{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/text-iss-2-an-extension-of-iterative-source","title":"ISS2: An Extension of Iterative Source Steering Algorithm for Majorization-Minimization-Based Independent Vector Analysis","arxiv_id":"2202.00875","date":"2022-02-02","proceeding":null,"authors":["Rintaro Ikeshita","Tomohiro Nakatani"],"abstract":"A majorization-minimization (MM) algorithm for independent vector analysis optimizes a separation matrix $W = [w_1, \\ldots, w_m]^h \\in \\mathbb{C}^{m \\times m}$ by minimizing a surrogate function of the form $\\mathcal{L}(W) = \\sum_{i = 1}^m w_i^h V_i w_i - \\log | \\det W |^2$, where $m \\in \\mathbb{N}$ is the number of sensors and positive definite matrices $V_1,\\ldots,V_m \\in \\mathbb{C}^{m \\times m}$ are constructed in each MM iteration. For $m \\geq 3$, no algorithm has been found to obtain a global minimum of $\\mathcal{L}(W)$. Instead, block coordinate descent (BCD) methods with closed-form update formulas have been developed for minimizing $\\mathcal{L}(W)$ and shown to be effective. One such BCD is called iterative projection (IP) that updates one or two rows of $W$ in each iteration. Another BCD is called iterative source steering (ISS) that updates one column of the mixing matrix $A = W^{-1}$ in each iteration. Although the time complexity per iteration of ISS is $m$ times smaller than that of IP, the conventional ISS converges slower than the current fastest IP (called $\\text{IP}_2$) that updates two rows of $W$ in each iteration. We here extend this ISS to $\\text{ISS}_2$ that can update two columns of $A$ in each iteration while maintaining its small time complexity. To this end, we provide a unified way for developing new ISS type methods from which $\\text{ISS}_2$ as well as the conventional ISS can be immediately obtained in a systematic manner. Numerical experiments to separate reverberant speech mixtures show that our $\\text{ISS}_2$ converges in fewer MM iterations than the conventional ISS, and is comparable to $\\text{IP}_2$.","url_abs":"https://arxiv.org/abs/2202.00875v3","url_pdf":"https://arxiv.org/pdf/2202.00875v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"text-iss-2-an-extension-of-iterative-source","repo_url":"https://github.com/tky823/ssspy","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}