The work is supported by funding from the National Institutes of Health (NIH), grant EY07977. The authors would also like to thank Usman Ayyaz for his assistance in testing the software, and Muhammad Naeem Ayyaz for his comments on the manuscript.

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The authors have nothing to disclose.

The protocol outlined here is effective for obtaining and analyzing similarity judgments for stimuli that can be presented visually. The experimental paradigm, the analysis, and possible extensions are discussed first, and later the advantages and disadvantages of the method.
Experimental paradigm: The proposed method is demonstrated using a domain of 37 animal names, and a sample dataset of perceptual judgments is provided so that one can follow the analysis in step 5 and reproduce parts of Figures 3-6&#160;(protocol step 1.4). The experimental design groups these 37 stimuli into 222 trials - each containing a reference stimulus in the center and eight comparison stimuli in the surrounding ring - such that several criteria hold: a) each of the 37 stimuli appears as the reference an equal number (six) of times (222 = 37&#215;6), b) over the six trials in which a stimulus is the reference, all of the remaining 36 stimuli are used as comparison stimuli at least once, c) 24 stimuli occur in exactly one comparison with a given reference, and d) six pairs of stimuli appear with the reference in two separate trials. This aspect of the paradigm, that six pairs of comparison stimuli occur in separate contexts for each reference stimulus, allows for checking context effects in step 5 (see Figure 4). This standard design yields 6216 = 222&#215;28 comparisons of the form &#34;Is the similarity of the reference to s1 greater or less than the similarity of the reference to s2.&#34; This efficiency is possible because each of the 222 trials yields a ranking of eight similarities, and the eight ranked similarities generate 28 pairwise comparisons. Of these 6216 comparisons, 222 are repeated, giving us 5994 unique comparisons.
Once the stimulus domain is chosen, the next most important design decision is the number of samples. Many alternative designs are possible (Table 1), with other choices for the way that stimuli are repeated in different contexts. As mentioned in Figure 4, within each trial there is a triplet - comprising the reference and two surrounding stimuli - that appear together in one other trial. The number of the surrounding stimuli overlapping with another trial with a common reference - in this case, equal to two - is controlled by the overlap&#160;parameter in the analysis configuration file. Increasing this parameter would result in more stimuli being shared between two trials, allowing for more extensive comparisons of distance ranking, e.g., &#34;Is s1 more similar to the reference than s2 and is&#160;s2&#160;more similar than s3?&#34; across two contexts. For examples of other experimental designs possible with different values of this and other parameters, see Table 1. For details on all the parameters, what they control, and where to change them, see Table 2. Notably, it is also possible to change the number of stimuli that appear around a reference in each trial by changing the parameters num_images_per_trial&#160;and num_words_per_trial for the image and word experiments respectively. Increasing the size of the surround would increase the number of comparisons per trial and better study context effects; decreasing it would reduce task complexity. The number of comparison stimuli in a trial (Ncircle), the number of stimuli in the experiment (Nstim), the number of trials (Ntrials), the number of unique comparisons (Ncomparisons) and the number of repeated comparisons (Nrepeated) are inter-related and depend on the size of the previously mentioned overlap between trials (Noverlap) and the number of trials per reference stimulus (k). The stimulus set size is determined by m, which is an arbitrary integer. These relationships are listed below:
<img alt="Equation 1" src="/files/ftp_upload/63461/63461eq01.jpg" /> 
<img alt="Equation 2" src="/files/ftp_upload/63461/63461eq02.jpg" /> 
<img alt="Equation 3" src="/files/ftp_upload/63461/63461eq03.jpg" /> 
<img alt="Equation 4" src="/files/ftp_upload/63461/63461eq04.jpg" /> 
<img alt="Equation 5" src="/files/ftp_upload/63461/63461eq05.jpg" /> 
<img alt="Equation 6" src="/files/ftp_upload/63461/63461eq06.jpg" />
There are other details of the paradigm and data collection procedures that help to minimize confounds. Randomizing the placement of stimuli and trial order (step 3.4) is important so that even when sessions are repeated, the subject does not begin to recognize spatial or temporal patterns in the placement of stimuli. It is also important not to give subjects any direct cues about how to gauge similarity (step 4) as this can bias the results. They should themselves decide on what similarity means to them in the context of the specific experiment. However, it is useful to debrief the subjects after they complete the experiment, as this may help understand how findings vary across subjects. If for some reason, a session is corrupted or aborted, then we recommend deleting the entire session, so that all trials are completed an equal number of times.
Analysis of similarity data: The experiment yields, for each trial, rank-orderings of similarity between the Ncircle&#160;comparison stimuli and the reference. When decomposed into comparisons of pairs of stimuli, these trials yield choice probabilities for each of the unique comparisons. The choice probabilities are then analyzed to search for geometric models of the perceptual space (protocol step 5). The analysis attempts to account for the choice probabilities in terms of distances between stimuli, d(si, sj), in a Euclidean space. That is, the goal is to assign coordinates to each stimulus so that the choice probability for clicking s1 before s2 reflects the probability that the subject judged d(ref, s1) &#60; d(ref, s2). This fitting procedure is described here both because it has some novel elements, and to enable a user to modify it (protocol step 5.2).
The analysis is a kind of multidimensional scaling problem, but with some distinguishing features. First, the data provide rank-ordering of dissimilarity judgments, rather than estimates of the distances. Second, the dataset, while extensive, only contains a subset of all possible comparisons of pairwise distances. Finally, the objective is to account for the choice probabilities, not just a binary decision of which distance is larger. With these considerations in mind, the cost function is chosen such that its value is minimized when model-predicted choice probabilities are most likely to yield the experimentally observed choice probabilities. It is therefore defined as the negative log-likelihood of the observed choice probabilities under the model, normalized by the total number of pairwise comparisons, and is adapted from previous work15:
<img alt="Equation 7" src="/files/ftp_upload/63461/63461eq07.jpg" />
where N0 = Ncomparisons.Nrepeats, and Nrepeats is the number of repeats of the protocol, (i.e., the number of times each unique trial is repeated), and
<img alt="Equation 8" src="/files/ftp_upload/63461/63461eq08.jpg" /> 
<img alt="Equation 9" src="/files/ftp_upload/63461/63461eq09.jpg" />
