Efficient linear dimensionality reduction and optimal multi-dimensional clustering

模式识别（PR）是人工智能的一个领域，它涉及获取原始数据并决定将样本分配到类别或类的过程。PR系统已经被研究人员广泛研究多年，在理论和应用方面-后者包括各种学科，如医学，分子生物学，生物信息学，基因组学，蛋白质组学，生物识别，安全和制造，仅举几例。PR系统的本质是设计和评估一个能够准确分类未知对象的有效分类器。无论类别是否已知，识别过程都被称为有监督或无监督。在任何情况下，设计分类器需要借助于特征（通常，作为多维向量）来表示底层对象，并且底层分类器根据对应的多维空间上的函数或算法来导出。

Pattern recognition (PR) is a field of artificial intelligence, which involves the process of taking raw data and making a decision to assign a sample to a category or class. PR systems have been extensively studied by researchers for many years, in both theoretical and application aspects - the latter includes a variety of disciplines such as medicine, molecular biology, bioinformatics, genomics, proteomics, biometrics, security and manufacturing, just to mention a few. The essence of a PR system is to devise and evaluate an efficient classifier which is able to accurately classify unknown objects. Whether or not the classes are known, the recognition process is called supervised or unsupervised. In any case, devising a classifier requires the underlying objects be represented by means of features, typically, as multi-dimensional vectors, and the underlying classifiers are derived in terms of functions or algorithms on the corresponding multi-dimensional space.