Binary Encoded Patterns

If alL features are binary encoded (x = 0 or 1) some simplifications and specialities exist. One possible feature selection method determines those features which have maximum variance among the a posteriori probabilities as calculated by the Bayes rule C170, 171, 3533. 

The a posteriori probability p(mlx.=1) of a particular pattern belonging to class m under the condition that feature i has the value 1 is given by equation (101). 

In a multi category classification problem with m classes, a set 

Lowry and Isenhour C170, 1713 expanded this method by introducing a cost factor for each feature. The cost factor of feature i is proportional to the number of times a 1 appears in feature i. The weight of feature i is calculated as the product of the corresponding cost factor 

Another approach C2443 to feature selection uses information theory. (A short introduction to the information theory is given in Chapter 11.6.1). The average amount of information on a feature to distinguish patterns of class 1 from patterns of class 2 is the mutual information 

---

The normalized distance is independent of the number of dimensions C1753 the Hamming and Tanimoto distances are suitable for binary encoded patterns C353, 356, 3573. 

X.. .. X., equivalent to a binary encoded pattern vector). A associ-1 d... 

The patterns used with this method are binary encoded patterns x. Groups Cn-tuples) of n (usually 3 or 4) pattern components are randomly chosen and associated with a "memory element". A memory element has 2 addressable 1-bit-storage locations. The configuration of the bit pattern of the n-tuple is used to address one of the 2 locations. Example For n = 4 a four-bit binary pattern is interpreted as one of the decimal numbers 0 to 15. In the training stage a 1 is written into the location addressed by the n-tuple. 

The method of binary template matching is equivalent to a learning network with n = 1. A binary template of a class is the superposition (Logical "and -function) of all binary encoded patterns of that class. 

The digital learning network is a simple and fast method for the classification of binary encoded patterns. The method suffers especially from the fact that a larger data set gives less satisfactory results. 

This classification method was first applied to chemical problems by Franzen and Hillig C86, 87, 108D. Although many simplifications have been introduced into this maximum likelihood method a considerable computational effort is necessary for the training and application of such parametric classifiers. However, the effort is much smaller if binary encoded patterns are used (Chapter 5.4). 

Bayes- and Maximum Likelihood Classifiers for Binary Encoded Patterns... 

In a binary encoded pattern x each component has the discrete value of 0 or 1. The d-dimensional probability density of a class m is only defined by d probabilities p(x m) with i = 1, 2,. .. d. 

The logarithm of (86) defines a Bayes classifier for binary encoded pattern x. The discriminant function B is linear and distinguishes between two classes (equation (87)). 

Difficulties arising in applications of feature selection methods to binary encoded patterns have been discussed by Niyashita et.al. C2133. 

A feature selection method - called attribute inclusion algorithm C3653, ("attribute" is equivalent to feature) - for binary encoded patterns was applied to chemical problems by Schechter and Jurs C118, 2603. 

Crawford and Morrison C603 found for a sophisticated mass spectral interpretation program a capability of the same order as that for an undergraduate student- A similar result has been reported C1193 about the interpretation of binary encoded infrared spectra. Kowalski et. al. C162 l emphasized the superiority of pattern recognition methods in the interpretation of multidimensional data. 

Hierarchical clustering was applied to find out those wavelengths in binary encoded infrared spectra with the smallest correlations. The result was utilized for a library search C104D- Methods similar to pattern recognition have been used for the detection of atmospheric constituents by a CO2 laser C214, 2153. 

C. Encoding converts binary information into patterns of magnetic flux on a hard disk s surface. This is how the data is written to the surface. 

---