Here, sr denotes the reference stimulus in a trial, si and sj and the stimuli in the ring around sr. P (d(sr, si) &#60; d(sr, sj)) represents the model probability that the distance between sr and si is judged as smaller than the distance between sr and sj and C denotes the number of times that the subject judged d(sr, si) &#60; d(sr, sj). The objective of the modeling analysis is to find a&#160;configuration of points in a Euclidean space, that accounts for the empirical choice probabilities. Iteratively, the minimization adjusts the coordinates assigned to each stimulus, and in so doing, the model choice probabilities (P). The minimization terminates when the cost function stops decreasing below the tolerance (an adjustable parameter named tolerance controls this) or if the maximum number of iterations is reached (controlled by parameter max_iterations).
To connect the stimulus coordinates with the model choice probabilities, it is assumed that a subject - when choosing between two stimuli to click in a trial - will make an internal comparison of their relative distances to the reference, namely d(sr, si) and d(sr, sj). These distances are (by default) the ordinary Euclidean distances between points assigned to stimuli sr, si and sj. Further, it is supposed that this mental comparison has an internal noise, which we model as an additive Gaussian source of standard deviation &#963;, a model introduced for one-dimensional domains by Maloney et al.16,17and also used for multidimensional domains15. The model choice probabilities are related to the coordinates by:
<img alt="Equation 10" src="/files/ftp_upload/63461/63461eq10v2.jpg" />
The internal noise, &#963;, can be controlled by varying sigma in the analysis config file. To initialize the algorithm with a set of stimulus coordinates, the rank-order judgments were used to obtain a set of approximate distances and then standard multidimensional scaling10&#160;was applied to these distances to obtain the initial coordinates. These approximate distances were determined by tallying the wins and losses for each pair of stimuli. That is, looking over all pairwise comparisons in the data, each time a distance, d(sr, sk) is judged larger than another, d(sr, sn), a win is logged for the bigger distance d(sr, sk) and a loss is logged for d(sr, sn). The core idea is that the greater the distance between two stimuli, the more often it would be judged as greater than another distance (in terms of wins) and vice versa. After iterating through all comparisons and tabulating the wins and losses of each pair of stimuli, distance estimates are calculated as follows:
<img alt="Equation 11" src="/files/ftp_upload/63461/63461eq11.jpg" />
Once this is done, the initial set of coordinates is determined by applying standard metric multidimensional scaling to dinit&#160;(si, sj).
The minimization routine thus described is run independently to obtain models of 1, 2, 3, 4, and 5 dimensions. In each case, the optimal coordinates of the inferred stimulus points, as well as the value of the cost function, i.e., the negative log-likelihood of the empirical choice probabilities are returned. The log-likelihood is plotted in Figure 5&#160;relative to the best possible log-likelihood, which is calculated similarly as in Equation 1, with
<img alt="Equation 12" src="/files/ftp_upload/63461/63461eq12.jpg" />,
for all comparisons. As a sanity check, in Figure 5, the random model log-likelihood, a lower bound by which to judge the performance of the models is also plotted. When calculating the random choice log-likelihood, we set
<img alt="Equation 13" src="/files/ftp_upload/63461/63461eq13.jpg" />
for all comparisons.
Possible extensions: Firstly, as mentioned previously, the experimental paradigm may be modified to accommodate stimulus sets of different sizes, and the number of stimuli in the ring can be altered to yield different numbers of pairwise comparisons per trial (see Table 1).
Secondly, it may be useful to utilize non-Euclidean distance metrics in the analysis. For example, one study found that the city-block metric better represented a perceptual space of surface lightness and illumination18. The proposed method can be generalized, so models with other distance metrics e.g., a city-block distance, a Minkowski distance, or a hyperbolic distance19, are fit to similarity data. To do so, one would have to modify the provided code and implement an alternative distance metric. The main change needed is in line 105 (function name: dist_model_ll_vectorized) in the file similarities/analysis/pairwise_likelihood_analysis.py.
Strengths and limitations: A key strength of the proposed approach is that it provides a flexible framework for designing experiments with various stimulus set sizes, various numbers of comparisons, repeats, or the number of stimuli per trial as well as various overlapping set sizes to measure context effects. By changing the size of overlap between trials and the size of the surround in a trial, one can probe the role of context in similarity judgments, while obtaining a high number of pairwise similarity judgments per trial. The method addresses many limitations of previous experimental paradigms for collecting similarity data. For example, unlike the arrangement-based methods12,20&#160;(that require stimuli to be arranged on a 2D Euclidean plane with similar items placed together and different items placed apart) and the sorting methods (that require stimuli to be categorized into piles),11&#160;the ranking method does not prompt subjects to project their internal representation onto any geometric structure. Another limitation of some past methods - e.g., confusion matrices in which two stimuli are considered similar if they are confused with each other in rapid recognition tasks21&#160;- is that they do not yield graded measures. This method does yield graded measures, i.e., the choice probabilities.
As emphasized above, the collection method is flexible in that it does not assume that the internal representation is a Euclidean space. Here, the analysis method tests only Euclidean models; however, it can be extended to include non-Euclidean models as well, by localized modifications in the source code. However, the modeling framework is not designed to take context effects into account. Were they significant, it would place a caveat on the conclusions that could be drawn.
The proposed method is more time-efficient than the paired comparison approach. Each trial of the paradigm takes about ~30 s (subjects perform 111 trials in an hour), yielding 111&#215;28 = 3108 comparisons per hour. Single-comparison trials are unlikely to take less than 3 s per trial, which would yield 1200 comparisons per hour. Additionally, there is a second level of efficiency: the present approach does not require comparisons of all pairwise distances. For the example in the manuscript, the full set of pairwise distances amounts to 221445 comparisons, but in the present approach, a sparse subset of 5994 unique comparisons, each repeated 5 or 10 times, suffice to model the similarity data. However, the method, though efficient, is still time-consuming, and it requires a significant commitment from subjects. As a result, it is not a feasible approach for a set of hundreds of stimuli, unless data are pooled across subjects. Finally, the approach is not directly applicable to nonvisual stimuli.

