## 1 Introduction  
Alzheimer's disease (AD) is an irreversible progressive cerebral disease with most of its symptoms appearing after 60 years of age. Alzheimer's disease currently affects approximately 46.8 million people worldwide and may reach 132 million people in 2050 [1]. To date, a complete cure for AD has remained elusive. Accurate and early diagnosis of AD is essential for treating patients and for developing future treatments. Accumulation of amyloid beta (A\(\beta\)) is considered as a diagnostic feature of Alzheimer's disease. Accordingly, 18F-florbetaben (FBB) amyloid positron emission tomography (PET) is a more powerful tool for understanding AD-related brain changes than magnetic resonance imaging (MRI) and computed tomography (CT) [2,3].  
According to the International Working Group, both pathophysiological markers and clinical phenotypes are required for an AD diagnosis. Pathophysiological markers include CSF (cerebrospinalfluid) A\(\beta\)/tau or amyloid PET [4], but clinical trials of A\(\beta\)-targeting drugs have been unsuccessful in clinical trials. This failure might be attributable to the late application of the treatment, highlighting the need for early treatment after early diagnosis [5]. Amyloid markers are the fastest appearing biomarkers early in the disease [6; 7; 8].  
In recent years, AD in MRI or PET brain images has been identified by various machine learning methods including deep learning [3; 9; 10; 11; 12; 13]. [PERSON] [9] classified AD and normal control images by a combined kernel technique with a support vector machine. [PERSON] [10] developed the program DeepAD for AD diagnosis which analyzes sMRI and fMRI brain scans separately on the slice and subject levels by two convolutional neural networks (CNNs) (LeNet and GoogleNet). [PERSON] [11] classified AD in MRI scans by a deep CNN-based multi-class classification algorithm based on GoogleNet and ResNet. In a related study of PET images, [PERSON] [12] proposed a classification method for scoring brain amyloid plaque load (BAPL) in FBB PET images which is based on a deep CNN developed by the Visual Geometry Group. [PERSON] [13] combined a CNN with recurrent neural networks (RNN) for classifying amyloids in fluorodeoxyglucose (FDG) PET images. Although [PERSON]'s method satisfactorily classified images as positive or negative for amyloids, it could not accurately identify BAPL2 in a ternary classification, because BAPL2 is a weaker amyloid load than BAPL1 [12]. In some cases, the interpreter cannot easily distinguish between BAPL1 and BAPL2. [PERSON] [13] studied FDG PET images, which are more appropriate for identifying progression markers than diagnostic markers, and clinically classified them as normal, mild cognitive impairment (MCI), or AD. [PERSON] [7] combined florbetapir (not FBB) amyloid PET and FDG PET images for clinical classification of normal, MCI, and AD diagnoses.  
In this paper, we added a discriminative intra-loss function to the conventional loss function (i.e., the cross-entropy loss function). The resulting joint discriminative loss function was intended to improve the accuracy of deep-learning-based AD classification. The performances of the proposed joint loss function and the conventional loss function were compared in three state-of-the-art deep neural network architectures. The intra-loss function significantly improved the classification accuracy, especially that of BAPL2 (a marker of MCI). In addition, we show that the mix-up data augmentation method, originally proposed for natural image classification [14], is also useful in medical image classification.  
The remainder of this paper is organized as follows. Sections 2 and 3 describe the dataset and methods of the study, respectively. The experimental results are presented and discussed in Section 4. Conclusions are given in Section 5.