[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-564033-105":53,"doc-detail-564033-en":127},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":120,"head_meta":122,"extra_data":124,"updated_unix":126},105,"en","optimizing-feature-ordering-in-radar-charts-for-multi-profile-comparison","Optimizing Feature Ordering in Radar Charts for Multi-Profile Comparison","","Radar charts are widely used to visualize multivariate data and compare multiple profiles across features, but visual clarity degrades when feature magnitudes alternate sharply around the circle, causing polygon collapse and misleading relative differences. This work proposes a permutation optimization strategy that reorders features to minimize polygon “spikiness” across profiles simultaneously. The method uses exhaustive search for moderate feature counts and a lexicographic minimax criterion prioritizing smoothness (mean jump) and then the largest single jump. Complexity, practical bounds, and relations to transformation and learning-based approaches are discussed, including a two-profile p=6 example demonstrating qualitative improvement.",{"@graph":63,"@context":119},[64,80,102],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":51,"@type":70,"position":76},"https://docshare.wps.com/template/general/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/optimizing-feature-ordering-in-radar-charts-for-multi-profile-comparison/564033/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/optimizing-feature-ordering-in-radar-charts-for-multi-profile-comparison/564033.png","ImageObject",442,249,{"name":88,"@type":89},"Well Done","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-11-03","2026-10-12",true,{"@type":98,"interactionType":99,"userInteractionCount":101},"InteractionCounter",{"@type":100},"ViewAction",6,{"@type":103,"mainEntity":104},"FAQPage",[105,111,115],{"name":106,"@type":107,"acceptedAnswer":108},"What problem does the paper address in radar chart comparisons?","Question",{"text":109,"@type":110},"Radar chart interpretation can be distorted by feature axis ordering: sharp magnitude changes between adjacent features produce exaggerated spikes or valleys, and can even cause inward collapse, misrepresenting similarity or dissimilarity across profiles.","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"How does the proposed method improve feature ordering?",{"text":114,"@type":110},"It reorders feature axes to minimize polygon “spikiness” across multiple profiles, optimizing for smoothness via a lexicographic minimax objective that first reduces the mean adjacent difference and then controls the largest single jump.",{"name":116,"@type":107,"acceptedAnswer":117},"When is the method computationally feasible?",{"text":118,"@type":110},"The approach uses exhaustive search for moderate numbers of features, and the paper discusses complexity and practical bounds, highlighting globally optimal and reproducible orderings for small to moderate dimensionalities.","https://schema.org",{"og:url":78,"og:type":121,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":123,"canonical":78},"index,follow",{"doc_id":125,"site_id":56},564033,1792174518,{"code":4,"msg":5,"data":128},{"doc_id":125,"user_id":129,"nickname":88,"user_avatar":130,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":61,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":101,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":136,"language":137,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":138,"faqs":139,"seo_title":140,"seo_description":61,"update_tm":141,"read_time":76},5909892210082,"https://ap-avatar.wpscdn.com/avatar/56001069da27c9f41e8?x-image-process=image/resize,m_fixed,w_180,h_180&k=1789614185077863061","arXiv :2510 .20738v1 [ cs .HC] 23 Oct 2025  \nOptimizing Feature Ordering in Radar Charts for Multi-Profile  \nComparison  \nAlbert Dorador  \n[trustalgorithm. dev@gmail. com](trustalgorithm. dev@gmail. com)  \nOctober 24, 2025  \nAbstract  \nRadar charts are widely used to visualize multivariate data and compare multiple profiles across features. However, the visual clarity of radar charts can be severely compromised when feature values alternate drastically in magnitude around the circle, causing areas to collapse, which misrepresents relative differences. In the present work we introduce a permutation optimization strategy that reorders features to minimize polygon “spikiness” across multiple profiles simultaneously. The method is combinatorial (exhaustive search) for moderate numbers of features and uses a lexicographic minimax criterion that first considers overall smoothness (mean jump) and then the largest single jump as a tie-breaker. This preserves more global information and produces visually balanced arrangements. We discuss complexity, practical bounds, and relations to existing approaches that either change the visualization (e.g., OrigamiPlot) or learn orderings (e.g., Versatile Ordering Network) . An example with two profiles and p = 6 features (before/after ordering) illustrates the qualitative improvement.  \n1 Introduction  \nRadar charts (also known as spiderweb or star plots) provide a compact visual summary of multivariate observations by placing feature axes radially and connecting the corresponding values into a polygon. Their appeal lies in the intuitive mapping between polygon shape and the underlying data, making them popular for visual comparisons at small dimensionalities. However, because features typically have no intrinsic circular order, the geometry of the radar chart – and thus human interpretation – depends greatly on how the axes are arranged.  \nThis dependence introduces a subtle but critical source of distortion. When adjacent features differ sharply in magnitude, the resulting polygon may exhibit exaggerated spikes or valleys, or even collapse inward when high and low values alternate. These artifacts can mislead viewers about the similarity or dissimilarity between profiles, creating illusory structure where none exists. Unlike time series or ordinal data, most radar chart features are unordered, meaning that any apparent trends or patterns can arise solely from arbitrary axis placement.  \nThe interpretive consequences of axis ordering are well documented. Human vision tends to treat polygon shape as a meaningful pattern (shape-driven perception), so abrupt transitions between neighboring features are perceived as instability or imbalance. In multi-profile comparisons, poor ordering can also exaggerate or obscure genuine contrasts, reducing the chart’s communicative value.  \nIn practical settings – such as exploratory data analysis, advanced model explanation pipelines, or market analytics – radar charts are often used to compare a small number of selected features across multiple profiles. In such contexts, an ordering that causes polygon collapse or excessive  \njaggedness is unappealing at best, and completely misleading at worst, as it may conceal structure that another permutation would reveal, or, conversely, artificially suggest structure where none exists.The challenge, then, is to determine a feature ordering that preserves geometric interpretability and visual balance across all profiles being compared.  \nMotivated by this problem, we introduce a deterministic, objective-driven reordering method that seeks feature permutations minimizing abrupt changes between consecutive axes. The proposed approach is data-driven, requires no manual intervention, transparent, and interpretable: it optimizes for smoothness across profiles without altering the traditional radar geometry. Rather than imposing semantic meaning on the order of features, our method aims to minimize visual distortion and enhan","cbCaidcd4xC6eoAv","https://ap.wps.com/l/cbCaidcd4xC6eoAv","pdf",708103,7,"English","# Abstract\n# 1 Introduction\n# 2 Related Work: How Our Approach Fits in the Landscape\n## 2.1 OrigamiPlot and area-invariant visual transforms\n## 2.2 Learning to order: Versatile Ordering Network (VON)\n## 2.3 Our contribution","[{\"question\":\"What problem does the paper address in radar chart comparisons?\",\"answer\":\"Radar chart interpretation can be distorted by feature axis ordering: sharp magnitude changes between adjacent features produce exaggerated spikes or valleys, and can even cause inward collapse, misrepresenting similarity or dissimilarity across profiles.\"},{\"question\":\"How does the proposed method improve feature ordering?\",\"answer\":\"It reorders feature axes to minimize polygon “spikiness” across multiple profiles, optimizing for smoothness via a lexicographic minimax objective that first reduces the mean adjacent difference and then controls the largest single jump.\"},{\"question\":\"When is the method computationally feasible?\",\"answer\":\"The approach uses exhaustive search for moderate numbers of features, and the paper discusses complexity and practical bounds, highlighting globally optimal and reproducible orderings for small to moderate dimensionalities.\"}]","Optimizing Feature Ordering in Radar Charts for Multi-Profile Comparison | PDF",1791839924]