Humans mentally process and represent incoming sensory information to perform a wide range of tasks, such as object recognition, navigation, making inferences about the environment, and many others. Similarity judgments are commonly used to probe these mental representations1. Understanding the structure of mental representations can provide insight into the organization of conceptual knowledge2. It is also possible to gain insight into neural computations, by relating similarity judgments to brain activation patterns3. Additionally, similarity judgments reveal features that are salient in perception4. Studying how mental representations change during development can shed light on how they are learned5. Thus, similarity judgments provide valuable insight into information processing in the brain.
A common&#160;model of mental representations using similarities is a geometric space model6,7,8. Applied to sensory domains, this kind of model is often referred to as a perceptual space9. Points in the space represent stimuli and distances between points correspond to the perceived dissimilarity between them. From similarity judgments, one can obtain quantitative estimates of dissimilarities. These pairwise dissimilarities (or perceptual distances) can then be used to model the perceptual space via multidimensional scaling10.
There are many methods for collecting similarity judgments, each with its advantages and disadvantages. The most straightforward way of obtaining quantitative measures of dissimilarity is to ask subjects to rate on a scale the degree of dissimilarity between each pair of stimuli. While this is relatively quick, estimates tend to be unstable across long sessions as subjects cannot go back to previous judgments, and context effects, if present, cannot be detected. (Here, a context effect is defined as a change in the judged similarity between two stimuli, based on the presence of other stimuli that are not being compared.) Alternatively, subjects can be asked to compare all pairs of stimuli to all other pairs of stimuli. While this would yield a more reliable rank ordering of dissimilarities, the number of comparisons required scales with the fourth power of the number of stimuli, making it feasible for only small stimulus sets. Quicker alternatives, like sorting into a predefined number of clusters11&#160;or free sorting have their own limitations. Free sorting (into any number of piles) is intuitive, but it forces the subject to categorize the stimuli, even if the stimuli do not easily lend themselves to categorization. The more recent multi-arrangement method, inverse MDS, circumvents many of these limitations and is very efficient12. However, this method requires subjects to project their mental representations onto a 2D Euclidean plane and to consider similarities in a specific geometric manner, making the assumption that similarity structure can be recovered from Euclidean distances on a plane. Thus, there remains a need for an efficient method to collect large amounts of similarity judgments, without making assumptions about the geometry underlying the judgments.
Described here is a method that is both reasonably efficient and also avoids the above potential pitfalls. By asking subjects to rank stimuli in order of similarity to a central reference in each trial13, relative similarity can be probed directly, without assuming anything about the geometric structure of the subjects&#39; responses. The paradigm repeats a subset of comparisons with both identical and different contexts, allowing for direct assessment of context effects as well as the acquisition of graded responses in terms of choice probabilities. The analysis procedure decomposes these rank judgments into multiple pairwise comparisons and uses them to build and search for Euclidean models of perceptual spaces that explain the judgments. The method is suitable for describing in detail the representation of stimulus sets of moderate sizes (e.g., 19 to 49).
To demonstrate the feasibility of the approach, an experiment was conducted, using a set of 37 animals as stimuli. Data was collected over the course of 10 one-hour sessions and then analyzed separately for each subject. Analysis revealed consistency across subjects and negligible context effects. It also assessed consistency of perceived dissimilarities between stimuli with Euclidean models of their perceptual spaces. The paradigm and analysis procedures outlined in this paper are flexible and are expected to be of use to researchers interested in characterizing the geometric properties of a range of perceptual spaces.

