A dictionary learning algorithm for sparse coding by the normalized bilateral projections

Sparse coding is a method of expressing the input vector as a linear combination of a few vectors taken from a set of template vectors, often called a dictionary or codebook. A good dictionary is the one that sparse codes most vectors in a given class of possible input vectors. There are currently several proposals to learn a good dictionary from a set of input vectors. Such methods are termed under the title of dictionary learning. We propose a new dictionary learning algorithm, called K-normalized bilateral projections (K-NBP), which is a modification to a widely used dictionary learning method, i.e., K-singular value decomposition (K-SVD). The main idea behind this was to standardize and normalize the input matrix as a preprocessing stage, and to correspondingly normalize the estimated source vectors in the dictionary update stage. The experimental results revealed that our method was fast, and when the number of iterations was limited, it outperformed K-SVD. Also, if only a coarse approximation was needed, it provided results that were almost like those from K-SVD, but with fewer iterations. This indicated that our method was particularly suited to large data sets with many dimensions, where each iteration took a long time.