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Pattern Recognition Ku-Yaw Chang Assistant Professor, Department of Computer Science and Information Engineering Da-Yeh University

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22004/03/02Pattern Recognition Outline Introduction Features and Classes Supervised v.s. Unsupervised Statistical v.s. Structural (Syntactic) Statistical Decision Theory

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32004/03/02Pattern Recognition Supervised v.s. Unsupervised Supervised learning Using a training set of patterns of known class to classify additional similar samples Using a training set of patterns of known class to classify additional similar samples Unsupervised learning Dividing samples into groups or clusters based on measures of similarity without any prior knowledge of class membership Dividing samples into groups or clusters based on measures of similarity without any prior knowledge of class membership

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42004/03/02Pattern Recognition Supervised v.s. Unsupervised Dividing the class into two groups: Supervised learning Male features Male features Female features Female features Unsupervised learning Male v.s. Female Male v.s. Female Tall v.s. Short Tall v.s. Short With v.s. Without glasses With v.s. Without glasses …

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52004/03/02Pattern Recognition Statistical v.s. Structural Statistical PR To obtain features by manipulating the measurements as purely numerical (or Boolean) variables To obtain features by manipulating the measurements as purely numerical (or Boolean) variables Structural (Syntactic) PR To design features in some intuitive way corresponding to human perception of the objects To design features in some intuitive way corresponding to human perception of the objects

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62004/03/02Pattern Recognition Statistical v.s. Structural Optical Character Recognition (OCR) Statistical PR Statistical PR Structural PR Structural PR

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72004/03/02Pattern Recognition Statistical Decision Theory An automated classification system Classified data sets Classified data sets Selected features Selected features

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82004/03/02Pattern Recognition Statistical Decision Theory Hypothetical Basketball Association (HBA) apg : average number of points per game apg : average number of points per game To predict the winner of the game To predict the winner of the game Based on the difference between the home team’s apg and the visiting team’s apg for previous games Training set Training set Scores of previously played games Home team classified as a winner or a loser

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92004/03/02Pattern Recognition Statistical Decision Theory Given a game to be played, predict the home team to be a winner or loser using the feature: dapg = Home Team apg – Visiting Team apg

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102004/03/02Pattern Recognition Statistical Decision Theory Gamedapg Home Team Gamedapg 11.3Won16-3.1Won 2-2.7Lost171.7Won 3-0.5Won182.8Won 4-3.2Lost194.6Won 52.3Won203.0Won 65.1Won210.7Lost 7-5.4Lost2210.1Won 88.2Won232.5Won Lost240.8Lost Won25-5.0Lost Won268.1Won Lost27-7.1Lost 132.5Won282.7Won Won Lost Lost30-6.5Won

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112004/03/02Pattern Recognition Statistical Decision Theory A histogram of dapg

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122004/03/02Pattern Recognition Statistical Decision Theory The classification cannot be performed perfectly using the single feature dapg. Probability of membership in each class Probability of membership in each class With the smallest expected penalty With the smallest expected penalty Decision boundary or threshold The value T for Home Team The value T for Home Team Won: dapg is less than or equal to T Lost: dapg is greater than T

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132004/03/02Pattern Recognition Statistical Decision Theory T = -1 Home team’s apg = Home team’s apg = Visiting team’s apg = Visiting team’s apg = dapg = – = 1.3 and 1.3 > T Home team will win the game Home team will win the game T = 0.8 or -6.5 T = 0.8 achieves the minimum error rate T = 0.8 achieves the minimum error rate

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142004/03/02Pattern Recognition Statistical Decision Theory Adding an additional feature to increase the accuracy of classification dwp = Home Team wp – Visiting Team wp dwp = Home Team wp – Visiting Team wp wp denotes the winning percentage wp denotes the winning percentage

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152004/03/02Pattern Recognition Statistical Decision Theory Gamedapgdwp Home Team Gamedapgdwp Won Won Lost Won Won Won Lost Won Won Won Won Lost Lost Won Won Won Lost Lost Won Lost Won Won Lost Lost Won Won Won Lost Lost Won

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162004/03/02Pattern Recognition Statistical Decision Theory Feature vector (dapg, dwp) Presented as a scatterplot Presented as a scatterplot L W W W WW W W W W W W W W W W W W W W W L L L LL L LL L

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172004/03/02Pattern Recognition Statistical Decision Theory The feature space can be divided into two decision region by a straight line Linear decision boundary Linear decision boundary If a feature space cannot be perfectly separated by a straight line, a more complex boundary line might be used.

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182004/03/02Pattern Recognition Exercise One The values of a feature x for nine samples from class A are 1, 2, 3, 3, 4, 4, 6, 6, 8. Nine samples from class B had x values of 4, 6, 7, 7, 8, 9, 9, 10, 12. Make a histogram (with an interval width of 1) for each class and find a decision boundary (threshold) that minimizes the total number of misclassifications for this training data set.

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192004/03/02Pattern Recognition Exercise Two Can the feature vectors (x,y) = (2,3), (3,5), (4,2), (2,7) from class A be separated from four samples from class B located at (6,2), (5,4), (5,6), (3,7) by a linear decision boundary? If so, give the equation of one such boundary and plot it. If not, find a boundary that separates them as well as possible.

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