[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118770-en":3,"doc-seo-118770-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},118770,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1785132997149421697",8,"Research & Report","Quadtree features for machine learning on CMDs - Abstract","Upcoming wide-field facilities such as the Vera C. Rubin Observatory will deliver extremely deep photometry for thousands of star clusters, enabling analysis out to the edge of the Galaxy and beyond. Color-magnitude diagrams (CMDs) represent these observations as point clouds in an N-dimensional space, but their variable star counts and required permutation equivariance limit direct use of standard tabular machine-learning methods. To overcome this, a new CMD featurization procedure summarizes each CMD using an iterative quadtree-like partitioning of the color-magnitude plane, yielding a fixed set of meaningful features. The approach remains robust to photometric noise and contamination and enables linear regression to predict distance modulus and metallicity with strong cross-validation performance.","Quadtree features for machine learning on CMDs  \nJ. Schiappacasse-Ulloa * 1 M. Pasquato * 1 2 3 4 S. Lucatello 5  \narXiv :2306 . 15487v1 [ astro-ph .IM] 27 Jun 2023  \nAbstract  \nThe upcoming facilities like the Vera C. Rubin Observatory will provide extremely deep photometry of thousands of star clusters to the edge of the Galaxy and beyond, which will require adequate tools for automatic analysis, capable of performing tasks such as the characterization of a star cluster through the analysis of color-magnitude diagrams (CMDs) . The latter are essentially point clouds in N-dimensional space, with the number of dimensions corresponding to the photometric bands employed. In this context, machine learning techniques suitable for tabular data are not immediately applicable to CMDs because the number of stars included in a given CMD is variable, and equivariance for permutations is required. To address this issue without introducing ad-hoc manipulations that would require human oversight, here we present a new CMD featurization procedure that summarizes a CMD by means of aquadtree-like structure through iterative partitions of the color-magnitude plane, extracting a fixed number of meaningful features of the relevant subregion from any given CMD. The present approach is robust to photometric noise and contamination and it shows that a simple linear regression on our features predicts distance modulus (metallicity) with a scatter of 0:33 dex (0:16 dex) in cross-validation.  \n*Equal contribution 1Dipartimento di Fisica e Astronomia, Universita' di Padova, Vicolo dell'Osservatorio 3, I- 35122, Padova, Italy. 2Dpartement de Physique, Universit de Montral, Montreal, Quebec H3T 1J4, Canada. 3Mila  \n- Quebec Artificial Intelligence Institute, Montreal, Quebec, Canada 4 Ciela, Computation and Astrophysical Data Analysis Institute, Montreal, Quebec, Canada 5INAF–Osservatorio Astronomico di Padova, Vicolo dell'Osservatorio 5, 35122 Padova, Italy. Correspondence to: Jose Schiappcasse-Ulloa \u003C[joseluis.schiappacasseulloa@studenti.unipd.it](joseluis.schiappacasseulloa@studenti.unipd.it) >. Proceedings of the 40 th International Conference on Machine Learning, Honolulu, Hawaii, USA. PMLR 202, 2023 . Copyright 2023 by the author(s) .  \n1. Introduction  \nThe photometric study of stellar populations typically relies on point-spread-function fitting to measure magnitudes in relevant bands. These are then combined to derive colormagnitude diagrams (CMDs) which are used to reconstruct stellar population characteristics. By comparing theoretical stellar evolutionary tracks and isochrones with the location of CMD landmarks (in terms of color and magnitude) such as the Red Clump, Horizontal Branch, turn-off, etc. we can estimate the age, metallicity, reddening, and distance in resolved Open Clusters (OCs) and Globular Clusters (GCs; e.g. Cassisi & Salaris, 2013) . Properties, such as the width of the evolutionary sequences or turn-off broadening, measure binary fraction or dispersion in age, metallicity, and rotational velocity (e.g. Milone et al., 2012) .  \nCurrently, the highest quality CMDs are derived from Hubble Space Telescope (HST) photometry which, however, was far limited to very small sections of the clusters given the small field of view (FOV; 2x2 arcmin) and WFC3 – HST's most advanced camera– that has a magnitude limit of up to V􀀘 25.5. On the other hand, the upcoming facility Vera C. Rubin Observatory will have a FOV of 9:6 square degrees and a magnitude limit of 27:5 in the r band over most of the southern hemisphere. Then, it is expected to yield accurate turn-off photometry of all star clusters in its survey volume out to the edge of the Milky Way (MW) . Alongside opportunities, the volume of data (roughly 20 TB/night) collected will bring extraordinary challenges in data handling, and developing new approaches to reduction and analysis strategies.  \nIn particular, the most common approaches to studying CMDs of stellar clusters are optimized f","cbCailMIo36KIWh4","https://ap.wps.com/l/cbCailMIo36KIWh4","pdf",1109990,1,10,"English","en",105,"# Introduction\n## State of the art","[{\"question\":\"Why are standard machine-learning methods difficult to apply directly to CMDs?\",\"answer\":\"CMDs correspond to point clouds with variable numbers of stars per diagram, so inputs are not fixed-size. Additionally, the learning model must respect permutation equivariance over stars, which tabular-focused methods typically do not handle naturally.\"},{\"question\":\"What is the proposed featurization approach for CMDs?\",\"answer\":\"The method partitions the CMD plane recursively in an iterative quadtree-like manner. From each relevant subregion, it extracts a fixed number of meaningful numeric features that summarize the full CMD without ad-hoc human interventions.\"},{\"question\":\"How well do the extracted features perform for predicting astrophysical properties?\",\"answer\":\"Using a simple linear regression on the proposed features, the model predicts distance modulus (and metallicity) with reported cross-validation scatter values of about 0.33 dex (and 0.16 dex), while remaining robust to photometric noise and contamination.\"}]","Quadtree features for machine learning on CMDs - Abstract | PDF",1785720149,25,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"quadtree-features-for-machine-learning-on-cmds-abstract","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/quadtree-features-for-machine-learning-on-cmds-abstract/118770/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why are standard machine-learning methods difficult to apply directly to CMDs?","Question",{"text":75,"@type":76},"CMDs correspond to point clouds with variable numbers of stars per diagram, so inputs are not fixed-size. Additionally, the learning model must respect permutation equivariance over stars, which tabular-focused methods typically do not handle naturally.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the proposed featurization approach for CMDs?",{"text":80,"@type":76},"The method partitions the CMD plane recursively in an iterative quadtree-like manner. From each relevant subregion, it extracts a fixed number of meaningful numeric features that summarize the full CMD without ad-hoc human interventions.",{"name":82,"@type":73,"acceptedAnswer":83},"How well do the extracted features perform for predicting astrophysical properties?",{"text":84,"@type":76},"Using a simple linear regression on the proposed features, the model predicts distance modulus (and metallicity) with reported cross-validation scatter values of about 0.33 dex (and 0.16 dex), while remaining robust to photometric noise and contamination.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":21,"slug":133},"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]