Spatial Arrangement Method Research Articles

Evidence-Theory-Based Reliability Analysis From the Perspective of Focal Element Classification Using Deep Learning Approach

Abstract Epistemic uncertainty is widespread in reliability analysis of practical engineering products. Evidence theory is regarded as a powerful model for quantifying and analyzing epistemic uncertainty. However, the heavy computational burden has severely hindered its application in practical engineering problems, which is essentially caused by the repeated extreme analysis of limit-state function (LSF). In order to address the issue, this paper proposes a novel method to solve the evidence-theory-based reliability analysis (ETRA). It transforms the conventional ETRA problem into the classification of three classes of joint focal elements (JFEs) and then solves the classification problem effectively through a deep learning approach. The core of solving an ETRA problem is to determine whether the joint focal element is located in the reliable region, failure region, or intersected with the LSF. A spatial position feature reduction and arrangement method is proposed to classify the JFEs, which can effectively reduce the feature dimension and take into account the integrity and correlation of features. The stacked autoencoders model is then constructed and updated by extracting the spatial position features of the sampled JFEs to achieve high-accuracy classification of the remaining JFEs, and the reliability interval is calculated efficiently according to the classification results. Finally, the effectiveness of the proposed method is demonstrated using several numerical examples.

Whether the Pairwise Rating Method and the Spatial Arrangement Method yield comparable dimensionalities depends on the dimensionality choice procedure

We investigate whether the Pairwise Rating Method (PRaM) and the Spatial Arrangement Method (SpAM) yield multidimensional scaling (MDS) solutions of comparable dimensionality. Across three studies that included twelve semantic categories with varying numbers of both pictorial and verbal exemplars, we did not find consistent dimensionality differences between the two similarity measurement methods. The results alleviate the concern that SpAM might underestimate the dimensionality of high-dimensional stimuli compared to PRaM. However, the resulting number of dimensions was found to be highly dependent on the dimensionality choice procedure, indicating the need for a more systematic investigation into dimensionality selection for MDS.

The representation of emotion knowledge across development.

The present study examined how children spontaneously represent facial cues associated with emotion. 106 three‐ to six‐year‐old children (48 male, 58 female; 9.4% Asian, 84.0% White, 6.6% more than one race) and 40 adults (10 male, 30 female; 10% Hispanic, 30% Asian, 2.5% Black, 57.5% White) were recruited from a Midwestern city (2019–2020), and sorted emotion cues in a spatial arrangement method that assesses emotion knowledge without reliance on emotion vocabulary. Using supervised and unsupervised analyses, the study found evidence for continuities and gradual changes in children's emotion knowledge compared to adults. Emotion knowledge develops through an incremental learning process in which children change their representations using combinations of factors—particularly valence—that are weighted differently across development.

A Comparison of the Spatial Arrangement Method and the Total-Set Pairwise Rating Method for Obtaining Similarity Data in the Conceptual Domain

We compare two methods for obtaining similarity data in the conceptual domain. In the Spatial Arrangement Method (SpAM), participants organize stimuli on a computer screen so that the distance between stimuli represents their perceived dissimilarity. In Total-Set Pairwise Rating Method (PRaM), participants rate the (dis)similarity of all pairs of stimuli on a Likert scale. In each of three studies, we had participants indicate the similarity of four sets of conceptual stimuli with either PRaM or SpAM. Studies 1 and 2 confirm two caveats that have been raised for SpAM. (i) While SpAM takes significantly less time to complete than PRaM, it yields less reliable data than PRaM does. (ii) Because of the spatial manner in which similarity is measured in SpAM, the method is biased against feature representations. Despite these differences, averaging SpAM and PRaM dissimilarity data across participants yields comparable aggregate data. Study 3 shows that by having participants only judge half of the pairs in PRaM, its duration can be significantly reduced, without affecting the dissimilarity distribution, but at the cost of a smaller reliability. Having participants arrange multiple subsets of the stimuli does not do away with the spatial bias of SpAM.

The spatial arrangement method of measuring similarity can capture high-dimensional semantic structures.

Psychologists collect similarity data to study a variety of phenomena including categorization, generalization and discrimination, and representation itself. However, collecting similarity judgments between all pairs of items in a set is expensive, spurring development of techniques like the Spatial Arrangement Method (SpAM; Goldstone, Behavior Research Methods, Instruments, & Computers, 26, 381-386, 1994), wherein participants place items on a two-dimensional plane such that proximity reflects perceived similarity. While SpAM greatly hastens similarity measurement, and has been successfully used for lower-dimensional, perceptual stimuli, its suitability for higher-dimensional, conceptual stimuli is less understood. In study 1, we evaluated the ability of SpAM to capture the semantic structure of eight different categories composed of 20-30 words each. First, SpAM distances correlated strongly (r = .71) with pairwise similarity judgments, although below SpAM and pairwise judgment split-half reliabilities (r's > .9). Second, a cross-validation exercise with multidimensional scaling fits at increasing latent dimensionalities suggested that aggregated SpAM data favored higher (> 2) dimensional solutions for seven of the eight categories explored here. Third, split-half reliability of SpAM dissimilarities was high (Pearson r = .90), while the average correlation between pairs of participants was low (r = .15), suggesting that when different participants focus on different pairs of stimulus dimensions, reliable high-dimensional aggregate similarity data is recoverable. In study 2, we show that SpAM can recover the Big Five factor space of personality trait adjectives, and that cross-validation favors a four- or five-dimension solution on this dataset. We conclude that SpAM is an accurate and reliable method of measuring similarity for high-dimensional items like words. We publicly release our data for researchers.

