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学而不思则罔●▂●思而不学则殆 专业分享，敬请收藏 Chemical Pattern Recognition and its recent development Yizeng liang College of Chemistry and Chemical Engineering, Central South University Procedure of pattern recognition Chemical pattern space In general, chemical sample or a chemical engineering procedure could be expressed by a vector or a group of parameters, that is, xi=(xi1, xi2, ..., xin). In chemical pattern recognition，these parameters can be called as variables. Thus, such a sample or a procedure could be regarded as a point in n dimensional space and such a space can also be regarded as a chemical pattern space. Dimensional advantage An example from TCM: Identification by fingerprints of the same herbs Identification by fingerprints of different herbs The HPLC fingerprints of Chuangxiong from 38 different Locations Fingerprints and Quality Control in Herbal medicines Fingerprints of Jingko Biloba injections from Several different companies, how could we evaluate them quickly and reasonably? Geometric sense of vector addition Geometric sense of vector subtraction Direction and length of vector The direction of a vector is decided by all its elements, since the different ratios between them can defines different directions in linear subspace; The length of a vector is also decided by magnitudes of its elements, since we have, ||a||=(a12+….+an2)1/2 different ratios between them can defines different directions in linear subspace Subtraction of two vectors defines the distance between the two points in n dimensional space Inner product and projection between vectors Distance in pattern space and measures of similarility Distance feature in chemical pattern space： (1) Dij ? 0 ；if xi=xj ，Dij = 0 (2) Dij = Dji (3) Dik + Djk ? Dij Several measures of distance in pattern space Minkowski distance： Dij,Minkowski={?(xik- xjk)d}1/d Euclidian distance : Dij,Euclidian ={?(xik- xjk)2}1/2 Manhatten distance : Dij,Manhatten =? |xik- xjk| Hami