{"id":11678,"date":"2021-06-24T10:20:43","date_gmt":"2021-06-24T07:20:43","guid":{"rendered":"https:\/\/umram.bilkent.edu.tr\/?p=11678"},"modified":"2021-06-24T10:22:11","modified_gmt":"2021-06-24T07:22:11","slug":"11678","status":"publish","type":"post","link":"https:\/\/umram.bilkent.edu.tr\/index.php\/tr\/2021\/06\/24\/11678\/","title":{"rendered":"UMRAM’dan Yeni Bir Makale: Graph Signal Processing: Vertex Multiplication"},"content":{"rendered":"

Ko\u00e7Lab<\/a>‘\u0131n Graph Signal Processing’e (GSP) temel bir katk\u0131s\u0131 yak\u0131n zamanda Vertex Multiplication adl\u0131 yeni bir i\u015flemin tan\u0131t\u0131ld\u0131\u011f\u0131 IEEE Signal Processing Letters’da yay\u0131nland\u0131.<\/p>\n

Klasik sinyal i\u015flemenin \u00d6klid alanlar\u0131nda, sinyal \u00f6rneklerinin alttaki koordinat yap\u0131s\u0131na ba\u011flanmas\u0131 basittir. Bununla birlikte, grafik sinyal i\u015flemedeki \u00f6nemli bir problem, bir grafi\u011fin k\u00f6\u015feleri, sadece s\u0131ra indeksleri d\u0131\u015f\u0131nda belirli a\u00e7\u0131k nicel de\u011ferlere kar\u015f\u0131l\u0131k gelmedi\u011finden, altta yatan bir koordinat yap\u0131s\u0131 ile k\u00f6\u015felerin a\u00e7\u0131k bir \u015fekilde ili\u015fkilendirilmemesidir.<\/p>\n

Grafikler i\u00e7in tan\u0131mlanan ve grafik sinyalleri \u00fczerinde \u00e7al\u0131\u015fabilen k\u00f6\u015fe \u00e7arpmas\u0131 (VM), bu ba\u011flant\u0131y\u0131 Fourier dualitesini kullanarak kurmu\u015f ve klasik sinyal i\u015flemede koordinat \u00e7arpma i\u015flemini genelle\u015ftirmi\u015ftir. VM, FT\/DFT teorisinin teorik yap\u0131s\u0131 ile tamamen tutarl\u0131 olarak tan\u0131mlan\u0131r.<\/p>\n

B\u00f6yle a\u00e7\u0131k bir koordinat ili\u015fkisi, klasik sinyal i\u015flemeden grafik sinyal i\u015flemeye kadar devam eden genellemelerde yard\u0131mc\u0131 olabilir.
\nAyr\u0131ca, yeni teorik ve hesaplamal\u0131 \u00e7abalara yol a\u00e7abilir ve k\u00f6\u015fe alan\u0131ndaki p\u00fcr\u00fczs\u00fczl\u00fck, mesafe \u00f6l\u00e7\u00fcmleri ve yerelle\u015ftirme kavram\u0131na olas\u0131 i\u00e7g\u00f6r\u00fcler ve uygulamalar ile k\u00f6\u015fe ve frekans alanlar\u0131 aras\u0131ndaki ba\u011flant\u0131ya ili\u015fkin teorik anlay\u0131\u015f\u0131m\u0131z\u0131 derinle\u015ftirebilir ve grafikler \u00fczerindeki sinyaller i\u00e7in d\u00f6n\u00fc\u015f\u00fcm tasar\u0131mlar\u0131 yapabilir. .
\nBu nedenle, grafikler ve ilgili grafik sinyalleri i\u00e7in altta yatan d\u00fczensiz k\u00f6\u015fe alan\u0131n\u0131 nicel bir koordinat yap\u0131s\u0131na yerle\u015ftirmenin do\u011fal ve teorik olarak uygun bir yolu olarak d\u00fc\u015f\u00fcn\u00fclebilir.<\/p>\n

Makaleye [buradan<\/a>] ula\u015fabilirsiniz.<\/p>\n

 <\/p>\n

\u00d6zet: <\/strong><\/p>\n

On the Euclidean domains of classical signal processing, linking of signal samples to underlying coordinate structures is straightforward. While graph adjacency matrices totally define the quantitative associations among the underlying graph vertices, a major problem in graph signal processing is the lack of explicit association of vertices with an underlying coordinate structure. To make this link, we propose an operation, called the vertex multiplication (VM), which is defined for graphs and can operate on graph signals. VM, which generalizes the coordinate multiplication (CM) operation in time series signals, can be interpreted as an operator that assigns a coordinate structure to a graph. By using the graph domain extension of differentiation and graph Fourier transform (GFT), VM is defined such that it shows Fourier duality that differentiation and CM operations are duals of each other under Fourier transformation (FT). Numerical examples and applications are also presented.<\/p>\n","protected":false},"excerpt":{"rendered":"

Ko\u00e7Lab‘\u0131n Graph Signal Processing’e (GSP) temel bir katk\u0131s\u0131 yak\u0131n zamanda Vertex Multiplication adl\u0131 yeni bir i\u015flemin tan\u0131t\u0131ld\u0131\u011f\u0131 IEEE Signal Processing Letters’da yay\u0131nland\u0131. Klasik sinyal i\u015flemenin \u00d6klid alanlar\u0131nda, sinyal \u00f6rneklerinin alttaki koordinat yap\u0131s\u0131na ba\u011flanmas\u0131 basittir. Bununla birlikte, grafik sinyal i\u015flemedeki \u00f6nemli bir problem, bir grafi\u011fin k\u00f6\u015feleri, sadece s\u0131ra indeksleri d\u0131\u015f\u0131nda belirli a\u00e7\u0131k nicel de\u011ferlere kar\u015f\u0131l\u0131k gelmedi\u011finden, […]<\/p>\n","protected":false},"author":7,"featured_media":11675,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[445],"tags":[],"_links":{"self":[{"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts\/11678"}],"collection":[{"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/comments?post=11678"}],"version-history":[{"count":3,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts\/11678\/revisions"}],"predecessor-version":[{"id":11681,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts\/11678\/revisions\/11681"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/media\/11675"}],"wp:attachment":[{"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/media?parent=11678"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/categories?post=11678"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/tags?post=11678"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}