the existence of the singular value decomposition and developing its theory.

This article explains the fundamental principles of transform coding; these principles apply equally well to images, audio, video, and various other types of data, so abstract formulations are given. Much of the material presented here is adapted from [14, Chap. 2, 4]. The details on wavelet transform-based image compression and the JPEG2000 image compression standard are given in the following two articles of this special issue [38], [37]

this paper was published in Proceedings of the 29th Annual ACM Symposium on Theory of Computing, pages 618--625, 1997

Spectral methods use selected eigenvectors of a data affinity matrix to obtain a data representation that can be trivially clustered or embedded in a low-dimensional space. We present a theorem that explains, for broad classes of affinity matrices and eigenbases, why this works: For successively smaller eigenbases (i.e., using fewer and fewer of the affinity matrix's dominant eigenvalues and eigenvectors), the angles between "similar" vectors in the new representation shrink while the angles between "dissimilar" vectors grow. Specifically, the sum of the squared cosines of the angles is strictly increasing as the dimensionality of the representation decreases. Thus spectral methods work because the truncated eigenbasis amplifies structure in the data so that any heuristic post-processing is more likely to succeed. We use this result to construct a nonlinear dimensionality reduction (NLDR) algorithm for data sampled from manifolds whose intrinsic coordinate system has linear and cyclic axes, and a novel clustering-by-projections algorithm that requires no post-processing and gives superior performance on "challenge problems" from the recent literature.

The Karhunen-Loeve transform (KLT) is a key element of many signal processing tasks, including approximation, compression, and classification. Many recent applications involve distributed signal processing where it is not generally possible to apply the KLT to the signal; rather, the KLT must be approximated in a distributed fashion.