<table><tbody><tr><td>Computer Workstation</td><td>N/A</td><td>N/A</td><td>OS: Windows/ MacOS 10 or higher/ Linux; 3.1 GHz Dual-Core Intel Core i5 or similar; 8GB or more memory; User permissions for writing and executing files</td></tr><tr><td>conda</td><td></td><td>Version 4.11</td><td>OS: Windows/ MacOS 10 or higher/ Linux</td></tr><tr><td>Microsoft Excel</td><td>Microsoft</td><td>Any</td><td>To open and shuffle rows and columns in trial conditions files.</td></tr><tr><td>PsychoPy</td><td>N/A</td><td>Version 2021.2</td><td>Framework for running psychophysical studies</td></tr><tr><td>Python 3</td><td>Python Software Foundation</td><td>Python Version 3.8</td><td>Python3 and associated built-in libraries</td></tr><tr><td>Required Python Libraries</td><td>N/A</td><td>numpy version: 1.17.2 or higher; matplotlib version 3.4.3 or higher; scipy version 1.3.1 or higher; pandas version 0.25.3 or higher; seaborn version 0.9.0 or higher; scikit_learn version 0.23.1 or higher; yaml version 6.0 or higher&amp;nbsp;</td><td>numpy, scipy and scikit_learn are computing modules with in-built functions for optimization and vector operations. matplotlib and seaborn are plotting libraries. pandas is used to reading in and edit data from csv files.</td></tr></tbody></table>

a psychophysics paradigm for the collection and analysis of similarity judgments

Similarity judgments are commonly used to study mental representations and their neural correlates. This approach has been used to characterize perceptual spaces in many domains: colors, objects, images, words, and sounds. Ideally, one might want to compare estimates of perceived similarity between all pairs of stimuli, but this is often impractical. For example, if one asks a subject to compare the similarity of two items with the similarity of two other items, the number of comparisons grows with the fourth power of the stimulus set size. An alternative strategy is to ask a subject to rate similarities of isolated pairs, e.g., on a Likert scale. This is much more efficient (the number of ratings grows quadratically with set size rather than quartically), but these ratings tend to be unstable and have limited resolution, and the approach also assumes that there are no context effects.
Here, a novel ranking paradigm for efficient collection of similarity judgments is presented, along with an analysis pipeline (software provided) that tests whether Euclidean distance models account for the data. Typical trials consist of eight stimuli around a central reference stimulus: the subject ranks stimuli in order of their similarity to the reference. By judicious selection of combinations of stimuli used in each trial, the approach has internal controls for consistency and context effects. The approach was validated for stimuli drawn from Euclidean spaces of up to five dimensions. 
The approach is illustrated with an experiment measuring similarities among 37 words. Each trial yields the results of 28 pairwise comparisons of the form, "Was A more similar to the reference than B was to the reference?" While directly comparing all pairs of pairs of stimuli would have required 221445 trials, this design enables reconstruction of the perceptual space from 5994 such comparisons obtained from 222 trials.

