or theoretical nature on discriminant analysis and statistical pattern recogni- tion. .. The probability density function (p.d.f.) of X in group Gi is denoted by fi(x). The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to. The book can be used as a source of reference on work of either a practical or theoretical nature on discriminant analysis and statistical pattern recognition.

Discriminant Analysis And Statistical Pattern Recognition Pdf

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Discriminant Analysis and. Statistical Pattern Recognition. GEOFFREY J. McLACHLAN. Department of Mathematics. The University of Queensland. St. Lucia. Request PDF on ResearchGate | Discriminant analysis and statistical pattern Discriminant Analysis Classification of different types of beer according to their. My recent Editor Reports have been systematically considering each of several new sampling texts in search of a good modern book that might improve on the.

The review articles of Kowalski and Render [ , Pratt et al. General information and comments are available in the book by Kowalski [35]. Although there are some applications in analytical chemistry and food analy- sis, the emphasis in this domain of sciences is on distribution-free non-para- metric methods. The known samples constitute three learning groups, namely asphalt, crude oil residue and No.

The 41 discriminating parameters absorption at particular wavelength positions caused only two misclassifications for known samples and none for the 16 unknowns. Earlier and related investigations of Kawahara et al. A more recent application described by Mattson et al. Powers and Keith used s.

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The diagnostic effectiveness of electrophoresis and specific protein assays for different diseases was evaluated in the same way by Werner et al. Seven diagnostic categories were considered normal, cirrhosis, hepatitis, A-plasmocytoma, G-plasmacytoma, systematic lupus erythematosus and nephritis.

The discriminating variables were 12 specific proteins and 5 elec- trophoresis fractions. RamsoB et al. A related but more extended investigation was done by Winkel et al. Two classification problems were considered: a 3-fold discrimination between hepatitis, fatty liver and chronic liver disease and a 5-fold discrimination which was an extension of the preceding 3-fold one.

This analysis demonstrated the need for more discriminating liver function tests in the diagnosis of chronic liver diseases and liver turnours, A supplementary study was carried out by Solberg et al. Validation of the results obtained by s1.

Different thyroid function tests were investigated by Bamett et al. Two in vitro tests PBI and T-3 uptake sufficed to give a good separation of thyrotoxic from euthyroid patients and permitted fairly good distinction of hypothyroid patients. The addition of a third test uptake made it possible to classify most patients correctly Other tests, including clinical questionnaires, were discarded as poor discriminants. Mayron et al. Very illustrative too is the paper of Wilding et al.

Jonckheer, P. Blockx, FL Bosman and J. Since each population P is normally distributed in its R parameters, this is also true for the total data set. When individual i of group p is characterized by its pattern vector Xpi, for each function f x 1,.

A-7 and A-8 where the single variates x values are replaced by the representative linear combined values which are also single variates - DS values.

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The F-ratio is maximized by seeking the appropriate vector v. Therefore the partial derivative of the ratio with respect to each component vi of v is equated to zero. It can be shown that vector v is determined except for a constant factor [lo]. If a Lagrange multiplier p and the condition expressed by eqn. The rank of B is at most that of H eqn. In fact, the number of significant discriminant dimensions is often smaller. Classification of unknown cases Now consider an individual whose group membership is unknown, for which one has measured R variables and wishes to assign it to one of the K groups.

The proba- bility of misclassification can be estimated if it is assumed that the x values are R-variate normal. Other decision rules that are also used are the minimum x2-rule and the minimum Mahalonobis distance rule.

Discriminant Analysis and Statistical Pattern Recognition

Dii is a classification function which makes it possible to decide if individual i is a member of group p. A is developed on the basis of un- standardized raw data.

It is also possible to develop discriminant functions after normalizing the variables standardizing among the groups. Basic statistical data are given in Table 2. For this purpose the standardized variables are used. The first discriminant function f I corresponds to an eigenvalue h 1 of 3. The discriminant scores for an individual i along the optimal discriminant function axes f 1 and fi are given by DS1.

Thus it can be seen that the V value far exceeds the significance level 0. A subsequent step is to establish whether the differentiation among the groups is due to both or only one discriminant function representing the highest eigenvalue X,.

Discriminant Analysis and Statistical Pattern Recognition.pdf

Since V - V, far exceeds the significance level O of the x2-distribution with 4 degrees of freedom which is Consequently both functions are retained for further analysis. Classification Figure 4 showsa map of the individuals of the three groups and the corresponding group centroids in the B-dimensional discriminant space 6Od Lsoo 3. The territorial diagram con- tains linear boundaries drawn orthogonally on half the distance between each pair of group centroids.

