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A Statistical Matrix Representation Using Sliced Orthogonal Nonlinear Correlations for Pattern Recognition

机译:基于切片正交非线性相关性的模式识别统计矩阵表示

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In pattern recognition, the choice of features to be detected is a critical factor to determine the success or failure of a method; much research has gone into finding the best features for particular tasks. When images are detected by digital cameras, they are usually acquired as rectangular arrays of pixels, so the initial features are pixel values. Some methods use those pixel values directly for processing, for instance in normal matched filtering, whereas other methods execute some degree of pre-processing, such as binarizing the pixel values. An important tool for pattern recognition is the correlation matrix between objects and its zero-mean cousin, the covariance matrix. Because the curse of dimensionality plagues so many pattern recognition procedures, a variety of methods for dimensionality reduction have been proposed. One of the classical statistical procedures is the principal component analysis. This method (known in the communication theory literature the Karhunen-Loeve expansion ) finds a lower-dimensional representation that accounts for the variance of the features. The diagonalization of the correlation or covariance matrix is significant for image processing, because among other advantages, it implies the decomposition of images into independent components, it minimizes entropy, it minimizes the mean squared error when some terms are removed, and it is related to principal value decomposition and to factor analysis. Unfortunately the diagonalization of large matrices corresponding to the covariance matrices of images with many pixels is often beyond the capacity of even today's powerful computers. So it is clear that finding an image decomposition that easily diagonalizes a correlation matrix is of interest; in this paper, we introduce such a decomposition, which we then use in order to see some familiar pattern recognition techniques in a new light, and to propose a new and powerful approach to pattern recognition. The correlation matrix that we propose should not be confused with the classical covariance matrix between objects. Our correlation matrix is between the non-linerly transformed features of two objects.
机译:在模式识别中,要检测的特征的选择是确定方法成功与否的关键因素。为找到适合特定任务的最佳功能,已经进行了大量研究。当数码相机检测到图像时,通常会以像素的矩形阵列形式获取图像,因此初始特征是像素值。一些方法直接使用那些像素值进行处理,例如在正常匹配滤波中使用,而其他方法则执行某种程度的预处理,例如将像素值二进制化。模式识别的重要工具是对象与其零均值表亲之间的相关矩阵,即协方差矩阵。由于维数的诅咒困扰着众多的模式识别程序,因此提出了多种降低维数的方法。经典统计程序之一是主成分分析。此方法(在通信理论文献中为Karhunen-Loeve展开所知)找到了解决特征变化的较低维表示。相关性或协方差矩阵的对角线化对于图像处理非常重要,因为除其他优点外,它还意味着将图像分解为独立的分量,将熵减到最小,将某些项删除后将均方误差减到最小,并且与主值分解和因素分析。不幸的是,与具有许多像素的图像的协方差矩阵相对应的大矩阵的对角化通常甚至超出了当今功能强大的计算机的能力。因此很明显,找到一个容易对角化相关矩阵的图像分解是很有意义的。在本文中,我们介绍了这样一种分解,然后使用它来以新的视角看待一些熟悉的模式识别技术,并提出一种新颖而强大的模式识别方法。我们建议的相关矩阵不应与对象之间的经典协方差矩阵混淆。我们的相关矩阵在两个对象的非线性变换特征之间。

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