Figure 1A shows part of a conditions file generated by the script in step 3.3, for the word experiment. Each row corresponds to a trial. The stimulus in the ref column appears in the center of the display. The column names stim1 to stim8 correspond to eight positions along a circle, running counterclockwise, starting from the position to the right of the central reference. A sample trial from the word experiment is shown in Figure 1B.
To demonstrate feasibility and reproducibility, an experiment was conducted in which the stimulus set comprised the names of 37 animals. Complete datasets were collected from eight healthy subjects with normal vision as part of a study. To demonstrate the method, data from three of those subjects are shown here, two of whom were na&#239;ve to the purpose of the study. Informed consent was obtained in accordance with the Declaration of Helsinki and the institutional guidelines of Weill Cornell Medical College.
After data collection, the initial processing outlined above (protocol step 4.10-4.12) was performed. Subjects&#39; responses in each trial were interpreted as a set of independent, binary choices of the form &#34;Is the distance between the reference and s1&#160;less than that between the reference and s2?&#34; for all pairs of stimuli in the surrounding ring. Rank judgments were decomposed into such pairwise choices, as shown in Figure 2C.
Figure 3A shows the distribution of these choice probabilities, which was highly consistent across subjects (protocol step 5.1). Since each trial was repeated five times, choice probabilities took the following values: 0, 0.2, 0.4, 0.6, 0.8, and 1. The most frequent choice probabilities are 0 and 1, amounting to 50%-70% of all decisions in each of the subjects; these are the judgments for which one option is chosen each time. For example, judging the distance between s1 and s2 as less than that between s1 and s3 0 out of 5 times would correspond to a choice probability of 0; making this judgment 5 out of 5 times would correspond to a choice probability of 1. Notably, there is a great deal of consistency in choice probabilities between the subjects, even for the judgments that are not at the extremes, as seen by the clustering of the data near the diagonal in each of the panels in Figure 3B.
Next, context effects were assessed. This was possible because of an important feature of the experimental design: many triplets of a reference stimulus and two comparison stimuli s1 and s2 are repeated in two contexts (i.e., with distinct sets of six other stimuli to complete the stimulus array). Then, the choice probability for each pairwise comparison was tabulated in each context separately. The dominant diagonal in Figure 4 indicates that for each subject the choice probabilities in the two contexts - including the choice probabilities that are intermediate between 0 and 1 - are close to identical. If choice probabilities were heavily dependent on context, they would not be strongly correlated, and this diagonal would not be prominent.
Context effects were also assessed by a statistical measure. The measure of context effect is constructed as follows. The first step is to compute an imbalance statistic for the observed dataset (detailed below), which quantifies the extent to which the observed judgments appear to depend on context. We then construct 10000 simulated datasets with the same trial configurations, trial counts, and overall choice probabilities as the actual data, but generated in a way that contains no context effects - by randomly assigning the observed judgments to the two contexts. We next compute the imbalance statistic for these simulated datasets just as was done for the observed responses. Finally, we compare the imbalance statistic for the observed responses with the imbalance statistic for the simulated datasets, to determine the probability that the observed imbalance could have been obtained from a dataset with no context effect. An empirical p-value of &#60; 0.05 suggests that a context effect is present. For the data in Figure 4, p-values were 0.98, 0.30 and 0.33, for S4, S7 and S9 respectively, i.e., all values were &#62; 0.05.
The imbalance statistic for a dataset is computed as a sum of contributions over all triads that occur in two contexts. The contribution for each triad (comparing, say, d(ref, s1) with d(ref, s2)) is determined as follows. First, the judgments for this triad are tallied into a 2 x 2 table. The columns correspond to the two contexts, so the column sums are constrained by the total number of presentations in that context. The rows correspond to counts of the alternative judgments, d(ref, s1) &#60; d(ref, s2) or d(ref, s1) &#62; d(ref, s2), so the row sums are constrained by the observed choices, summed across contexts. Since the two-tailed Fisher exact test14&#160;yields the probability that a table with the observed (or greater) interaction between rows and columns (judgments and contexts) would be seen if no interaction is actually present, we use the negative logarithm of this probability as the contribution of this triad to the overall imbalance statistic. Summing the negative logarithms to create an overall imbalance statistic thus captures the joint probability of the observed imbalance across triads, under the null hypothesis of no context effect.
To model the mental representation of the animal names, Euclidean models of perceptual spaces of 1, 2, 3, 4, and 5 dimensions were derived using a maximum likelihood approach. Subjects&#39; responses were modeled as decisions reflecting the comparison of two distances with additive Gaussian noise representing errors in estimation, i.e., noise at the decision stage. Figure 5&#160;shows log-likelihoods (per decision) of five Euclidean models. The log-likelihoods are shown relative to the log-likelihood of the best model, i.e., a model that assigns the observed choice probability to each comparison, without constraining these probabilities by any geometric consideration. To put these log-likelihoods into perspective, the log-likelihood of a random-choice model is also indicated; this serves as a lower bound for model performance. The model fit improves with each added dimension. The biggest jump is between the 1D and 2D models, indicating that a simple 1D model fails to fully explain the data. However, the plateau around dimensions 4 to 5 indicates that even the 5D model does not completely capture the distances that account for the similarity judgments. To validate the approach, the pipeline was also run on simulated data. Separate experiments were simulated to generate similarity judgments between points drawn from 1D, 2D, 3D, 4D and 5D spaces respectively. In all cases, the method correctly identified the dimensionality. Furthermore, a model with the correct dimensionality yielded a log-likelihood that agreed with the ground truth log-likelihood obtained from the model.
Finally, the organization of points in the perceptual space models was visualized. Figure 6 shows these data for one subject, S7. Principal component analysis (PCA) was performed on the points from the 5D model of the perceptual space. Points projected onto the first two and first and third principal components respectively are shown in Figures 6A and Figure 6B, with axes normalized for equal variance. Distances between points aligned with the similarity judgments obtained experimentally: animals perceived as similar were denoted by points that were near each other.
<img alt="Figure 3" class="xfigimg" src="/files/ftp_upload/63461/63461fig03.jpg" /> 
Figure 3: Consistency across subjects. (A) Distribution of choice probabilities across three subjects for all pairwise comparisons. (B)&#160;Choice probabilities for the same pairwise comparisons across pairs of subjects. The color bar shows the ratio of the observed joint probability to the independent joint probability. High values along the main diagonal indicate consistency across subjects. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/63461/63461fig03large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 4" class="xfigimg" src="/files/ftp_upload/63461/63461fig04.jpg" /> 
Figure 4: Context effects. Choice probabilities for all pairwise comparisons that were made in two contexts, for each of three subjects. A refers, arbitrarily, to one context in which a triad was presented, and B refers to the other context. The color bar shows the ratio of the observed joint probability to the independent joint probability. High values along the main diagonal indicate a lack of context effects. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/63461/63461fig04large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 5" class="xfigimg" src="/files/ftp_upload/63461/63461fig05v2.jpg" /> 
Figure 5: Results of model-fitting analysis. Relative log-likelihoods for models of different dimensions as well as for the random choice (lower bound) model, shown for three subjects. A relative log-likelihood of zero corresponds to the log-likelihood of the best model, in which choice probabilities match the empirical choice probabilities without consideration of geometry. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/63461/63461fig05large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 6" class="xfigimg" src="/files/ftp_upload/63461/63461fig06.jpg" /> 
Figure 6: The perceptual space of one subject (S7) in more detail. The projection of 5D coordinates obtained from the modeling projected onto the first two principal components in&#160;(A) and onto the first and third principal components in (B). Axes are scaled so that the variance along each axis is equal. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/63461/63461fig06large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
Table 1: Example parameter sets. The experimental paradigm can be varied to have fewer or more stimuli, trials, and pairwise comparisons. The row in bold font indicates the parameters we used. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/63461/Table_1.xlsx" target="_blank">Please click here to download this Table.</a>
Table 2: Parameters in analysis/config.yaml and experiments/config.yaml. <a href="https://www-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/63461/Table_2.xlsx" target="_blank">Please click here to download this Table.</a>

Watch this Scientific Journal Video about A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments at JoVE.com

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

The protocol presents an experimental psychophysics paradigm to obtain large quantities of similarity judgments, and an accompanying analysis workflow. The paradigm probes context effects and enables modeling of similarity data in terms of Euclidean spaces of at least five dimensions.

