Classification matrix

Table IV SIMCA results, classification matrix for fractional concentrations at three sites.

The discriminate function analysis also yields classification functions for each variable (Fe, Pb, or Ni) within each group (TC, MB, TB, NMDB, KVDB, NMSB, and KVSB) and a constant for each group. Once known, the classification functions can be used to classify each of the original sherds into one of the seven possible groups. The classification matrix, obtained by treating data from the 32 original sherds with the classification functions, is given as Table VI. 

Table VI. Classification Matrix Obtained from the Original Sherd Data as Predicted from the Classifications Functions...

Table 13.18 Results of applying LDA to the data of 10 volatile compounds in order to discriminate the four groups of varietal wines. Classification matrix ...

Table 6. Classification matrix obtained by using SDA with Cross Validation...

Using the WLN-derived CROSSBOW substructure keys, modified and extended by us to a total of 336 keys, the discriminant analysis equation presented in Table VII was developed. The results of this study are shown in the classification matrix given in Table VIII. 

The evaluation of measures, which are active during the pre-crash phase, includes all possible system responses. As those systems are subject to a variety of uncertainties (e.g., due to limitations of the sensors, variability in the situation when making predictions, etc.) they will not work ideally [2]. That means they will produce unintended side effects together with the intended effects they can be visualized using a classification matrix [3] as given in Table2.1. 

As a proof-of-concept, the Lavigne group has investigated the sensor response for simple a,co-diamines with a chain lengths between two and six methylene groups. In addition, histamine was used as an analyte. The analysis was performed with the UV-Vis data obtained for a constant polymer concentration of 0.4mM, and for five different analyte concentrations between 0.5 and 5.0mM. The normalized absorption values at nine wavelengths were subjected to a LDA (see Glossary in Box 7.1). A jack-knifed classification matrix showed that the analyte can be identified with an accuracy of over 99% [23]. 

Binders improve the strength of compacts through increased plastic deformation or chemical bonding. They may be classified as matrix type, film type, and chemical. Komarek [Chem. Eng., 74(25), 154 (1967)] provides a classification of binders and lubricants used in the tableting of various materials. 

The PLS calibration set was built mixing in an agate mortar different amounts of Mancozeb standard with kaolin, a coadjuvant usually formulated in agrochemicals. Cluster analysis was employed for sample classification and to select the adequate PLS model acording with the characteristics of the sample matrix and the presence of other components. 

As a slight departure from the present classification scheme, oxide-based cermets can be either oxide particles in a metal matrix or metal particles in an oxide matrix. Such cermets are used in tool making and high-temperature applications where erosion resistance is needed. 

Matrix and tensor notation is useful when dealing with systems of equations. Matrix theory is a straightforward set of operations for linear algebra and is covered in Section A.I. Tensor notation, treated in Section A.2, is a classification scheme in which the complexity ranges upward from scalars (zero-order tensors) and vectors (first-order tensors) through second-order tensors and beyond. 

NAS. 1975. Matrix of Electrical and Fire Hazard Properties and Classification of Chemicals. National Academy of Sciences Report to US Coast Guard, Contract No. DOT-CG-41680-A(1975). 

The authors of [203-205] proposed a theory according to which the normal stresses of the matrix and filler may differ only under one condition i.e. the filler content by volume is above some critical value — when its concentration is sufficient to generate the so-called secondary network. In accordance with Privalko and Lipatov s classification [102], this concentration corresponds to the lower boundary of the high-filled class of composites. 

We will use constraint matrices to describe the classification of the isomers into various classes a given ligand partition is characterized by a matrix where each row is associated with a class and each column with an isomer in the general ligand partition. Such a matrix 0 has therefore z rows and twenty columns. In a given row, we put one in the column of the isomers belonging to the class of the row. Of course, there is one and only one non-vanishing element in each column, and... 

As stated earlier, LDA requires that the variance-covariance matrices of the classes being considered can be pooled. This is only so when these matrices can be considered to be equal, in the same way that variances can only be pooled, when they are considered equal (see Section 2.1.4.4). Equal variance-covariance means that the 95% confidence ellipsoids have an equal volume (variance) and orientation in space (covariance). Figure 33.10 illustrates situations of unequal variance or covariance. Clearly, Fig. 33.1 displays unequal variance-covariance, so that one must expect that QDA gives better classification, as is indeed the case (Fig. 33.2). When the number of objects is smaller than the number of variables m, the variance-covariance matrix is singular. Clearly, this problem is more severe for QDA (which requires m < n ) than for LDA, where the variance-covariance matrix is pooled and therefore the number of objects N is the sum of all objects... 

As an extension of perceptron-like networks MLF networks can be used for non-linear classification tasks. They can however also be used to model complex non-linear relationships between two related series of data, descriptor or independent variables (X matrix) and their associated predictor or dependent variables (Y matrix). Used as such they are an alternative for other numerical non-linear methods. Each row of the X-data table corresponds to an input or descriptor pattern. The corresponding row in the Y matrix is the associated desired output or solution pattern. A detailed description can be found in Refs. [9,10,12-18]. 

---