  The dimensionality reduction has been widely introduced to use the
high-dimensional data for regression, classification, feature analysis, and
visualization. As the one technique of dimensionality reduction, a stochastic
neighbor embedding (SNE) was introduced. The SNE leads powerful results to
visualize high-dimensional data by considering the similarity between the local
Gaussian distributions of high and low-dimensional space. To improve the SNE, a
t-distributed stochastic neighbor embedding (t-SNE) was also introduced. To
visualize high-dimensional data, the t-SNE leads to more powerful and flexible
visualization on 2 or 3-dimensional mapping than the SNE by using a
t-distribution as the distribution of low-dimensional data. Recently, Uniform
manifold approximation and projection (UMAP) is proposed as a dimensionality
reduction technique. We present a novel technique called a q-Gaussian
distributed stochastic neighbor embedding (q-SNE). The q-SNE leads to more
powerful and flexible visualization on 2 or 3-dimensional mapping than the
t-SNE and the SNE by using a q-Gaussian distribution as the distribution of
low-dimensional data. The q-Gaussian distribution includes the Gaussian
distribution and the t-distribution as the special cases with q=1.0 and q=2.0.
Therefore, the q-SNE can also express the t-SNE and the SNE by changing the
parameter q, and this makes it possible to find the best visualization by
choosing the parameter q. We show the performance of q-SNE as visualization on
2-dimensional mapping and classification by k-Nearest Neighbors (k-NN)
classifier in embedded space compared with SNE, t-SNE, and UMAP by using the
datasets MNIST, COIL-20, OlivettiFaces, FashionMNIST, and Glove.
