Non-negative Matrix Factorization (NMF) is a part-based image representation method. It comes from the intuitive idea that entire face image can be constructed by combining several parts. In this paper, we propose a framework for face recognition by finding localized, part-based representations, denoted “Iterative weighted non-smooth non-negative matrix factorization” (IWNS-NMF). A new cost fun...

In this paper, we consider a particular class of integral equations of the fourth kind and show that tractability and differentiability index of the given system are 3. Tractability and dierentiability index are introduced based on the-smoothing property of a Volterra integral operator and index reduction procedure, respectively. Using the notion of index, we give sucient conditions for the exi...

In this study, by using Fibonacci Q-matrix and Lucas Q^'-matrix we define bicomplex Q^'-matrix. After that matrix representation, give some identities.

Representation of belief states is an important issue for knowledge based systems. In this paper, we develop a matrix representation for ordered belief states and show that belief reasoning, revision and fusion can all be interpreted as operations of matrix algebra. Thus, the matrix representation can serve as the basis of algebraic semantics for belief logic.

In this paper, we discuss the use of binary decision diagrams to represent general matrices. We demonstrate that binary decision diagrams are an efficient representation for every special-case matrix in common use, notably sparse matrices. In particular, we demonstrate that for any matrix, the BDD representation can be no larger than the corresponding sparse-matrix representation. Further, the ...

In various cases we need to transform a process model into a matrix representation for further analysis. In this paper, we introduce the notion of Order Matrix, which enables unique representation of blockstructured process models. We present algorithms for transforming a block-structured process model into a corresponding order matrix and vice verse. We then prove that such order matrix consti...

Baum (1992) and Ragan (1992b) independently devised a method that uses additive binary coding and parsimony to combine trees derived from di€ erent data sets, a procedure Ragan termed matrix representation with parsimony analysis (MRP). Because the method utilizes the topology of source trees rather than the orig inal data, (1) trees derived from di€ erent data types (e.g., molecular sequences,...