Data Mining - Concepts and Techniques.

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

National Institute of Standards and Technology における超伝導研究及び生活

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

The increasing usage of the Internet and other best-effort networks for diverse multimedia communications, brings with it a stringent need for reliable transmission. For a long time, the research efforts have been concentrated on enhancing the existing error correction techniques, but during the last decades an alternative solution has emerged and gained more and more popularity. This solution mainly answers to the situation in which immediate data retransmission is either impossible (network congestion or broadcast applications) or undesirable (e.g. in conversational applications with very low delay requirements). We are referring to a specific joint source-channel coding technique known as Multiple Description Coding (MDC). Multiple description coding builds several correlated but independently decodable (preferably with equivalent quality) bitstreams, called descriptions, that are to be sent over as many independent channels. In an initial scenario these channels are working in a binary manner, in other words, if an error occurs on one channel this is considered entirely damaged and the conveyed bitstream is unusable at the so-called side decoder end. As in other robust coding methods, some amount of redundancy has to be added to the source signal, such that an acceptable reconstruction can be achieved from any of the bitstreams. Then, similar to layered coding, the reconstruction quality will be enhanced with every bitstream received, maximal reconstruction quality being attained at the so-called central decoder. The major difference with layered coding is that all “layers” have equal importance in MDC. This thesis focuses on new approaches to Multiple Description Coding in low-redundancy scenarios. We will present their application to the transmission of still images and video sequences. To this end, we have proposed new schemes based on wavelet frame decompositions, which, for computational convenience, are implemented in a lifting form. We first study new methods of building two descriptions in the temporal axis of a ”t+2D” video codec. The redundancy of the schemes is inherent to the wavelet frame transform which is equivalent to an oversampled filter bank. However, keeping the whole set given by this decomposition would yield a redundancy of a factor of 2 which could be highly inefficient if both paths were error-less. In our schemes we perform an additional subsampling of the detail subbands while keeping the obtained approximation subbands entirely. Thus the redundancy is tuned to the size of an approximation subband in a classical wavelet decomposition. However this raises a new problem which is the perfect reconstruction of such a scheme. In this part we have proven the perfect reconstruction for certain schemes and we have established choice criteria among them based on the minimization of the quantization noise. We have compared the performances of several schemes among the efficient ones in a scalable video coding context provided by the MC-EZBC (Motion Compensated Embedded Zero-trees Block Coding) codec. Two scenarios losing a whole descriptions versus losing only packets in each description have been implemented and the results have been compared to the classical critically 9 pa st el -0 00 05 90 6, v er si on 1 23 M ar 2 01 0

Présentée pour obtenir le Grade de Docteur de l'Ecole Nationale Supérieure des Télécommunications

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Présentée pour obtenir le Grade de Docteur de l'Ecole Nationale Supérieure des Télécommunications