Similarity judgments are commonly used to study mental representations and their neural correlates. This approach has been used to characterize perceptual ...

a-psychophysics-paradigm-for-collection-analysis-similarity

Nanyang Technological University

Research

JoVE Journal

Neuroscience

2.4K Views.  Weill Cornell Graduate School of Medical Sciences. The protocol presents an experimental psychophysics paradigm to obtain large quantities of similarity judgments, and an accompanying analysis workflow. The paradigm probes context effects and enables modeling of similarity data in terms of Euclidean spaces of at least five dimensions.

Video: A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Perceptual and Category Processing of the Uncanny Valley Hypothesis' Dimension of Human Likeness: Some Methodological Issues

Mori's Uncanny Valley Hypothesis1,2 proposes that the perception of humanlike characters such as robots and, by extension, avatars (computer-generated characters) can evoke negative or positive affect (valence) depending on the object's degree of visual and behavioral realism along a dimension of human likeness (DHL) (Figure 1). But studies of affective valence of subjective responses to variously realistic non-human characters have produced inconsistent findings 3, 4, 5, 6. One of a number of reasons for this is that human likeness is not perceived as the hypothesis assumes. While the DHL can be defined following Mori's description as a smooth linear change in the degree of physical humanlike similarity, subjective perception of objects along the DHL can be understood in terms of the psychological effects of categorical perception (CP) 7. Further behavioral and neuroimaging investigations of category processing and CP along the DHL and of the potential influence of the dimension's underlying category structure on affective experience are needed. This protocol therefore focuses on the DHL and allows examination of CP. Based on the protocol presented in the video as an example, issues surrounding the methodology in the protocol and the use in "uncanny" research of stimuli drawn from morph continua to represent the DHL are discussed in the article that accompanies the video. The use of neuroimaging and morph stimuli to represent the DHL in order to disentangle brain regions neurally responsive to physical human-like similarity from those responsive to category change and category processing is briefly illustrated.

Investigation of the Uncanny Valley Hypothesis and affective experience requires an understanding of the hypothesis' dimension of human likeness (DHL). This protocol allows representation of the DHL and examination of categorical perception. Use of the same stimuli and fMRI to distinguish brain regions responsive to physical and category change is illustrated.

Mori's Uncanny Valley Hypothesis1,2 proposes that the perception of humanlike characters such as robots and, by extension, avatars (computer-generated ...

Behavior

The Crossmodal Congruency Task as a Means to Obtain an Objective Behavioral Measure in the Rubber Hand Illusion Paradigm

The rubber hand illusion (RHI) is a popular experimental paradigm. Participants view touch on an artificial rubber hand while the participants' own hidden hand is touched. If the viewed and felt touches are given at the same time then this is sufficient to induce the compelling experience that the rubber hand is one's own hand. The RHI can be used to investigate exactly how the brain constructs distinct body representations for one's own body. Such representations are crucial for successful interactions with the external world. To obtain a subjective measure of the RHI, researchers typically ask participants to rate statements such as "I felt as if the rubber hand were my hand". Here we demonstrate how the crossmodal congruency task can be used to obtain an objective behavioral measure within this paradigm.
The variant of the crossmodal congruency task we employ involves the presentation of tactile targets and visual distractors. Targets and distractors are spatially congruent (i.e. same finger) on some trials and incongruent (i.e. different finger) on others. The difference in performance between incongruent and congruent trials - the crossmodal congruency effect (CCE) - indexes multisensory interactions. Importantly, the CCE is modulated both by viewing a hand as well as the synchrony of viewed and felt touch which are both crucial factors for the RHI.
The use of the crossmodal congruency task within the RHI paradigm has several advantages. It is a simple behavioral measure which can be repeated many times and which can be obtained during the illusion while participants view the artificial hand. Furthermore, this measure is not susceptible to observer and experimenter biases. The combination of the RHI paradigm with the crossmodal congruency task allows in particular for the investigation of multisensory processes which are critical for modulations of body representations as in the RHI.

We demonstrate how an objective measure can be employed in the widely employed rubber hand illusion paradigm. This measure is obtained by modifying the well-established crossmodal congruency task. This task allows the investigation of multisensory processes which are critical for modulations of body representations as in the rubber hand illusion.

The rubber hand illusion (RHI) is a popular experimental paradigm. Participants view touch on an artificial rubber hand while the participants' own hidden ...

Holistic Facial Composite Creation and Subsequent Video Line-up Eyewitness Identification Paradigm

The paradigm detailed in this manuscript describes an applied experimental method based on real police investigations during which an eyewitness or victim to a crime may create from memory a holistic facial composite of the culprit with the assistance of a police operator. The aim is that the composite is recognized by someone who believes that they know the culprit. For this paradigm, participants view a culprit actor on video and following a delay, participant-witnesses construct a holistic system facial composite. Controls do not construct a composite. From a series of arrays of computer-generated, but realistic faces, the holistic system construction method primarily requires participant-witnesses to select the facial images most closely meeting their memory of the culprit. Variation between faces in successive arrays is reduced until ideally the final image possesses a close likeness to the culprit. Participant-witness directed tools can also alter facial features, configurations between features and holistic properties (e.g., age, distinctiveness, skin tone), all within a whole face context. The procedure is designed to closely match the holistic manner by which humans&#8217; process faces. On completion, based on their memory of the culprit, ratings of composite-culprit similarity are collected from the participant-witnesses. Similar ratings are collected from culprit-acquaintance assessors, as a marker of composite recognition likelihood. Following a further delay, all participants &#8212; including the controls&#160;&#8212; attempt to identify the culprit in either a culprit-present or culprit-absent video line-up, to replicate circumstances in which the police have located the correct culprit, or an innocent suspect. Data of control and participant-witness line-up outcomes are presented, demonstrating the positive influence of holistic composite construction on identification accuracy. Correlational analyses are conducted to measure the relationship between assessor and participant-witness composite-culprit similarity ratings, delay, identification accuracy, and confidence to examine which factors influence video line-up outcomes.

