Constrained Subclass Division Based Discriminant Analysis

GNG-LDA fails to show consistent improvement of hand motion recognition accuracy mainly because of the totally unconstrained subclass division where all the pooled data are simultaneously divided into subclasses without using their original class labels. In contrast to the aforementioned unconstrained subclass division, a constrained subclass division with the hard constraint of the original data labels in the phase of relabelling is adopted in this section to remedy the performance ambiguity. Specifically, the inter-sample distance based sorting and KNN are exploited to divide the samples from a certain class into several subclasses according to their Euclidean distances. The training and and testing are based on the new subclass labels using a LDA classifier, and their original class labels are retrieved by the end of the recognition. The 4-step KNN-LDA is described as follows.

Step 1. Half of the data belonging to a certain class i are first sorted and categorised into Cisubclasses according to their inter-sample distances. A Ci-class KNN classifier is then

formed by the samples.

Step 2. For every class out of the total C classes of the training data, the rest half samples belonging to class i are classified by KNN into Cisubclasses. The number of samples in each

subclass is set equal. The labels are re-assigned for each sample according to the cluster they belong to, which leads to a total of Cknnsubclasses.

C_knn=

C

∑

i=1

C_i (3.13)

Step 3. A Cknn-class LDA classifier is trained with the relabelled training data and

represented by their means and covariance. And the label of an unseen data x is predicted by the Bayesian decision rule, where µiis the mean vector of the samples belonging to subclass i,

Σ and Σiare the pooled covariance matrix of all samples and the sample covariance matrix of

samples from subclass i, p(i) is the prior probability of subclass i. And the prior probability is equal for all subclasses in the adopted settings because of the strict constraint of subclass size. arg max_iµiTΣ−1x− 1 2µi T Σ−1µi+ ln p(i) (3.14) Σ = Cknn

∑

Step 4. The C_knn predicted labels of testing data are mapped back into the original C labels, which forms the final hand motion recognition results.

The experiments are conducted on the 3 experienced subjects with 2 days’ data for training and the rest days’ data for testing, which can be considered as training with inadequate data while the total number of testing samples is large enough in an exhausted comparison. And the training phase is repeated with 9 out of 10 folded data from the 2 days’ training set. The results shown in Fig. 3.6 and Fig. 3.7 reflect the inter-day hand motion recognition accuracy with and without the preprocessing of normalisation respectively. It can be seen that the KNN-LDA outperforms the single LDA in both cases which validates the feasibility of a constrained and explicit subclass division for long-term sEMG based hand motion recognition. It is worth noting that all the 3 subjects are experienced users of the sEMG based hand motion recognition system, who can exert more consistent muscle contraction than others. A detailed numerical comparison between KNN-LDA and LDA is shown in Table 3.1, where a larger improvement is achieved by the KNN-LDA method for normalised sEMG data than that of the sEMG data without normalisation. Despite the difference between the two settings, a consistent improvement of classification accuracy is seen for the inadequate training of 2 days’ data.

S1 S2 S3 −5 0 5 10 15 20 25 30 35

Recognition Error Rate %

KNN+LDA LDA

Fig. 3.6 Comparison of inter-day recognition error rate between KNN-LDA and LDA methods for 3 subjects with normalisation

In comparison with the totally unconstrained subclass division based GNG-LDA, the con- strained KNN-LDA shows a favourable support to the explicit subclass division. A plausible explanation is that the unconstrained subclass division is conducted on the pooled training

S1 S2 S3 0 2 4 6 8 10 12 14

Recognition Error Rate %

KNN+LDA LDA

Fig. 3.7 Comparison of inter-day recognition error rate between KNN-LDA and LDA methods for 3 subjects without normalisation

samples without any priori knowledge of their classes, while the constrained operation is confined to those belonging to the same class, which avoids the false label assignment against the given conditions. And the bias incorporated by an imbalanced subclass division is avoided in this scheme. Despite the improvement brought by subclass division, it is worth noting that the number of samples in a subclass can be few when the number of subclassess increases, which potentially leads to an inferior classifier training with the explicitly divided subclasses. Thus it is necessary to further utilise the subclass division implicitly in the discriminant analysis in the next section.