A Gaussian Mixture Model Approach to Classifying Response Types

Abstract

Visual perception is influenced by prior experiences and learned expectations. One example of this is the ability to rapidly resume visual search after an interruption to the stimuli. The occurrence of this phenomenon within an interrupted search task has been referred to as rapid resumption. Previous attempts to quantify individual differences in the extent to which rapid resumption occurs across participants relied on using an operationally defined cutoff criteria to classify response types within the task. This approach is potentially limited in its accuracy and could be improved by turning to data-driven alternatives for classifying response types. In this chapter, I present an alternative approach to classifying participant responses on the interrupted search task by fitting a Gaussian mixture model to response distributions. The parameter estimates obtained from fitting this model can then be used in a naïve Bayesian classifier to allow for probabilistic classification of individual responses. The theoretical basis and practical application of this approach are covered, detailing the use of the Expectation-Maximisation algorithm to estimate the parameters of the Gaussian mixture model as well as applying a naïve classifier to data and interpreting the results.

Appendix: Additional Methods

1.1 II Participants

A total of 27 healthy male participants completed the interrupted visual search task. All participants were right handed and had normal or corrected-to-normal vision. The mean age of the group was 30.42(SD = 9.18), and the mean performance IQ (measured using the WASI [17]) was 114.11(SD = 11.97). These participants were recruited as the control group in a larger study that was conducted. Participants were recruited from the Cambridge Psychology Volunteers Database or through classified adverts on websites such as Gumtree.

1.2 II Stimuli Presentation

Stimuli were presented using the Psychtoolbox extension [18, 19] in MATLAB [20]. Stimuli were displayed on a 24″ monitor running at a resolution of 1920 × 1080. Participants were sat with a viewing distance of 60 cm from the screen in a darkened room.

Overall the stimuli presented and procedure used in this study closely match the methods outlined in experiment 1 from Lleras et al. [4]. Participants were required to locate a target T shape within an array of L shapes. Trials either contained 16 visual items (1 target and 15 distractors) or 32 visual items (1 target and 31 distractors). An even amount of 16 and 32 item trials were presented to each participant in a random order. The effects of distractor density were not considered as part of the analysis presented here.

Items were presented within a centrally positioned white square which subtended a 9^∘ visual angle. The area of the screen outside of the central square was coloured grey. Item positions were generated by randomly placing them inside an invisible 6 × 6 grid. The height and width of each invisible cell within the grid was 1.5^∘. During display generation, items were initially placed centrally within their grid positions and then a random amount of jitter (±0.2) was applied to this initial position in order to avoid the objects being collinearly aligned.

After generating item positions, one of the items was selected at random to be the target item, and the others were presented as distractor items. All items were generated using two lines of equal length at 90 degrees to each other, with target ‘T’ shapes placing the second line in the middle of the first line and distractor ‘L’ shapes placing the second line at the end of the first line. Each of the line segments within the items subtended 0.5^∘ of visual angle. The orientation of each item was randomly selected from four possible options (at 90 degree rotations). Items could be either blue or red in colour and were balanced to ensure an equal number of items of each colour in the display.

1.3 II Procedure

During each trial, a new search display was generated using the methods detailed above. Trials were preceded by a fixation cross in the centre of the screen for 500 ms. The search display was shown for 100 ms at a time with a 900 ms blank display period in between. Blank display periods showed a white square without any of the search items present. Each cycle of a 100 ms search display presentation and 900 ms blank display will be referred to as an epoch [21]. Trials terminated after a total of 8000 ms without a response or as soon as the participant responded. This meant that on each trial the search display would be visible for a maximum of 8 times (8 epochs). Participants were shown feedback on each trial which stayed on the screen for 1000 ms. This procedure is demonstrated in Fig. 1.5.

Fig. 1.5

Diagram showing the stimuli sequence for any given trial. At the start of each trial, participants are presented with a fixation cross for 500 ms. After the fixation cross, the search display is presented for 100 ms followed by a 900 ms interval with a blank screen. The search display is shown a maximum of 8 times in total. Feedback is given for 1000 ms (‘Correct’ or ‘Incorrect’) once the participant responds or the trial times out (8000 ms from initial presentation of the search display)

Participants were given instructions on the screen which were repeated verbally by the experimenter. Once the participants were happy with the instructions, they were given 15 practice trials to do. After completing the practice trials, all participants completed a control task designed to assess their base reaction time. The control task consisted of 30 trials in which a target object appeared without the addition of any distractor objects. Participants were asked to report the colour of the target shape (red or blue) as quickly as possible by pressing the ‘z’ key for a blue target or the ‘m’ key for a red target. Coloured stickers were placed on the keys to indicate which key corresponded to which colour.

After completing the control task, participants were given a short break before starting the main task. In the main task, participants were again required to report the colour of a target T shape. However, these T shapes were now presented alongside distractor L shapes. Participants completed a total of 10 blocks of 30 trials. Each block was followed by a 30 s rest period. The duration of the full session including the instructions, practice trials, control task and main task was approximately 30 min. Two participants were removed from further analysis for having median reaction times in the control task that were greater than 2 standard deviations from the group mean. An additional participant was removed for having an error rate in the main task that was greater than 2 standard deviations from the group mean. This left a final sample of 24 subjects for the main analyses. Data for all response trials were pooled together for all the participants. Only correct responses were included in this dataset.