Predicted and recorded place fields in environment B.

<p>The squares represent firing rates at each point of the big square environment, with hot colors marking high firing rates, and cold colors low firing rates (the plots have been scaled to fit the page - see main text for the actual proportions of the environments). The model prediction was made based on parameters estimated from the other environments (environments A, C and D). The overall mean proportion of explained variance was (Data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0089762#pone.0089762-OKeefe4" target="_blank">[69]</a>).</p

Place field sizes, and predicted uncertainty, on a circular track with objects, using the extended model.

<p>The blue lines show the smoothed place field sizes (10-point moving average), normalized to a mean of 0 and variance of 1, and the red lines show the location uncertainty predicted by the extended Bayesian model (which takes into account only a subset of the objects on the track at each point). Pearson's correlation coefficient between the recorded place field sizes and the predicted uncertainty was both for rat 1 and rat 2. The proportions of explained variance were for rat 1 and for rat 2. (Data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0089762#pone.0089762-Burke1" target="_blank">[42]</a>).</p

Effects of spatial representation structure on distance estimation, walking time estimation, and response times.

<p>All of these estimated magnitudes, as well as response times, are significantly smaller when both buildings are on the same sub-map (i.e. on the same representation) compared to when they are not. Data from 380 pairs of buildings were compared (269 across sub-maps, and 111 within sub-map). Apart from the representation-dependent biases, subject estimations were reasonably accurate (correlation of <i>r</i> = 0.40 between estimated and actual Euclidean distance, and <i>r</i> = 0.48 between estimated and actual walking time as calculated by Google Maps).</p

Results of a predictive clustering model using subjects’ feature importances, learned using the decision hyperplane approach.

<p>Each sub-plot reports all prediction results for one subject, using green cells for correct predictions, red cells for incorrect predictions (one or more buildings grouped to the wrong sub-map), and white cells for subject maps either not better than random chance or without apparent structure. Top 3 rows in each subplot show results on the training trials (dark colours), and the 4th, bottom row shows the prediction accuracies on the test trials (bright colours). On average, 75% of all test map structures could be predicted correctly (green cells). For comparison, the probability of prediction by random chance is 0.4% for two sub-map and 3.1% for one sub-map structures.</p

Learning a Gaussian-based non-linear metric.

<p>Left: based on a participant’s known map structure, a probabilistic model (GDA) can be trained which can predict the probability of two buildings being co-represented, given their feature differences. Right: These probabilities from a trained GDA model can be taken as similarities and used as the distance metric for a psychological space model. As in the linear models above, map structure predictions for new environments are made by clustering under the learned metric.</p

Correlations between probabilities of being on the same sub-map, and distances along each feature, for pairs of buildings in Experiments (from top to bottom): 1, Experiment 2 in virtual reality (therefore lacking geospatial features), and 3A, 3B.

<p>Correlations are reported separately for each feature. The three bars per feature show results at three different window sizes <i>w</i> used for calculating co-representation probabilities (higher <i>w</i> lead to less noisy probability estimates through smoothing, resulting in higher correlations). Empty bars show levels of correlation that would be expected if maps were clustered according to the single respective feature only.</p

Predicted and recorded place fields in environment B.

<p>The squares represent firing rates at each point of the big square environment, with hot colors marking high firing rates, and cold colors low firing rates (the plots have been scaled to fit the page - see main text for the actual proportions of the environments). The model prediction was made based on parameters estimated from the other environments (environments A, C and D). The overall mean proportion of explained variance was (Data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0089762#pone.0089762-OKeefe4" target="_blank">[69]</a>).</p

Prediction accuracies (and Rand indices) in Experiment 3, for all features and subject-specific GDA+DP-GMM model (second column), for features known a-priori, without having to ask subjects to rate similarities or draw sketch maps (third column), and finally using a subject-general model, without learning subject-specific feature weights.

<p>Rows: Condition 3A (19 subjects, 48 map structures from as many distinct environments, 112 sub-maps), and condition B (54 subjects, 185 map structures from as many distinct environments, 310 sub-maps).</p

Training and testing procedure for learning a metric and evaluating it against participant data.

<p>Training and testing procedure for learning a metric and evaluating it against participant data.</p

A part of the virtual reality experiment interface of Experiment 2 (the recall sequence interface was equivalent to the real-world experiments; see Fig 2).

<p>A part of the virtual reality experiment interface of Experiment 2 (the recall sequence interface was equivalent to the real-world experiments; see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0157343#pone.0157343.g002" target="_blank">Fig 2</a>).</p