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The human ability to succeed in navigational tasks of any kind depends on howhu- mans understand the space in which they are navigating. This involves an implicitly developed representation of the spatial layout, usually in the shape of so-called cognitive maps (see Section 3.2.2). Despite its significance, the process of building such represen- tations raises difficulties. The classical methods for studying cognitive models such as interviews, protocol analysis or map drawing present limitations related primarily to the implicit content of the information which the researchers try to elicit (see Section 3.2.4). Therefore, this thesis advocates employing ANNs as a suitable tool for rule extraction. The RNN successfully learned to predict user’s next position and orientation. The prediction accuracy of greater than 68% suggested that the neural network succeeded in acquiring the underlying regularities characterising user trajectory patterns (Sec- tion 8.3.3).

The next step consisted of extracting rules that characterise human heuristics for ex- ploring an unfamiliar, indoor environment. This section proposes a hybrid connectionist- symbolic model for investigating rules governing human exploratory behaviour within VEs. Its final aim is to extract a spatial grammar underlying spatial knowledge acqui- sition. Such a spatial grammar is an inherent part of user mental model of navigation, which will be harnessed for designing adaptive VEs able to support low spatial users to improve their spatial behaviour (see Sections 11.4.3 and 11.4.5).

The analysis of the representation in the RNN hidden layer suggested that distinct groups of hidden units become specialised for place and direction (Section 8.3.5). The distributed representations acquired by RNN should be also investigated by analysing the individual pattern error in the network prediction (see Section 6.4.1).

8.4.1 Pattern Error Analysis

Before starting to analyse the pattern error for each of the RNN’s predictions, a deci- sion should be made regarding the sample of these predictions which are worth being thoroughly investigated. It is clear that not all the predictions could act as indicators of the regularities embedded in the movement paths, but only the best predictions can qualify for this. Thus, a conservative criterion of selection has been chosen, which has been met only by the best predictions, such as the top 10% of them.

The best predictions have been identified on the basis of the following performance criterion, which requires that the threshold values should be set up rather low. For a particular input vector: (ix, iy, irot, idist, ixlandmark, iylandmark, ilevel), the predicted user’s position or landmark position coordinates could differ only by±0.5 virtual metre from the input position coordinates, the predicted user’s heading should be higher or smaller with no more than 15 degrees from the input heading, the predicted distance to the nearest landmark could differ only with±1 virtual metre from the input distance and the predicted floor value should not differ with more than±0.3 virtual metre from the input floor value.

8.4.2 Clustering Neural Network Predictions

The analysis of the individual pattern error in the network prediction could prove ben- eficial in understanding the internal representation acquired by the network (Plunkett and Elman, 1997). The RNN is able to predict accurately specific patterns, only when it previously acquired the regularities underlying those patterns. The rule extraction process aimed to reveal the regularities which allow the RNN to make highly accurate predictions of user’s position, heading, nearest landmark and floor.

I conjecture that understanding howand why the RNN succeeded or failed to predict accurately particular patterns could offer an understanding of navigation procedures or strategies employed by the participants in this study.

Given the specifics of these data and the objective of this thesis, a data mining technique has been employed. Self-Organising Maps (SOM) have been already intro- duced in Section 6.3.1. SOM is based on an unsupervised learning process, allowing cluster identification and visualisation within the input data. This process is carried out without any prior knowledge regarding the number and content of the clusters to be obtained (Kaski, 1997). When a set of already clustered input data is available, a supervised learning process, such as Learning Vector Quantisation (Kohonen et al., 1995) can be employed to identify to which class an unknown data vector belongs (see Section 6.4.4).

The use of SOM (Kohonen et al., 1996) and LVQ (Kohonen et al., 1995) for per- forming the cluster analysis of RNN error prediction requires several steps, as described in Section 8.2. These generic steps have been adapted for the current analysis and the modules which serve each of these steps are presented in Figure 8.16.

