Subset classification

Englehart, K, Hudgins, B, Stevenson, M et al. A dynamic feedforward neural network for subset classification of myoelectric signal patterns. Engineering in Medicine and Biology Society, 1995., IEEE 17th Annual Conference 2002 1 819-820... 

As the number of conformations increases exponentially with the number of rotatable bonds, for most molecules it is not feasible to take all possible conformations into account. However, a balanced sampling of the conformational space should be ensured if only subsets arc being considered. In order to restrict the number of geometries output, while retaining a maximum of conformational diversity, ROTATE offers the possibility of classifying the remaining conformations, i.c., similar conformations can be combined into classes. The classification is based on the RMS deviation between the conformations, either in Cartesian (RMS y 7if [A]) or torsion space in [ ], The RMS threshold, which decides whether two... 

The participation of the lone-pair orbital in the cyclization process allows its classification as a so-called pseudopericyclic reaction (76JA4325 97JA4509), which is a subset of a general type of pericyclic reactions... 

The preceding strategy for the construction of decision trees provides an efficient way for inducing compact classification decision trees from a set of (x, y) pairs (Moret, 1982 Utgoff, 1988 Goodman and Smyth, 1990). Furthermore, tests based on the values of irrelevant variables are not likely to be present in the final decision tree. Thus, the problem dimensionality is automatically reduced to a subset of decision variables that convey critical information and influence decisively the system performance. 

It was noted, however, that a subset of responses known to be triggered by histamine failed to be blocked by the classical antihistaminic drugs. This, as well as further sophisticated pharmacological work, led to the classification of histamine receptors as and Hg. To simplify grossly, the receptor controls the responses familiar to every hayfever sufferer these effects can be alleviated readily by classicial antihistamines. The latter interestingly bear little or no structural similarity to histamine... 

Figure 6.12 Classification of all types of extremum or critical point that can occur in one-, two-, and three-dimensional functions a one-dimensional function can possess only a maximum or a minimum a two-dimensional function has maxima, minima, and one type of saddle point a three-dimensional function may have maxima, minima, and two types of saddle point. The arrows schematically represent gradient paths and their direction. At a maximum all gradient paths are directed toward the maximum, whereas at a minimum all gradient paths are directed away from the minimum. At a saddle point a subset of the gradient paths are directed toward the saddle point, whereas another subset are directed away from the saddle point (see Box 6.2 for more details).

Variable classification is the essential tool for the design or revamp of monitoring systems. After fixing the degree of required knowledge of the process, that is to say, the subset of variables that must be known, this technique is repeated until the selected set of instruments allows us to obtain the desired information about the process. There is a great economic incentive for robust classification because a deficient procedure will require the installation of extra instrumentation. 

Romagnoli and Stephanopoulos (1980) proposed a classification procedure based on the application of an output set assignment algorithm to the occurrence submatrix of unmeasured variables, associated with linear or nonlinear model equations. An assigned unmeasured variable is classified as determinable, after checking that its calculation may be possible through the resolution of the corresponding equation or subset of equations. 

Remark 2. The permutation matrix IIU, obtained as a by-product of the Q-R factorization procedure of A2, enables an easy classification of the unmeasured process variables, as is indicated by Eq. (4.15). The variables in subset un ru correspond to the minimum number and the location of measurements needed for the system to satisfy the estimability condition, that is, that all unmeasured variables be determinable. 

Fig. 6. All paths leading from the initial to the final points in time t contribute an interfering amplitude to the path sum describing the resultant probability amplitude for the quantum propagation. In this double slit free particle case, two paths of constant speed are local functional stationary points of the action, and these two dominant paths provide the basis for a (semiclassical) classification of subsets of paths which contribute to the path integral. In the statistical thermodynamic path expression, the path sum is equal to the off-diagonal electronic thermal density matrix...

In actual practice a number of tests must be passed at various nodes before final classification takes place. Also, a prohibitive time would be required to search a large database of models for ones which most closely approximated the actual data set. For this reascxi the concept of similarity nets is introduced. In this case, a more general model is first chosen, one which is clearly not conpletely absurd. A subset of other models which are variations of this first general model then provides the index for the final choice of model. Such a reduction in the model lists greatly reduces the search space for the closest fit. 

Decision Trees are also a well-known technique in the field [151]. They arrange a subset of the descriptor components in a hierarchical fashion (a binary tree) such that on a particular node in the tree a classification on a single descriptor component decides whether the left or the right branch underneath is followed. The leaves of the tree determine the overall classification label. Decision trees have been found useful, especially on large-scale descriptors like binary pharmacophore descriptors [152]. 

There are many advantages in using this approach to feature selection. First, chance classification is not a serious problem because the bulk of the variance or information content of the feature subset selected is about the classification problem of interest. Second, features that contain discriminatory information about a particular classification problem are usually correlated, which is why feature selection methods using principal component analysis or other variance-based methods are generally preferred. Third, the principal component plot... 

Two methods are used to evaluate the predictive ability for LDA and for all other classification techniques. One method consists of dividing the objects of the whole data set into two subsets, the training and the prediction or evaluation set. The objects of the training set are used to obtain the covariance matrix and the discriminant scores. Then, the objects of the training set are classified, so obtaining the apparent error rate and the classification ability, and the objects of the evaluation set are classified to obtain the actual error rate and the predictive ability. The subdivision into the training and prediction sets can be randomly repeated many times, and with different percentages of the objects in the two sets, to obtain a better estimate of the predictive ability. 

Table 13-4 Therapeutic Classification of Subsets in Acute Myocardial Infarction. ...

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