ଐ iȲ. 0|, Ƭ l x P )D HiȲ. \, Ĭ , d} ,X Dȹt (Hadamard) D 0<\ 0\ ¤\D l1X, Ĭ ,\0 ] lp| XՔ d} \ MR (membership representation)D HiȲ. d ,D 0Ŕ 50 L8 8X ] DT (convex relaxation)| Ȳ. L, d} \D Ӹ t췤0 \ Ĭ ǔ ܭT d ,\ XX0 \ 8| l1X t 8X ] DT| Ȳ. \ͅ t췤0 Ӹ t췤0D X ŵȲ. X̹ MR@ L t }` ǔ 8@ t췤0| >0 t m Ӹ t췤0D t| XՔ 8 ǵȲ. P \, t췤0| >D ǔ U` t췤0 d}D X0 t \ U` (MAP) \T 8\ T\ D )x U` d} \ PMR (probabilistic membership representation)D HiȲ. Ĭ , \ ĳ U` 1X pi<\ X t췤0 d ȴ פ D 0<\ D<\ Xp, t췤0 d} \ U`@ 8| ܭYTX0 t tt \ X)Ȳ. t MAP 8| t Ӹ t췤0 t , U`t \x t췤0| X \ͅ t췤0 d}D Ĭ` ǵȲ. H )@ t췤0 ) L$ pt0 t @ 1D ŰȲ. H )X 8T Uĳ@ ܭT 8 Hopkins155 X pt0ѠtǤ 0.09-1.12%@ 0.88-3.88%, Yale t pt0ѠtǤ B 0.91% @ 0.08-0.63% iȲ.ZRecent advance of subspace clustering has provided a new way of constructing affinity matrices for clustering. Unlike the kernel-based subspace clustering, which needs tedious tuning among infinitely many kernel candidates, the self-expressive models, the new way derived from linear subspace assumptions, are rigorously combined with the sparse or the low-rank optimization theory to yield a coefficient matrix as a solution of an optimization problem. The coefficient matrices expected to have a (approximately) block-diagonal structure are applied to spectral clustering in order to find the final clusters. Nevertheless, these matrices have quite different meanings from the traditional ones consists of metric similarities of spectral clustering. In fact, most subspace clustering methods perform some sort of value rearrangement as post-processing. However, there is no definitive way to construct the affinity matrices from the coefficient matrices and it is unclear whether these affinity matrices are good enough to apply spectral clustering. In this dissertation, we want to find the clusters directly from the cluster membership estimated from the coefficient matrix without applying spectral clustering. Thus, we propose two framework methods. First, we propose membership representation (MR) which is an alternative approach to detect the block-diagonal structure from the coefficient matrix by constructing a self-expressive system based on a Hadamard product of the coefficient matrix and a membership matrix. To resolve the difficulty in handling the membership matrix, we solve the convex relaxation of the problem. Then another problem is constructed to transform the representation to a normalized membership matrix that is closely related to spectral clustering. We also solve the convex relaxation of the problem. The final cluster result is obtained by performing spectral clustering. However, since MR has a problem that it may be vulnerable to noise and outliers, and that spectral clustering must be performed in order to find clusters. Second, therefore, we propose probabilistic membership representation (PMR) which is a nonparametric method formulated as a maximum a posteriori (MAP) optimization problem to estimate the probabilistic cluster membershi<p that can directly find the clusters from. The likelihood for the coefficient matrix is defined nonparametrically based on histograms given the cluster membership, which is defined as a combination of probability simplices, and the prior probability for the cluster membership is defined as a Bernoulli distribution to regularize the problem. Solving this MAP problem replaces the spectral clustering procedure, and the final cluster membership can be calculated by selecting the clusters with maximum probabilities. The proposed methods provide the state-of-the-art performance for well-known subspace clustering methods on popular benchmark databases. The segmentation accuracy and the normalized mutual information of the proposed methods increase to 0.09-1.12% and 0.88-3.88% for Hopkins155 motion database, and 0.91% and 0.08-0.63% for Yale face database B, respectively./https://dspace.ajou.ac.kr/handle/2018.oak/15196Dhttp://dcoll.ajou.ac.kr:9080/dcollection/common/orgView/000000028568-2T[})"D?adwGiXza&H*C+B \-$/ dMbP?_*+%" ,,??U >@ !"#$%&'Root EntryWorkbook0SummaryInformation(DocumentSummaryInformation8