SOLID-Similar object and lure image database

Stimulus selection is a critical part of experimental designs in the cognitive sciences. Quantifying and controlling item similarity using a unified scale provides researchers with the tools to eliminate item-dependent effects and improve reproducibility. Here we present a novel Similar Object and Lure Image Database (SOLID) that includes 201 categories of grayscale objects, with approximately 17 exemplars per set. Unlike existing databases, SOLID offers both a large number of stimuli and a considerable range of similarity levels. A common scale of dissimilarity was obtained by using the spatial-arrangement method (Exps. 1a and 1b) as well as a pairwise rating procedure to standardize the distances (Exp. 2). These dissimilarity distances were then validated in a recognition memory task, showing better performance and decreased response times as dissimilarity increased. These methods were used to produce a large stimulus database (3,498 images) with a wide range of comparable similarities, which will be useful for improving experimental control in fields such as memory, perception, and attention. Enabling this degree of control over similarity is critical for high-level studies of memory and cognition, and combining this strength with the option to use it across many trials will allow research questions to be addressed using neuroimaging techniques.

A general valence asymmetry in similarity: Good is more alike than bad.

The density hypothesis (Unkelbach, Fiedler, Bayer, Stegmüller, & Danner, 2008) claims a general higher similarity of positive information to other positive information compared with the similarity of negative information to other negative information. This similarity asymmetry might explain valence asymmetries on all levels of cognitive processing. The available empirical evidence for this general valence asymmetry in similarity suffers from a lack of direct tests, low representativeness, and possible confounding variables (e.g., differential valence intensity, frequency, familiarity, or concreteness of positive and negative stimuli). To address these problems, Study 1 first validated the spatial arrangement method (SpAM) as a similarity measure. Using SpAM, Studies 2-6 found the proposed valence asymmetry in large, representative samples of self- and other-generated words (Studies 2a/2b), for words of consensual and idiosyncratic valence (Study 3), for words from 1 and many independent information sources (Study 4), for real-life experiences (Study 5), and for large data sets of verbal (i.e., ∼14,000 words reported by Warriner, Kuperman, & Brysbaert, 2013) and visual information (i.e., ∼1,000 pictures reported in the IAPS; Lang, Bradley, & Cuthbert, 2005; Study 6). Together, these data support a general valence asymmetry in similarity, namely that good is more alike than bad. (PsycINFO Database Record

Developmental changes in semantic knowledge organization

Semantic knowledge is a crucial aspect of higher cognition. Theoretical accounts of semantic knowledge posit that relations between concepts provide organizational structure that converts information known about individual entities into an interconnected network in which concepts can be linked by many types of relations (e.g., taxonomic, thematic). The goal of the current research was to address several methodological shortcomings of prior studies on the development of semantic organization, by using a variant of the spatial arrangement method (SpAM) to collect graded judgments of relatedness for a set of entities that can be cross-classified into either taxonomic or thematic groups. In Experiment 1, we used the cross-classify SpAM (CC–SpAM) to obtain graded relatedness judgments and derive a representation of developmental changes in the organization of semantic knowledge. In Experiment 2, we validated the findings of Experiment 1 by using a more traditional pairwise similarity judgment paradigm. Across both experiments, we found that an early recognition of links between entities that are both taxonomically and thematically related preceded an increasing recognition of links based on a single type of relation. The utility of CC–SpAM for evaluating theoretical accounts of semantic development is discussed.

SpAM is convenient but also satisfying: Reply to Verheyen et al. (2016).

Hout, Goldinger, and Ferguson (2013) critically examined the spatial arrangement method (SpAM), originally proposed by Goldstone (1994), as a fast and efficient way to collect similarity data for multidimensional scaling. We found that SpAM produced high-quality data, making it an intuitive and user-friendly alternative to the classic "pairwise" method. Verheyen, Voorspoels, Vanpaemel, and Storms (2016) reexamined our data and raised 3 caveats regarding SpAM. In this reply, we suggest that Verheyen et al. mischaracterized our reported data as representing the entire range of potential SpAM data. SpAM results might appear more nuanced with modified instructions or stimuli. By contrast, the pairwise method is inherently limited because of its laborious, serial nature. We also demonstrate that, when the methods are equated in terms of required data-collection time, SpAM is clearly superior in terms of predicting classification data. We agree that caution is required when adopting a new method but suggest that fair assessment of SpAM requires a richer data set.

