کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898204 | 1631324 | 2018 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Similarity matrix framework for data from union of subspaces
ترجمه فارسی عنوان
چارچوب ماتریس شباهت برای داده ها از اتحاد از زیر فضای
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کلمات کلیدی
تقسیم بندی زیر فضای، اتحاد زیرمجموعه ها، خوشه بندی داده ها، ماتریس مشابهی، شکل ماتریس تعامل، تجزیه اسکلت،
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
This paper presents a framework for finding similarity matrices for the segmentation of data W=[w1â¯wN]âRD drawn from a union U=âi=1MSi of independent subspaces {Si}i=1M of dimensions {di}i=1M. It is shown that any factorization of W=BP, where columns of B form a basis for data W and they also come from U, can be used to produce a similarity matrix ÎW. In other words, ÎW(i,j)â 0, when the columns wi and wj of W come from the same subspace, and ÎW(i,j)=0, when the columns wi and wj of W come from different subspaces. Furthermore, ÎW=Qdmax, where dmax=maxâ¡{di}i=1M and QâRNÃN with Q(i,j)=|PTP(i,j)|. It is shown that a similarity matrix obtained from the reduced row echelon form of W is a special case of the theory. It is also proven that the Shape Interaction Matrix defined as VVT, where W=UΣVT is the skinny singular value decomposition of W, is not necessarily a similarity matrix. But, taking powers of its absolute value always generates a similarity matrix. An interesting finding of this research is that a similarity matrix can be obtained using a skeleton decomposition of W. First, a square sub-matrix AâRrÃr of W with the same rank r as W is found. Then, the matrix R corresponding to the rows of W that contain A is constructed. Finally, a power of the matrix PTP where P=Aâ1R provides a similarity matrix ÎW. Since most of the data matrices are low-rank in many subspace segmentation problems, this is computationally efficient compared to other constructions of similarity matrices.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied and Computational Harmonic Analysis - Volume 45, Issue 2, September 2018, Pages 425-435
Journal: Applied and Computational Harmonic Analysis - Volume 45, Issue 2, September 2018, Pages 425-435
نویسندگان
Akram Aldroubi, Ali Sekmen, Ahmet Bugra Koku, Ahmet Faruk Cakmak,