Naoki Saito

Wai Ho Chak, Naoki Saito, David Weber

We propose to use the Generalized Morse Wavelets (GMWs) instead of commonly-used Morlet (or Gabor) wavelets in the Scattering Transform Network (STN), which we call the GMW-STN, for signal classification problems. The GMWs form a parameterized family of truly analytic wavelets while the Morlet wavelets are only approximately analytic. The analyticity of underlying wavelet filters in the STN is particularly important for nonstationary oscillatory signals such as music signals because it improves interpretability of the STN representations by providing multiscale amplitude and phase (and consequently frequency) information of input signals. We demonstrate the superiority of the GMW-STN over the conventional STN in music genre classification using the so-called GTZAN database. Moreover, we show the performance improvement of the GMW-STN by increasing its number of layers to three over the typical two-layer STN.}

Wai Ho Chak, Naoki Saito

The scattering transform network (STN), which has a similar structure as that of a popular convolutional neural network except its use of predefined convolution filters and a small number of layers, can generates a robust representation of an input signal relative to small deformations. We propose a novel Monogenic Wavelet Scattering Network (MWSN) for 2D texture image classification through a cascade of monogenic wavelet filtering with nonlinear modulus and averaging operators by replacing the 2D Morlet wavelet filtering in the standard STN. Our MWSN can extract useful hierarchical and directional features with interpretable coefficients, which can be further compressed by PCA and fed into a classifier. Using the CUReT texture image database, we demonstrate the superior performance of our MWSN over the standard STN. This performance improvement can be explained by the natural extension of 1D analyticity to 2D monogenicity.

Chelsea Weaver, Naoki Saito

Sparse representation-based classification (SRC), proposed by Wright et al., seeks the sparsest decomposition of a test sample over the dictionary of training samples, with classification to the most-contributing class. Because it assumes test samples can be written as linear combinations of their same-class training samples, the success of SRC depends on the size and representativeness of the training set. Our proposed classification algorithm enlarges the training set by using local principal component analysis to approximate the basis vectors of the tangent hyperplane of the class manifold at each training sample. The dictionary in SRC is replaced by a local dictionary that adapts to the test sample and includes training samples and their corresponding tangent basis vectors. We use a synthetic data set and three face databases to demonstrate that this method can achieve higher classification accuracy than SRC in cases of sparse sampling, nonlinear class manifolds, and stringent dimension reduction.