DISCUSSION

BIBLIOGRAPHY 

INTRODUCTION

METHODS Subjects22 subjects (12 females and 10 males) aged 25-40 were trained by a psychologist on the TMTB test [1,2,3]. Subjects were seated at viewing distance of 78cm from a 32” color monitor (51cmx31cm). Eye position was recorded using ASL 6000 system.

RESULTS

BAYESIAN HYPOTHESIS ON SELECTIVE ATTENTION Giacomo Veneri1,2, Emanuele Olivetti3,4, Paolo Avesani3,4, Antonio Federico2, Alessandra Rufa1,2

BACKGROUNDVisual search is an activity that enables humans to explore the real world. It depends on sensory, perceptual and cognitive processes. Given the visual input, during visual search, it is necessary to select some aspects of input in order to move to the next location. The aim of this study is to understand the selection process, that modulates the exploration mechanism, during the execution of a high cognitively demanding task such as a simplified trial making B test (sTMTB). The sTMTB is a neuropsychological instrument when number and letters should be connected each other in numeric and alphabetic order (1-A-2-B-3-C-4-D-5-E).

OBJECTIVEThe aim of the study is to understand the process of target averaging during the selection process. We analyzed the probability to select the target after a fixation outside ROIs from the duration of fixations and the distance to the target. We aimed to respond to the question “is it possible to predict the selected area?” . In this study we tested the presence of information in non-ROI fixation data about the occurrence of a target at the next saccade. A classification algorithm was trained to predict the target vs. non-target outcome (dependent variable) of a saccade from summary statistics of fixation data (covariates). We claim that significantly accurate predictions are substantial evidence to support the hypothesis of "presence of information".

Bayesian hypothesis

[1] G. Veneri, P. Piu, F. Rosini, P. Federighi, A. Federico, A. Rufa - 'Automatic Eye Fixations Identification Based On Analysis Of Variance And Covariance ' Pattern Recognition Letters; Volume 32, Issue 13, 1 October 2011, Pages 1588-1593, [2] G. Veneri, E. Pretegiani, F. Rosini, P. Federighi, A. Federico, A. RUFA - 'Evaluating The Human Ongoing Visual Search Performance By Eye Tracking Application And Sequencing Tests ‘ Computer Methods And Programs In Biomedicine[3] G. Veneri, P. Federighi, F. Rosini, A. Federico, A. RUFA - 'Influences Of Data Filtering On Human-computer Interaction By Gaze-contingent Display And Eye Tracking Applications ' (2010) Computers In Human Behavior , Vol.26, 1555.

Distribution probability

1. Eye tracking & Vision Applications Lab - University of Siena, Italy2. Department of Neurological and Behavioural Sciences - University of Siena , Italy3. Center for Mind and Brain Sciences (CIMeC), University of Trento, Italy4. NeuroInformatics Laboratory (NILab), Bruno Kessler Foundation - University of Trento , Italy

The predictions of the classifier supported the hypothesis of accurate classification, thus confirming the “Presence of information“.

Results reported that the model learned the exploration strategies and visual search was efficient when the target was attended and the observer's internal model matched the environment. We conclude that: subjects planned the entire target averaging cycle before the first fixation and selected the next location under a Bayesian process, thanks to information available in the peripheral vision; this process has a preferential pathway when the attended target is close. Our Bayesian framework and results are very similar to the model proposed by Najemnik & Geisler [4,5]. Our model was able to correctly discriminate the 65% of fixation in target vs. non-target.

The Trial making Task Part B : the subject is required to connect 1-A-2-B-3-

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http://www.evalab.unisi.ithttp://nilab.cimec.unitn.it/blog/ With the financial support of the Tuscany region http://www.progettosissi.it

Presence of informationThe fixation from a non-ROI area and preceding a saccade were summarized in a vector of 6 covariates: fixation duration, varX, varY, covXY, distance to ROI, distance to target. A sample of 288 vectors was extracted from the fixations of the whole set of subjects of this study and defined the whole dataset for the classification problem. A subset of 50 vectors resulted in saccades actually reaching the target and 238 in non-target. The dataset was split in two groups, the train set and the test set, the first for training/fitting the classifier and the second to assess how accurate were its predictions. The classification algorithm adopted in this study is the "Gaussian naive Bayes" (GNB) [0]. The GNB algorithm assumes: independence between each pair of the 6 covariates and a Gaussian likelihood for each covariate. Under those assumptions the GNB algorithm is derived directly from the Bayes theorem. The predicted outcome of the classifier is then:

where ci and ci 2 are the maximum likelihood estimates of each covariate for each class over the

train data and p(c), c={target, non-target}, is the prior probability for each value of the dependent variable.We used a 10-fold cross-validation, a resampling approach, for assessing the results and split the dataset in 10 parts via stratified sampling. At each step one part of the dataset, the test set, was kept out for computing the confusion matrix and the remaining nine parts were used for training the GNB algorithm. The confusion matrix summarises the agreement of the predictions and actual values over each value of the dependent variable. The test of independence proposed in [6] (implementation: https://github.com/emanuele/Bayes-factor-multiclass) was carried out on the aggregated confusion matrix.

[4] Najemnik, J., & Geisler, W. S. (2005). Optimal Eye Movement Strategies In Visual Search. Nature, 434 , 387–91[5] Najemnik, J., & Geisler, W. S. (2008). Eye movement statistics in humans are consistent with an optimal search strategy. Journal of Vision, 8 , 1–14.[6] Kass, Robert E. and Raftery, Adrian E.(1995) Bayes Factors, Journal of the American Statistical Association, 430, 773—795[7] Casella, George and Moreno, Elìas (2009) Assessing Robustness of Intrinsic Tests of Independence in {Two-Way} Contingency Tables, Journal of the American Statistical Association, 104, 1261—1271[8] Domingos, Pedro and Pazzani, Michael, (1997) On the Optimality of the Simple Bayesian Classifier under Zero-One Loss, Machine Learning, 29, 103-130

Presence of information: the logarithm of the Bayes factor against the null hypothesis of independence ranged between 85 and 291. According to [6] such values for the Bayes factor correspond to a strong evidence supporting the dependence between predictions and actual values, thus

confirming sufficiently accurate classification. The average per class accuracy was 65%.