1. Making classifiers by supervised learning
Naïve Bayes
Support Vector Machine
Fisher’s discriminant
Logistic
Mahalanobis
Optimal hyperplane
Non-plasma cells
Plasma cells

2. Naïve Bayes Classifier
where, C and ¬C represent plasma cell and non-plasma cell, and Fi represent i-th different discrete fluorescence data. Using Bayes’ theorem,
Statistical independence
Our model makes the simplifying assumption that, conditional on the state of the cell (i.e. C/¬C), the fluorescence data are independent: i.e.,
Conditional independence
Similarly, for the non-plasma cell, we can calculate its probability by the following equation,
Finally, log-likelihood ratio can be written as following,

3. SVM (Hard margin) Distance between hyper plane and xi :
Maximize margin:
Scaling:
Pattern Recognition And Machine Learning (Christopher M. Bishop)

4. Quadratic programming (Primal and dual form)
Lagrangian:
KKT conditions
QP:
By SMO
Only a few ai will be greater than 0 (support vectors), which lie on the margin and satisfy

5. SVM (Soft margin)
Lagrangian:
QP:

6. Kernel trick (non-linear classification)
Ex.

7. Fisher discriminant analysis
射影されたクラスの平均の分離度
Within class variance with label k
(1), (2), (3), (4)を代入
Maximize J(w)
scalar

8. Cluster 16 = plasma cells

9. Naïve Bayes Classification
Plasma cells
Non-plasma cells
Naïve Bayes Classification
True
Plasma
Non-plasma
prediction
1477 99
Non-Plasma
135
98289
Sensitivity = %
Specificity = %

10. SVM classification (Radial kernel)
Plasma cells
Non-plasma cells
SVM Classification
True
Plasma
Non-plasma
prediction
1564 26
Non-Plasma 48
98362
Sensitivity = %
Specificity = %

11. Summary of classification

12. Distance from a point to a plane