TL;DR
This thesis builds on an existing diagnostics toolkit mainly for t-SNE and UMAP and turns it into a more accessible package for interested practitioners, while also extending it with diagnostics tools.
It is common for two-dimensional embeddings of high-dimensional data to be read far beyond what they can support. Distances in and between clusters, the meaning behind empty spaces, and the amount of structure hidden at each point are generally invisible in the output of methods such as t-SNE and UMAP. This is because the information that could support the meaning of these properties is discarded during the optimisation process. Here, we present FloDR, a dimensionality reduction method that embeds data through an invertible normalising flow. While FloDR only uses the first two output coordinates to create a two-dimensional embedding, it retains the remaining coordinates rather than discarding them. In addition to the embedding, an exact inverse and an exact density are properties of a trained mapping, which enable diagnostic visualisations that are computed from the exact inverse of the model that drew the layout rather than from an approximate one. Specifically, we draw two fields, the conditional spread, which measures how much of the original data remains undetermined at each embedding position in input units, and the hidden contrast, which measures how much information about a labelled contrast the two plotted coordinates discard. Both fields are rendered with a prespecified test against a held out portion of the input data and a bootstrap confidence. A field that fails the test is reported as refused.
Widely used non-linear dimensionality reduction (NLDR) methods such as UMAP and t-SNE are stochastic--repeated runs on the same data can produce different low-dimensional projections. In this paper, we explore two problems related to projection variability: on some datasets clusters, structure, and outliers may change run-to-run, and on others projections can be extremely stable when overfitting noise. To address the first problem, we propose visualizing the median of multiple NLDR outputs rather than relying on individual projections. To address the second, we perturb input data before creating consensus embeddings. We find that taking the median of multiple projections performs comparably to individual runs on multiple quality metrics, while increasing perturbation emphasizes global over local structure. We show through a set of exploratory visualizations that even relatively simple ensemble presentations can be used to better communicate the reliability of projection patterns.
Motivation: Low-dimensional embeddings are widely used to explore cell-state heterogeneity in single-cell and other high-dimensional biological data. Although many methods preserve local neighborhoods, they may distort the apparent sampling density of processed observations, altering the visual contrast between dense and sparse regions and complicating the interpretation of rare, transitional, or continuous cell-state populations. Results: We present DMT-Dens, a parametric manifold-visualization method built on a latent-token Transformer encoder. The model integrates rank-based manifold alignment with hard-pair aggregation. To preserve density, it optimizes a loss based on the Pearson correlation between k-nearest-neighbor log-radius estimates in the processed input and two-dimensional embedding spaces. Benchmark evaluations demonstrate strong density preservation, particularly on biological datasets, while retaining competitive label separability. Availability: Source code, data-processing scripts, and resolved experiment configurations are available at https://github.com/Ruizhe-wang/DMT-Dens.
A progressive multi-objective optimization framework is proposed that enhances t-SNE by integrating complementary loss functions, including a ranking-aware divergence (KLmax) and a Wasserstein-based term for global alignment.
It is found that sharpening improves preservation of the very nearest neighbors, while smoothing improves preservation of broader local neighborhoods, outperforming alternative affinity constructions including multiscale methods in the mid-local range.
The K-Means clustering algorithm is a fundamental tool in machine learning, but its performance is often strongly affected by the instability of traditional random initialization methods, which can lead to convergence to poor local optima. Although many studies have proposed deterministic models to address this issue, they often involve high computational cost with O ( n 2 ) complexity. This paper introduces a new engineering approach that is lightweight and efficient. Specifically, the method uses the L2 norm to directly map each multi-dimensional data point into a one-dimensional scalar value. This value serves as a sorting criterion and is stored in a dictionary data structure to deterministically extract K initial centroids. Experimental evaluation shows that the proposed method completely eliminates variability, fixing the Adjusted Rand Index (ARI) at stable values of 0.6345 for the Digits dataset and 0.7302 for the Iris dataset across all runs. These results demonstrate that a practical data structure-based approach can achieve high reliability with very low computational cost.