1. MAS 622J Course Project
Classification of Affective States - GP Semi-Supervised Learning, SVM and kNN
Hyungil Ahn

2. Objective & Dataset Recognize the affective states of a child solving
a puzzle
Affective Dataset
features from Face, Posture, Game
- 3 affective states, labels annotated by teachers
High interest (61), Low interest (59), Refreshing (16)
The dataset consists of samples on which all teachers agreed on the label of affective states
Refreshing?
Affective Dataset
features from the three modalities (face, posture and game information)
- 3 affective states (labels) annotated by teachers (high interest, low interest
and refreshing)
- High (61 samples), Low (59 samples), Refreshing (16 samples)
Classification Task
Binary classification -- { High interest } vs. { Low interest or Refreshing }

3. Task & Approaches Binary Classification High interest (61 samples) vs.
Low Interest or Refreshing (75 samples)
Approaches
- Semi-Supervised Learning: Gaussian Process (GP)
- Support Vector Machine
- k-Nearest Neighbor (k = 1)

4. GP Semi-Supervised Learning
Given , predict the labels of unlabeled pts
Assume the data, data generation process
X : inputs, y : vector of labels,
t : vector of hidden soft labels,
Each label (binary classification)
Final classifier y = sign[ t ] = sign [ ]
Define
Similarity function
 Infer given

5. GP Semi-Supervised Learning
Infer given
 Bayesian Model
 : Prior of the classifier
: Likelihood of the classifier given the labeled data

6. GP Semi-Supervised Learning
 How to model the prior & the likelihood ?
The prior : Using GP,
(Soft labels vary smoothly across the data manifold!)
The likelihood :

7. GP Semi-Supervised Learning
EP (Expectation Propagation)  approximating the posterior as a Gaussian
Select hyperparameter { kernel width σ, labeling error rate ε } that maximizes evidence !
Advantage of using EP  we get the evidence
as a side product
EP estimates the leave-one-out predictive performance without performing any expensive cross-validation.

8. Support Vector Machine
OSU SVM toolbox
RBF kernel :
Hyperparameter {C, σ} Selection  Use leave-one-out validation !

9. kNN (k = 1) The label of test point follows that of its nearest point
This algorithm is simple to implement and the accuracy of this algorithm can be used as a base line.
However, sometimes this algorithm gives a good result !

10. Split of the dataset & Experiment
GP Semi-supervised learning
- randomly select labeled data (p % of overall data), use the remaining data as unlabeled data, predict the labels of unlabeled data (In this setting, unlabeled data == test data)
- 50 tries for each p (p = 10, 20, 30, 40, 50)
- Each time select the hyperparameter that maximizes the evidence from EP
SVM and kNN
- randomly select train data (p % of overall data), use the remaining data as test data, predict the labels of test data
- In the SVM, leave-one-out validation for hyperparameter selection was achieved by using the train data

11. GP – evidence & accuracy
The case of Percentage of train points per class = 50 % (average over 10 tries)
(Note) An offset was added to log evidence to plot all curves in the same figure.
Max of Rec Accuracy ≈ Max of Log Evidence
 Find the optimal hyperparameter by using evidence from EP

12. SVM – hyperparameter selection
Evidence from Leave-one-out validation
Log (C)
Log (1/ )
Select the hyperparameter {C, sigma} that maximizes the evidence from leave-one-out validation !

13. Classification Accuracy
As expected, kNN is bad at small # of train pts and better at large # of train pts
SVM has good accuracy even when the # of train pts is small, why?
GP has bad accuracy when the # of train pts is large, why?

14. Analysis-SVM Why does SVM give a good test accuracy
even when the number of train points is small ?
The best things I can tell…
{# Support Vectors} / {# of Train Points} is high in this task, in particular when the percentage of train points is low.
The support vectors decide the decision boundary. But it is not guaranteed that the SV ratio is highly related with the test accuracy.
Actually it is known that {Leave-one-out CV error} is less than {# Support Vectors} / {# of Train Points}.
CV accuracy rate is high even when the # of train pts is small. CV accuracy rate is very related with Test accuracy rate.

15. Analysis-GP Why does GP give a bad test accuracy
when the number of train points is small ?
Percentage of train points per class = 50 %
Max of Rec Accuracy ≈ Max of Log Evidence
Percentage of train points per class = 10 %
Log Evidence curve is flat  fail to find optimal Sigma !

16. Conclusion GP SVM kNN (k = 1)
Small number of train points  bad accuracy
Large number of train points  good accuracy
SVM
Regardless of the number of train points  good accuracy
kNN (k = 1)