The Parzen Window method: In terms of two vectors and one matrix.
The Parzen Window method: In terms of two vectors and one matrix.
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DOI：
10.1016/j.patrec.2015.06.002
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发表时间：
2015-10-01
影响因子：
5.1
通讯作者：
Afzal AM
中科院分区：
文献类型：
--
作者：
Mussa HY;Mitchell JB;Afzal AM
我们重新审视了模式识别中广泛使用的Parzen窗口方法。Parzen窗口方法可能遭受严重的计算瓶颈。本文介绍了一种新的计划，以改善这一计算缺陷。模式分类方法基于从对象（模式）的观察属性提取的特征将对象分配到若干预定义类/类别中的一个。当L判别特征的模式可以准确地确定，模式分类问题提出了没有困难。然而，精确识别相关特征以使分类算法（分类器）能够无错误地对真实的世界模式进行分类通常是不可行的。在这种情况下，模式分类问题通常被转换为设计一个分类器，使错误分类率最小化。这样做的一种方法是将模式属性及其类别标签都视为随机变量，估计给定模式的后验类概率，然后将该模式分配给估计的后验类概率值最大的类别/类别。通常情况下，后验类概率的形式是未知的。所谓的Parzen窗口方法被广泛用于估计给定模式的类条件概率（类特定概率）密度。然后，可以利用这些概率密度来估计该模式的适当后验类概率。然而，当训练数据集的大小为数万并且L也很大（几百或更多）时，Parzen Window方案在计算上可能变得不切实际。多年来，已经提出了各种方案来改善Parzen窗口方法的计算缺陷，但该问题仍然是突出的和未解决的。在本文中，我们重新审视了Parzen窗口技术，并介绍了一种新的方法，可以绕过上述计算瓶颈。目前的论文提出了我们的想法的数学方面。所提出的方案的实际实现将在别处给出。
We revisit the Parzen Window approach widely employed in pattern recognition. The Parzen Window approach can suffer from a severe computational bottleneck. This manuscript introduces a new scheme to ameliorate this computational drawback. Pattern classification methods assign an object to one of several predefined classes/categories based on features extracted from observed attributes of the object (pattern). When L discriminatory features for the pattern can be accurately determined, the pattern classification problem presents no difficulty. However, precise identification of the relevant features for a classification algorithm (classifier) to be able to categorize real world patterns without errors is generally infeasible. In this case, the pattern classification problem is often cast as devising a classifier that minimizes the misclassification rate. One way of doing this is to consider both the pattern attributes and its class label as random variables, estimate the posterior class probabilities for a given pattern and then assign the pattern to the class/category for which the posterior class probability value estimated is maximum. More often than not, the form of the posterior class probabilities is unknown. The so-called Parzen Window approach is widely employed to estimate class-conditional probability (class-specific probability) densities for a given pattern. These probability densities can then be utilized to estimate the appropriate posterior class probabilities for that pattern. However, the Parzen Window scheme can become computationally impractical when the size of the training dataset is in the tens of thousands and L is also large (a few hundred or more). Over the years, various schemes have been suggested to ameliorate the computational drawback of the Parzen Window approach, but the problem still remains outstanding and unresolved. In this paper, we revisit the Parzen Window technique and introduce a novel approach that may circumvent the aforementioned computational bottleneck. The current paper presents the mathematical aspect of our idea. Practical realizations of the proposed scheme will be given elsewhere.