SOM Training LVQ Training Labeled weights Prediction error cluster identification Map Visualisation Prediction error cluster accuracy Pattern preprocessing RNN pattern error analysis

Figure 8.16: Modular System for Clustering the RNN Prediction Error

8.4.3 Pre-Processing Data

Navigation is a spatio-temporal event, where the position of each moment t depends on the position of moments t−1, t−2,. . . , t−n, and in the same time, influences the position at subsequent times: t+ 1, t+ 2,. . . ,t+n. Thus, one should consider not only the pattern which has been successfully predicted, but also the history in terms of previous patterns which had led to that highly accurate prediction. In other words, the attention is paid to the interesting pattern, considered in its context. Therefore, once a particular pattern has been identified as described above, the context in terms of its previous nine patterns has been also recorded.

For each of these patterns, the predicted values for user’s position and heading have been retained and concatenated with the corresponding values from the previous patterns. The values have been normalised between −1 and 1. The obtained vector consisted of 30 input elements, three for each of the ten moments in time, and looks like it follows:

(px[9], py[9], prot[9], px[8], py[8], prot[8], . . . , px[0], py[0], prot[0]) (8.6) 8.4.4 Training SOM

The training set and the testing set have been identified by analysing the prediction errors associated with the counterpart sets used for training and testing the RNN. The training set consisted of 1367 vectors (54%), while the testing set consisted of 1167 vectors (46%). Each of these two sets covered the top 10% best predictions produced by the RNN, during training and testing respectively.

A SOM of 20×16 neurons was used to perform a topology-preserving mapping. The first phase of training was carried out for 1700 epochs, a radius of 20 and a learning rate of 0.3, while the second phase lasts for 21 000 epochs, with a learning rate of 0.07 and a radius of 2. The random seed of 115 was identified by using thevfind program. These parameters were retained, after more than 100 networks with different architectures and learning rates have been tried, because these particular parameters led to the smallest quantisation error (Kohonen et al., 1996) for the testing set: 0.36, while for training set it was 0.31.

8.4.5 Map Visualisation

Training the SOM led to seven clusters of RNN best predictions, as shown in Figure 8.17. For their identification, within the area corresponding to each of them, the assigned cluster number has been placed. For example, cluster number 1 consists of segments of trajectories standing for best predictions, within area designated by number 1, located down on the right hand side of the map.

8.4.6 Cluster Identification

The winner nodes within each cluster are represented as plots on the Cartesian coordi- nates system (X,Y), on a zoomed-in area of the SOM map. For a better understanding, both user’s position and heading have been plotted (Figures 8.18, 8.19, 8.20, 8.21, 8.22, 8.23 and 8.24), for each of the 10 moments in time (i.e. one when the best prediction has been identified, and the previous nine). The lightest colour is used to represent the further position and heading in time, while the darkest one marks the present moment when the best prediction has been identified. The different shades of grey on the light– dark continuum offer an intuitive understanding of the temporal dimension embedded in these data, from past to present.

8.4.7 Training LVQ

In order to test the accuracy of classification provided by SOM, the LVQ algorithm has been used. The training and testing sets for LVQ have been derived from the SOM training and testing set respectively, while the cluster labels have been attached to each input element as the SOM map suggested. In addition, once the SOM was trained, the codebook vectors have been used for initialising the weights for the LVQ algorithm.

The obtained classification accuracy was 95.15%. Within each cluster, the classifi- cation accuracy varies as follows: cluster 1 — 92.65%, cluster 2 — 100%, cluster 3 — 98.48%, cluster 4 — 94.72%, cluster 5 — 93.44%, cluster 6 — 95.28%, and cluster 7 — 91.49%. As can be seen, the accuracy for the all the clusters is high. This outcome suggests the validity of the clusters previously identified. Once the clusters have been identified, the following step consists of their interpretation.

Figure 8.17: SOM of the Best Predictions of RNN Used for Trajectory Prediction