This applied experimental paradigm replicates circumstances by which an eyewitness to a real crime may create a holistic facial composite of the culprit from memory, and then attempt to identify the culprit from a video line-up containing the culprit or one in which he or she is not present.

The paradigm detailed in this manuscript describes an applied experimental method based on real police investigations during which an eyewitness or victim ...

Psychophysically-anchored, Robust Thresholding in Studying Pain-related Lateralization of Oscillatory Prestimulus Activity

In perceptual studies, it is often important to objectively assess the equality of delivered stimulation across participants or to quantify the intra-individual sensation magnitude that is evoked by stimulation over multiple trials. This requires a robust mapping of stimulus magnitude to perceived intensity and is commonly achieved by psychophysical estimation methods such as the staircase procedure. Newer, more efficient procedures like the QUEST algorithm fit a psychophysical function to the data in real time while at the same time maximizing the efficiency of data collection. A robust estimate of the threshold intensity between painful and nonpainful perceptions can then be used to reduce the influence of variations in sensory input in subsequent analyses of oscillatory brain activity. By stimulating at a constant threshold intensity determined by an adaptive estimation procedure, the variance in the ratings can be directly attributed to perceptual processes. Oscillatory activity can then be contrasted between &#34;pain&#34; and &#34;no-pain&#34; trials directly, yielding activity that closely relates to perceptual classification processes in nociception.

Psychophysical methods such as the QUEST estimation procedure can efficiently yield robust estimates of the stimulation intensity at which nonpainful sensations transition into painful sensations. By stimulating repeatedly at the threshold intensity, the variability in rating responses can directly be attributed to perceptual classifications in subsequent analyses.

In perceptual studies, it is often important to objectively assess the equality of delivered stimulation across participants or to quantify the ...

Cross-Modal Multivariate Pattern Analysis

Multivariate pattern analysis (MVPA) is an increasingly popular method of analyzing functional magnetic resonance imaging (fMRI) data1-4. Typically, the method is used to identify a subject's perceptual experience from neural activity in certain regions of the brain. For instance, it has been employed to predict the orientation of visual gratings a subject perceives from activity in early visual cortices5 or, analogously, the content of speech from activity in early auditory cortices6.
Here, we present an extension of the classical MVPA paradigm, according to which perceptual stimuli are not predicted within, but across sensory systems. Specifically, the method we describe addresses the question of whether stimuli that evoke memory associations in modalities other than the one through which they are presented induce content-specific activity patterns in the sensory cortices of those other modalities. For instance, seeing a muted video clip of a glass vase shattering on the ground automatically triggers in most observers an auditory image of the associated sound; is the experience of this image in the "mind's ear" correlated with a specific neural activity pattern in early auditory cortices? Furthermore, is this activity pattern distinct from the pattern that could be observed if the subject were, instead, watching a video clip of a howling dog?
In two previous studies7,8, we were able to predict sound- and touch-implying video clips based on neural activity in early auditory and somatosensory cortices, respectively. Our results are in line with a neuroarchitectural framework proposed by Damasio9,10, according to which the experience of mental images that are based on memories - such as hearing the shattering sound of a vase in the "mind's ear" upon seeing the corresponding video clip - is supported by the re-construction of content-specific neural activity patterns in early sensory cortices.

Classical multivariate pattern analysis predicts sensory stimuli a subject perceives from neural activity in the corresponding cortices (e.g. visual stimuli from activity in visual cortex). Here, we apply pattern analysis cross-modally and show that sound- and touch-implying visual stimuli can be predicted from activity in auditory and somatosensory cortices, respectively.

Multivariate pattern analysis (MVPA) is an increasingly popular method of analyzing functional magnetic resonance imaging (fMRI) data1-4. Typically, the ...

A Two-interval Forced-choice Task for Multisensory Comparisons

We provide a procedure for a psychophysics experiment in humans based on a previously described paradigm aimed to characterize the perceptual duration of intervals within the range of milliseconds of visual, acoustic, and audiovisual aperiodic trains of six pulses. In this task, each of the trials consists of two consecutive intramodal intervals where the participants press the upward arrow key to report that the second stimulus lasted longer than the reference, or the downward arrow key to indicate otherwise. The analysis of the behavior results in psychometric functions of the probability of estimating the comparison stimulus to be longer than the reference, as a function of the comparison intervals. In conclusion, we advance a way of implementing standard programming software to create visual, acoustic, and audiovisual stimuli, and to generate a two-interval forced-choice (2IFC) task by delivering stimuli through noise-blocking headphones and a computer&#39;s monitor.

Psychophysics is essential for studying perception phenomena through sensory information. Here we present a protocol to perform a two-interval forced-choice task as implemented in a previous report on human psychophysics where participants estimated the duration of visual, auditory, or audiovisual intervals of aperiodic trains of pulses.

We provide a procedure for a psychophysics experiment in humans based on a previously described paradigm aimed to characterize the perceptual duration of ...