Table 3 gives an example for individual of the thyroid data set. The previous classification procedure was also applied to all patients, and the number of correctly classified individuals was determined. The classification results are given in Table 4. It must be noted that when this method is used, the efficiency is somewhat too optimistic However, the same results were obtained when the classification was based on Bayes estimation see eqn.

A computational example for patient is given in Table 5. Smeyers-Verbeke, D.

Masaart and D. Coomans, J. Coomans, I. Broeckaert, M. Blockx and D. Massart, Anal.

Acta, Shoenfeld and 3. Frank, W. Massy and D.

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Morrison, J. Market Res. Kowalski and C.

Bender, Anal: Chem. Nie, C. Hull, J. Jenkins, K. Steinbrenner and D. Eskes, P. Dupuis, A. Dijkstra, H.

Cooley and P. Kendall and A. Duda and P. Young and T. Massart, A. Dijkstra and L. Bender, J. There are several reasons why an initial prediction of the eventual outcome of the injury may be needed. For instance, in situations where the management of the patient is closely linked to the outcome, it provides a guide to the clinician as to whether his or her particular course of management is appropriate. It also provides a firmer basis for advice to relatives of an injured patient on the chances of recovery.

These and other reasons are discussed by Titterington et al. For these patients, the three possible outcomes were dead or vegetative, severe disability, and moderate or good recovery.

The feature vector for a patient included background information such as age and cause of injury and four clinical variables eye opening, motor response, motor re- sponse pattern, and pupil reaction.

Situations in medical diagnosis where outright rather than tentative alloca- tions to groups are made occur in mass screening programs. Suppose that in the detection of a disease, G1 consists of those individuals without the disease and G2 of those with the disease. Then in a screening program for this disease, a patient is assigned outright to either GI or G2, according to whether the diagnostic test is negative or positive. Usually, with a positive re sult, further testing is done before a final assignment is made.

For example, with the enzyme-linked immunosorbent assay ELISA test used to screen do- nated blood for antibodies to the AIDS virus, a positive test would result in a more definitive test such as the Western blot being performed Gastwirth, Anderson has given an example on patient care where an irrevocable outright assignment has to be made. It concerns the decision on whether to administer a preoperative anticoagulant therapy to a patient to reduce the risk of postoperative deep vein thrombosis.

Discriminant analysis is widely used also in the field of pattern recognition, which is concerned mainly with images. The aim of pattern recognition is to automate processes performed by humans.

For example, automatic analysis and recognition of photomicrographs of tissue cells can be used in blood tests, cancer tests, and brain-tissue studies. Another example of much current inter- est concerns the automatic recognition of images remotely sensed from earth satellites.

It is considered in Chapter In statistical pattern recognition, each pattern is considered as a single entity and is represented by a finite dimen- sional vector of features of the pattern. Hence, the recognition of patterns with respect to a finite number of predefined groups of patterns can be form- ulated within the framework of discriminant analysis.

The number of fea- tures required for recognition of a pattern may become very large if the pat- terns under study are very complex or if, as in fingerprint identification, the number of possible pattern groups is very large. Consequently, the above approach may have to be modified; see, for example, Fu and Mantas By now, there is an enormous literature on discriminant analysis, and so it is not possible to provide an exhaustive bibliography here. However, we have at- tempted to cover the main results, in particular the more recent developments.

Additional references on the earlier work may be found in the books devoted to the topic as a whole or in part by Lachenbruch a , Goldstein and Dil- lon , Klecka , and Hand a, The accompanying bibliography contains over 1, references. Please check your email for instructions on resetting your password. If you do not receive an email within 10 minutes, your email address may not be registered, and you may need to create a new Wiley Online Library account.

If the address matches an existing account you will receive an email with instructions to retrieve your username. Skip to Main Content. Geoffrey J. First published: Print ISBN: All rights reserved.If you do not receive an email within 10 minutes, your email address may not be registered, and you may need to create a new Wiley Online Library account. Another difference between parametric selection procedures is their position in the s. Steinbrenner and D. The so-called leave-one-out procedure [7] can also be used, but it is very time-consuming.

Choosing between logistic regression and discriminant analysis. Massart, Anal. The discriminating variables were 12 specific proteins and 5 elec- trophoresis fractions.