Recursive unsupervised fully constrained least squares methods

Linear spectral mixture analysis (LSMA) generally performs with signatures assumed to be known to form a linear mixing model to be known. Unfortunately, this is generally not the case in real world applications. An unsupervised fully constrained least squares (UFCLS) method has been proposed to find these desired signatures. Unfortunately, it requires prior knowledge about the number of signatures, p needed to be generated. The recently proposed virtual dimensionality (VD) can be used for this purpose. This paper develops a recursive UFCLS (RUFCLS) method to accomplish these two tasks in one-shot operation, viz., determine the value of p as well as find these p signatures simultaneously. Such RUFCLS can perform data unmixing progressively signature-by-signature via a recursive update equation with signatures used to form a linear mixing model for linear spectral unmixing generated by UFCLS. Most importantly, RUFCLS does not require any matrix inverse operation but only matrix multiplications and outer products of vectors. This significant advantage provides an effective computational means of determining the VD.