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This chapter explains how cluster analysis organizes information in applications such as Computer Vision and Pattern Recognition. Information is represented as points in multidimensional feature spaces where each coordinate represents a measurement. Some tools from exploratory data analysis are discussed, with an emphasis on linear projections derived from the covariance matrix. Two types of clustering are reviewed — hierarchical and partitional. Hierarchical clustering leads to nested partitions of the data. SAHN algorithms for hierarchical clustering are defined and some of the common characteristics are explained. Partitional clustering arranges data in separate clusters, as with the K-Means algorithm. The chapter ends with a discussion of validation that centers on external and internal tests of validity and tests for the number of clusters. A bibliography is provided for further reading.

A distribution function F is more peaked about a point a than the distribution G is about the point b if F((x + a)⁻) − F(−x + a) ≥ G((x + b)⁻) − G(−x + b) for every x > 0. The problem of estimating symmetric distribution functions F or G, or both, under this constraint is considered in this paper. It turns out that the proposed estimators are projections of the empirical distribution function onto suitable convex sets of distribution functions. As a consequence, the estimators are shown to be strongly uniformly consistent. The asymptotic distribution theory of the estimators is also discussed.

The aim of this paper is to use the theory of biorthogonal polynomials to derive many algorithms for solving a system of linear equations in a unified framework. These algorithms include extrapolation and projection algorithms, the most important ones being conjugate gradient-type algorithms. New algorithms are also obtained.

The speed and the accuracy of face detection algorithm are very important for network sensors applied in human-computer-interface. A new method of face detection is presented in this paper. The algorithm is based on skin color clustering features and projecting distribution characteristic. Firstly, the approach utilizes the skin color features to transform the original image into a binary-image. Then projecting the binary-image to X-axes and Y-axes respectively, two curves are obtained. Their means and variances can be obtained. Gaussian distribution curves with same means and variances can be calculated. Finally, according to the solution of Gaussian equation, an accurate face region is found. Simulation shows that the method proposed is fast and needs less computation.

The Josephson bifurcation amplifier (JBA) readout process of a superconducting qubit is analyzed quantum mechanically. We examined the dynamics of the density operator of a probe (a driven nonlinear oscillator) and a qubit coupled system during the measurement process. We have observed the qubit-probe (JBA) entangled state and it is divided into two separable states at the moment of the JBA transition begins. To readout the measurement result, however, we must wait until the two JBA states are macroscopically well separated.

This chapter explains how cluster analysis organizes information in applications such as Computer Vision and Pattern Recognition. Information is represented as points in multidimensional feature spaces where each coordinate represents a measurement. Some tools from exploratory data analysis are discussed, with an emphasis on linear projections derived from the covariance matrix. Two types of clustering are reviewed—hierarchical and partitional. Hierarchical clustering leads to nested partitions of the data. SAHN algorithms for hierarchical clustering are defined and some of the common characteristics are explained. Partitional clustering arranges data in separate clusters, as with the K-Means algorithm. The chapter ends with a discussion of validation that centers on external and internal tests of validity and tests for the number of clusters. A bibliography is provided for further reading.

Elements of the exocenter of a generalized pseudoeffect algebra (GPEA) correspond to decompositions of the GPEA as a direct sum and thus the exocenter is a generalization to GPEAs of the center of a pseudoeffect algebra. The exocenter of a GPEA is shown to be a boolean algebra, and contains the central elements as a special subclass.

In India, speed and red light violation are the main cause of accidents. Over speed reduces our reaction time and it makes difficult to control a vehicle during obstacle moves into our path. Violating the red light increases our chances of crashing. At present in India to detect the over speed vehicles and red light violation there should be an efficient and automated system. In this paper we proposed the framework of smart city traffic management and surveillance system for automatic over speeding vehicle detection and red light violation detection system. The proposed model will help to detect the vehicles having over speed and red light violation. This proposed system is based on pattern recognition and image processing techniques.