# Effect of Probabilistic Similarity Measure on Metric-Based Few-Shot Classification
###### Abstract  
In developing a few-shot classification model using deep networks, the limited number of samples in each class causes difficulty in utilizing statistical characteristics of the class distributions. In this paper, we propose a method to treat this difficulty by combining a probabilistic similarity based on intra-class statistics with a metric-based few-shot classification model. Noting that the probabilistic similarity estimated from intra-class statistics and the classifier of conventional few-shot classification models have a common assumption on the class distributions, we propose to apply the probabilistic similarity to obtain loss value for episodic learning of embedding network  
good performance [21], there would be further room for improvement in the classification module [22; 23; 24]. In this paper, we try to improve the performance of the few-shot classifiers by elaborating on the distance-based classification module. It is well-known that the accuracy of a distance-based classifier can be improved by using a statistical measure such as Mahalanobis distance [25] rather than simple geometric measures such as Euclidean distance. Under the situation of few-shot classification, however, it is difficult to utilize the statistical measure because the estimation of accurate distribution is hard due to the extremely limited number of samples. Inaccurate estimation on the class distributions lead to poor distance measure, resulting in low classification accuracy. To overcome this limitation, we propose to combine the probabilistic similarity based on intra-class statistics [26; 27; 28; 29] with the prototypical network [9] that is a representative few-shot classification model. In [26; 27], the probabilistic similarity between two samples is defined as a probability that they belong to the same class, and its probability density function is estimated under the assumption that a data point is generated from two factors: a class-specific factor and a class-independent factor. The class-specific factor can be represented by a prototype vector that is defined as the mean vector of support samples in the prototypical network [9]. The class-independent factor can be considered as an environmental factor that is irrelevant to each class, and thus can be estimated through an episodic learning strategy developed for few-shot learning [8; 9; 30]. Based on these considerations, we develop a method for applying the probabilistic similarity measure in the learning of embedding function as well as in the recognition of unseen classes. Moreover, by exploiting the similarity in learning of the embedding function as well, it is also expectable to obtain better feature representation, which is more suitable to the assumption on the data distribution for the prototype-based classifier. Additionally, since the distribution of the class-independent factor can be estimated more accurately as the number of classes increases even when each class has few samples, the proposed method is expected to be more effective in the case of a large number of classes. This can be an advantage of the proposed method, which cannot be expected from the conventional works using Euclidean distance. The aim and main contributions of our work are summarized below:  
* In order to improve the performance of few-shot classification, we propose to combine the probabilistic similarity measure with deep embedding function networks. * We define an explicit function of probabilistic similarity based on the intra-class statistics and propose a modified episodic learning algorithm that simultaneously performs estimation of the similarity and optimization of the embedding function. * Whereas the conventional methods have been tested for a limited number of classes, we evaluate the change of performance as the number of classes increases, and confirm the apparent superiority of the proposed method, especially in the case of many classes.