Pattern Recognition Results

The techniques to discriminate states based on the eleven features used a Fisher linear discriminant projection [7] and the leave one out test method. For each trial, a single point, x, was excluded from the data set and a Fisher projection matrix, W was calculated for remaining members of the set. The excluded point was then projected using W and classified using quadratic and linear classifiers, in the standard method described by Therrien [8].

The Fisher projection matrix which in some sense maximizes the ratio of the between-class scatter, S_B, to the within class scatter, S_W [7], where these matrices are defined as:

$$S_{W}=\sum_{i=1}^{c} \sum_{x\in\chi_{i}}^{n} (x - m_{i})(x - m_{i})^{t}$$

$$S_{B}=\sum_{i=1}^{c} n_{i}(m_{i} - m)(m_{i} - m)^{t},$$

given c is the number of classes, n_i is the number of sample vectors in a class, m_i is the sample mean for class i, m is the total mean, and $x\in\chi_{i}$ are the 11-dimensional feature vectors comprising class i. The Fisher projection matrix is the matrix W whose columns, w_i correspond to the largest eigenvalues in:

$$S_{W}^{-1} S_{B} w_{i} = \lambda w_{i}$$

This matrix is then used to project the test point onto the classifier space using

y = W^T x

The results of the recognition on a number of subsets of data are reported in Table 3. The discrimination is best between anger and a set of more peaceful emotions containing the classes: no emotion, love and reverence. The entire set of eight emotion classes can also be well separated into two categories: high arousal containing anger, grief, romantic love and joy, and low arousal containing no emotion, hate, love and reverence. However, no good discrimination was found for positive valence vs. negative valence emotions.

  

Figure: Anger is well separated from more peaceful emotions, in this example the states of No Emotion, Love and Reverence make up the set of peaceful states

 

Table: The results of discriminating between subsets of emotions. For these results the peaceful class contains no emotion, reverence, and love; the aroused class contains anger, grief, romantic love, and joy; the calm class contains no emotion, hate, love, and reverence; the positive valence class contains love, romantic love, and joy, and the negative valence class contains anger, hate, and grief. Anger was most easily distinguished, and good discrimination was achieved for the high vs. low arousal states. Positive and negative valence were not well separated.

Emotion	Set	Linear		Quadratic
Set	Size	error	correct	error	correct
anger	20	2	90%	0	100%
peaceful	60	1	98%	1	98%
high arousal	80	15	81%	16	80%
low arousal	80	11	86%	10	88%
positive	60	15	75%	11	82%
negative	60	29	53%	30	50%

 

Although specific patterns were not found to discriminate all eight emotions, certain subsets of three emotions could be well separated as shown in Table 4.