Classification mean vectors

FIGURE 5.4 Linear discriminant scores dj for group j by the Bayesian classification rule based on (Equation 5.2). mj, mean vector of all objects in group j Sp1, inverse of the pooled covariance matrix (Equation 5.3) x, object vector (to be classified) defined by m variables Pj, prior probability of group j. 

A whole spectrum of statistical techniques have been applied to the analysis of DNA microarray data [26-28]. These include clustering analysis (hierarchical, K-means, self-organizing maps), dimension reduction (singular value decomposition, principal component analysis, multidimensional scaling, or correspondence analysis), and supervised classification (support vector machines, artificial neural networks, discriminant methods, or between-group analysis) methods. More recently, a number of Bayesian and other probabilistic approaches have been employed in the analysis of DNA microarray data [11], Generally, the first phase of microarray data analysis is exploratory data analysis. 

Therefore, when it is advisable the feature selection, weighing methods determine the importance of the scaled features for a certain classification problem Consider a pattern vector X = (X j,X 2/--- ip) Assuming that the data matrix X can be p>artitioned into a number Q of classes, let xj a pattern vector belonging to class C. The averaged patterns m and represent the general mean vector and the C-class mean, according to ... 

In this work, classification through HCA was based on the Euclidean distance and the average group method. This method established links between samples/cluster. The distance between two clusters was computed as the distance between the average values (the mean vector or centroids) of the two clusters. The descriptors employed in HCA were the same selected in... 

The mean vector of a class is defined by the centre of gravity. For a binary classification of an unknown pattern vector x the scalar products with both mean vectors are calculated ... 

This clustering algorithm operates in a two-pass mode. In the first pass, the program reads through the data set and sequentially builds clusters (group of points in spectral space). There is a mean vector associated with each cluster. In the second pass, a minimum distance classification to mean vector algorithm is applied, pixel wise, where each pixel is assigned to one mean vector created in pass 1. 

The classification is based on simple Boolean logic. Training data in n spectral bands are used in performing the classification. Brightness values from each pixel of the multi-spectral imagery are used to produce an -dimensional mean vector,... 

This is a simple and commonly used classification algorithm and the classification accuracies are comparable to any other classification. The user in this classification has to provide the mean vectors for each class in each band from the training sets. In this classification distance of each mean vector is calculated for each unknown pixel this distance is calculated using Euchdian distance based on... 

Each unknown pixel is then placed in the class closest to the mean vector in this band space. For this classified image there were 16 gray levels, each representing a class, to which a color is assigned. This minimum distance classification has all seven TM bands, including the thermal (Fig. 17). 

Raw Measurement Plot In Figure 4.48 the raw data for the four unknown samples are plotted with the mean of the training samples for the four classes (A-D). The mean is the average of the measurement vectors for all samples within a class and is used as a representation of the expected features for samples that belong to the respective class. The differences in the features may indicate the source of problems for unknowns where the classifications are suspect. Figure 4.48 confirms the other diagnostic tools, which indicate that ( ) unknown 1 is not a member of any class, ( ) unknown 2 is a member of class A, (c) unknown 3 is a member of class D, and (rf) unknown 4 is most like A but has different features. 

Ciosek, P., Brudzewski, K., and Wroblewski, W. (2006a). Milk classification by means of an electronic tongue and Support Vector Machine neural network. Meas. Sci. Technol. 17(6), 1379-1384. 

The trained map can be graphically presented by 2D planes for each variable, with the variable distribution values being indicated by different colors on the different regions of the map. Additionally, the node coordinates (vectors) can be clustered by the nonhierarchical A -means classification algorithm. 

An important application of PCA is classification and pattern recognition. This particular application of PCA is described in detail in Chapter 9. The fundamental idea behind this approach is that data vectors representing objects in a high-dimensional space can be efficiently projected into a low-dimensional space by PCA and viewed graphically as scatter plots of PC scores. Objects that are similar to each other will tend to cluster in the score plots, whereas objects that are dissimilar will tend to be far apart. By efficient, we mean the PCA model must capture a large fraction of the variance in the data set, say 70% or more, in the first few principal components. 

In Figures 5.4 and 5.5 the changes that, as a consequence of the presence of the vector of infarction, are generated in the ventricular depolarisation loops in the presence of two prototype infarctions (anteroseptal and inferolateral areas, respectively) are represented. Said changes explain the presence of Q waves in the different leads by means of the loop-hemifield correlation. Some of the ECG morphologies and the QRS loops correlations in the seven types of infarctions, according to the classification... 

The most popular classification methods are Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA), Regularized Discriminant Analysis (RDA), Kth Nearest Neighbors (KNN), classification tree methods (such as CART), Soft-Independent Modeling of Class Analogy (SIMCA), potential function classifiers (PFC), Nearest Mean Classifier (NMC), Weighted Nearest Mean Classifier (WNMC), Support Vector Machine (SVM), and Classification And Influence Matrix Analysis (CAIMAN). 

Fig. 2.1. Outline of the hybrid algorithm. The unstructured array of sensors is clustered using multi-dimensional scaling (MDS) with a mutual information (MI) based distance measure. Then Vector Quantization (VQ) is used to partition the sensor into correlated groups. Each such group provides input to one module of an associative memory layer. VQ is used again to provide each module unit with a specific receptive field, i.e. to become a feature detector. Finally, classification is done by means of BCPNN.

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