Interaction between Phonological and Semantic Processes in Visual Word Recognition using Electrophysiology

Controversies have always existed in research related to reading abilities; on whether printed words are perceived in a feedforward manner based on orthographic information after which, other representations, such as phonology and semantics are activated, or whether these are fully interactive and high-level semantic information affects early processing. An interference paradigm was implemented in the presented protocol of phonological and semantic judgment tasks that utilized the same precede-target pairs to explore the relative order of phonological and semantic activation. The high- and low-frequency target words were preceded with three conditions: semantically related, phonological-related (homophones), or unrelated. The results showed that the induced P200 component of low-frequency word pairs was significantly greater than high-frequency words in both the semantic and phonological tasks. In addition, both the homophones in the semantic task and the semantically related pairs in the phonological task caused reduction in N400 when compared to the the control condition, word frequency-independently. It is worth noting that for the low-frequency pairs in the phonological judgment task, the P200 released by the semantically related word pairs was significantly larger than that in the control condition. Overall, semantic processing in phonological tasks and phonological processing in semantic tasks were found in both high- and low-frequency words, suggesting that the interaction between semantics and phonology may operate in a task-independent manner. However, the specific time this interaction occurred may have been affected by the task and frequency.

We present a protocol to explore the relative activation sequence of phonology and semantics in visual word recognition. The results show that consistent with interactive accounts, semantic and phonological representations may be processed interactively, and higher-level linguistic representations may affect early processing.

Controversies have always existed in research related to reading abilities; on whether printed words are perceived in a feedforward manner based on ...

Assessment and Communication for People with Disorders of Consciousness

In this experiment, we demonstrate a suite of hybrid Brain-Computer Interface (BCI)-based paradigms that are designed for two applications: assessing the level of consciousness of people unable to provide motor response and, in a second stage, establishing a communication channel for these people that enables them to answer questions with either &#39;yes&#39; or &#39;no&#39;. The suite of paradigms is designed to test basic responses in the first step and to continue to more comprehensive tasks if the first tests are successful. The latter tasks require more cognitive functions, but they could provide communication, which is not possible with the basic tests. All assessment tests produce accuracy plots that show whether the algorithms were able to detect the patient&#39;s brain&#39;s response to the given tasks. If the accuracy level is beyond the significance level, we assume that the subject understood the task and was able to follow the sequence of commands presented via earphones to the subject. The tasks require users to concentrate on certain stimuli or to imagine moving either the left or right hand. All tasks are designed around the assumption that the user is unable to use the visual modality, and thus, all stimuli presented to the user (including instructions, cues, and feedback) are auditory or tactile.

With this experiment, one might be able to detect consciousness in people with disorders of consciousness. Furthermore, the approach can create a simple communication channel that enables people to give simple YES/NO answers to questions.

In this experiment, we demonstrate a suite of hybrid Brain-Computer Interface (BCI)-based paradigms that are designed for two applications: assessing the ...

The Joint Effect of Social Comparison and Social Distance on Evaluation of Intertemporal Choice Outcomes in Event-related Potential Studies

Intertemporal choice plays a crucial role in our daily lives, influencing decisions related to education, health, consumption, and investment. This research proposes an innovative experimental protocol that examines how social comparison and social distance jointly affect the neural processes involved in outcome assessment for intertemporal choices. The study is based on the theoretical framework of cognitive resource competition. This protocol enables researchers to dynamically establish an indifference point for each participant, effectively eliminating the influence of any biased indifference points on the assessment of intertemporal choices. Consequently, the study solely measures the combined impact of social comparison and social distance on how participants evaluate intertemporal choice outcomes. The findings reveal that individuals are more inclined to opt for immediate outcomes under negative unfair conditions. Moreover, compared to the fair and positive unfair conditions, people tend to undervalue delayed outcomes in the negative unfair condition. The strength of this approach lies in its dynamic indifference point setting, making it an effective method to investigate the influence of various external factors (such as social status and power level) on intertemporal decision-making. While the protocol is designed to measure electrophysiological events like event-related potentials, it can also be tailored for use with fMRI.

This protocol aims to investigate the neural activity related to social comparison and social distance during the processing of intertemporal decision outcomes. Indifference points will be measured using event-related potentials as part of the study.

Intertemporal choice plays a crucial role in our daily lives, influencing decisions related to education, health, consumption, and investment. This ...

Evaluating the Accuracy of Snap Judgments

Source: Diego Reinero &#38; Jay Van Bavel&#8212;New York University
Social psychologists have long been interested in the way people form impressions of others. Much of this work has focused on the errors people make in judging others, such as the exaggerated influence of central traits (such as &#34;warm&#34; and &#34;cold&#34;), the insufficient weight given to the context in which others&#39; behavior takes place, and the tendency for people to make judgments that conform to their initial expectations about another. However, this focus on errors masks the fact that people are quite good at making fairly accurate judgments about other people&#39;s characteristics, an ability that was no doubt important over the course of human evolution.
Indeed, the human ability to make quick sense of social situations and people ranks among our most valuable skills. What is particularly impressive about our ability to make sense of others is not just how little information we need to make inferences, but how well calibrated we can be with so little information. This video shows some experimental techniques used by psychology researchers, including Ambady and Rosenthal in their seminal work,1 and explores the process of making inferences in the context of students&#39; evaluations of their teachers.

Source: Diego Reinero &#38; Jay Van Bavel&#8212;New York University
Social psychologists have long been interested in the way people form impressions of ...