## 1 Introduction
The feature extraction by _Zernike Moment_ (ZM) and _Pseudo-ZM_ (PZM) captures global information and does not require any closed boundary such as Fourier-based-descriptors [26]. [PERSON] and [PERSON] [27] utilized the properties of PZM for the identification of MCI from AD and HC groups using structural fMRI. In this study, they utilize all the PZMs up to the maximum order of 30 to construct the feature vectors. _Polar Cosine Transform_ (PCT), _Polar Sine Transform_ (PST), and _Polar Complex Exponential Transform_ (PCET) were introduced by [PERSON] et al. [28]. Because the kernels are harmonics in nature, these are jointly called as the Polar Harmonic Transforms (PHTs) which have been adopted in many pattern recognition applications including medical imaging [24], invariant feature extraction [29], color object detection [25], and image hashing [30]. The kernel computation of PCTs is much simpler than ZMs and PZMs. Hence, PHTs perform to a great extent higher speed compared to ZMs [31]. Moreover, PHTs are free from any numerical stability issue [32]. On the classification part, we use Wavelet neural networks (WNNs) for feature classification [33]. WNNs are a new type of feedforward neural networks where the discrete wavelet function is used for activation. WNNs use a gradient descent technique for optimization that often suffers from the local minima, long convergence time problems. Further, the activation function must be differentiable. Therefore, in addition to their own good performance, WNNs face problems with initial parameter tuning and parameter settings. To solve these issues, particle swarm optimization (PSO) and differential evolution (DE) approaches are often used to optimize the WNNs parameters. In [34], authors use DE algorithm to train a WNN and named it Differentially optimized WNN (DEWNN). The model was tested on bankruptcy data set and other datasets such as Iris, breast cancers. The results confirm the advantages of DE with WNN compared to WNN only. In the other work [35], to improve the classification accuracy of WNN in mammograms, the authors use the PSO approach. Compared to PSO, DE optimized WNNs are robust to noise and show consistent performance over many trials. However, it is likely to be premature and a situation may arrive where one cannot give the guarantee of the diversity of the population. To solve these issues, we adopt the self-adaptation technique [36] for parameter control using two parameters of standard DE, i.e., the mutation scale factor(F) and the cross-over rate (CR). In this paper, we propose a new hybrid method for early diagnosis of Alzheimer's disease using Polar Harmonic Transforms (PHT) and Self-adaptive Differential Evolution Wavelet Neural Network (SaDE-WNN). 1. [label=()]
2. PHT is utilized for feature extraction. PHT not only has excellent reconstruction properties but also can be constructed without difficulty in an arbitrarily higher order [28]. More importantly, PHT shows robustness to noise, less information redundancy problems, and competent reconstruction ability in image analysis in comparison with ZMs and PZMs. 3. SaDE-WNN is an improvement of the _Differential Evolution optimized WNN_ (DEWNN) [29] with the self-adaptation technique [30] for parameter control using two parameters of the standard DE. The proposed method is free from any human involvement. The proposed SaDE-WNN improves DE-WNN in terms of parameter tuning. The rest of the paper are organized as follows. Section 2 presents the material and methods used in this study. Section 3 presents the results and discussion. Section 4 covers the conclusion and future works.