Paper:
Geometry Based Data Generation
We propose a new type of generative model for high-dimensional data that learns a manifold geometry of the data, rather than density, and can generate points evenly along this manifold. This is in contrast to existing generative models that represent data density, and are strongly affected by noise and other artifacts of data collection. We demonstrate how this approach corrects sampling biases and artifacts, thus improves several downstream data analysis tasks, such as clustering and classification. Finally, we demonstrate that this approach is especially useful in biology where, despite the advent of single-cell technologies, rare subpopulations and gene-interaction relationships are affected by biased sampling. We show that SUGAR can generate hypothetical populations, and it is able to reveal intrinsic patterns and mutual-information relationships between genes on a single-cell RNA sequencing dataset of hematopoiesis.

Review:
It is the difficult to discover small clusters from imbalanced dataset in classification/clustering tasks. The authors try to tackle this problem by imputing new data points into the original dataset using a diffusion map based approach. Diffusion map is a Gaussian kernel normalized by a diagonal matrix D, whose diagonal elements are the total connectivity of the corresponding data point. This kernel can be further extended to measure-based Gaussian Correlation (MGC) kernel, which only considers a set of reference points. The main idea is to generate new data points using the MGC kernel in neighbourhood of each original data point and combine them for downstream classification/clustering tasks.  The authors then discusses how to select the bandwidth of the Gaussian kernel, how many new data points to generate for each original data point, how to set the number of multiplication steps of the Gaussian kernel. After that the authors provide a proof about setting l(i) which I do not go through.  The MNIST experiment shows the method is able to interpolate data points in low density regions, while variational autoencoder is not. After that the authors check the generated data points are uniformly distributed in the manifold. Then they show SUGAR achieves better performance compared with other data sampling methods on classification and clustering of imbalanced datasets. In the final single cell dataset, they show SUGAR helps to separate different cell types from the data.  In general I feel the key strength of SUGAR comes from the random walk near the original data points, which may help to connect the low density regions. The exploration property comes from the diffusion distance (line 141). The larger t used in the diffusion distance, the closer the newly generated data points to the original. While solving the minor cluster problem, I have a gut feeling imputing new data points may bring up new problems such as fake new clusters.  I have some questions regarding the experiments: 1. MINST: this experiments may be too simple. Only one "6" is rotated to generate the whole dataset, so there is no noise in principle. Comparison with GAN instead of VAE may be more realistic. In Figure 1, how is t determined? 2. Clustering of imbalanced data: Figure 3a shows the contribution of SUGAR is merging the two clusters in "S" but not imputing the low density regions in "G" (bottom part), what is the t used here? How is K chosen in k-means for the newly generated dataset? 3. Biological data: Figure 4d, what are the x-axis and y-axis? 4. what is "f" in line 133?  Although with flaws, I feel this is a nice paper to be accepted.   Updates: Based on the authors' feedback, it seems to be a nice paper.