Caveats for the spatial arrangement method: Comment on Hout, Goldinger, and Ferguson (2013).

The gold standard among proximity data collection methods for multidimensional scaling is the (dis)similarity rating of pairwise presented stimuli. A drawback of the pairwise method is its lengthy duration, which may cause participants to change their strategy over time, become fatigued, or disengage altogether. Hout, Goldinger, and Ferguson (2013) recently made a case for the Spatial Arrangement Method (SpAM) as an alternative to the pairwise method, arguing that it is faster and more engaging. SpAM invites participants to directly arrange stimuli on a computer screen such that the interstimuli distances are proportional to psychological proximity. Based on a reanalysis of the Hout et al. (2013), data we identify three caveats for SpAM. An investigation of the distributional characteristics of the SpAM proximity data reveals that the spatial nature of SpAM imposes structure on the data, invoking a bias against featural representations. Individual-differences scaling of the SpAM proximity data reveals that the two-dimensional nature of SpAM allows individuals to only communicate two dimensions of variation among stimuli properly, invoking a bias against high-dimensional scaling representations. Monte Carlo simulations indicate that in order to obtain reliable estimates of the group average, SpAM requires more individuals to be tested. We conclude with an overview of considerations that can inform the choice between SpAM and the pairwise method and offer suggestions on how to overcome their respective limitations.

Supplemental Material for Caveats for the Spatial Arrangement Method: Comment on Hout, Goldinger, and Ferguson (2013)

Supplemental Material for Caveats for the Spatial Arrangement Method: Comment on Hout, Goldinger, and Ferguson (2013)

MM-MDS: a multidimensional scaling database with similarity ratings for 240 object categories from the Massive Memory picture database.

Cognitive theories in visual attention and perception, categorization, and memory often critically rely on concepts of similarity among objects, and empirically require measures of “sameness” among their stimuli. For instance, a researcher may require similarity estimates among multiple exemplars of a target category in visual search, or targets and lures in recognition memory. Quantifying similarity, however, is challenging when everyday items are the desired stimulus set, particularly when researchers require several different pictures from the same category. In this article, we document a new multidimensional scaling database with similarity ratings for 240 categories, each containing color photographs of 16–17 exemplar objects. We collected similarity ratings using the spatial arrangement method. Reports include: the multidimensional scaling solutions for each category, up to five dimensions, stress and fit measures, coordinate locations for each stimulus, and two new classifications. For each picture, we categorized the item's prototypicality, indexed by its proximity to other items in the space. We also classified pairs of images along a continuum of similarity, by assessing the overall arrangement of each MDS space. These similarity ratings will be useful to any researcher that wishes to control the similarity of experimental stimuli according to an objective quantification of “sameness.”

함정 내부 공간별 기능 및 상호관계를 고려한 함정 공간배치 방법에 관한 연구

This paper presents a method that generates alternatives of spatial arrangement for naval ships with limited information. To attain this end, GA (General Arrangement) methodology and GA reports of existing naval ships are analyzed. In order to improve the current naval ship spatial arrangement method that relies on the experience and know-hows of designers, we propose a systematic spatial arrangement process using SLP (Systematic Layout Planning), which determines relative positions of the components by analyzing relationships among them. The proposed method, along with the GA process, is applied to a virtual naval ship and layout alternatives are generated to verify usefulness of the method.

The versatility of SpAM: a fast, efficient, spatial method of data collection for multidimensional scaling.

Although traditional methods to collect similarity data (for multidimensional scaling [MDS]) are robust, they share a key shortcoming. Specifically, the possible pairwise comparisons in any set of objects grow rapidly as a function of set size. This leads to lengthy experimental protocols, or procedures that involve scaling stimulus subsets. We review existing methods of collecting similarity data, and critically examine the spatial arrangement method (SpAM) proposed by Goldstone (1994a), in which similarity ratings are obtained by presenting many stimuli at once. The participant moves stimuli around the computer screen, placing them at distances from one another that are proportional to subjective similarity. This provides a fast, efficient, and user-friendly method for obtaining MDS spaces. Participants gave similarity ratings to artificially constructed visual stimuli (comprising 2-3 perceptual dimensions) and nonvisual stimuli (animal names) with less-defined underlying dimensions. Ratings were obtained with 4 methods: pairwise comparisons, spatial arrangement, and 2 novel hybrid methods. We compared solutions from alternative methods to the pairwise method, finding that the SpAM produces high-quality MDS solutions. Monte Carlo simulations on degraded data suggest that the method is also robust to reductions in sample sizes and granularity. Moreover, coordinates derived from SpAM solutions accurately predicted discrimination among objects in same-different classification. We address the benefits of using a spatial medium to collect similarity measures.