This study presents a pipeline leveraging t-Distributed Stochastic Neighbor Embedding (t-SNE) for interpretable visualizations of chirp features across diverse outcome scenarios. The dataset, comprising chirp-based temporal, spectral, and frequency metrics. Using t-SNE, local neighborhood relationships were preserved while addressing the crowding problem through Student t-distribution-based similarity optimization. Three classification tasks were formulated on the 2D t-SNE embeddings: (1) distinguishing clinical success from failure/no-resection, (2) separating high-difficulty from low-difficulty cases, and (3) identifying optimal cases, defined as successful outcomes with minimal clinical difficulty. Four classifiers, namely, Random Forests, Support Vector Machines, Logistic Regression, and k-Nearest Neighbors, were trained and evaluated using stratified 5-fold cross-validation. Across tasks, the Random Forest and k-NN classifiers demonstrated superior performance, achieving up to 88.8% accuracy in optimal case detection (successful outcomes with minimal clinical difficulty). Additionally, feature influence sensitivity maps were generated using SHAP explanations applied to model predicting t-SNE coordinates, revealing spatially localized feature importance within the embedding space. These maps highlighted how specific chirp attributes drive regional clustering and class separation, offering insights into the latent structure of the data. The integrated framework showcases the potential of interpretable embeddings and local feature attribution for clinical stratification and decision support.

Dimensionality reduction (DR) methods map high-dimensional data to a low-dimensional embedding, which enables data visualization. DR methods for visualization have played a critical role to gain insights into high-dimensional data, and the toolkit of DR methods has been rapidly growing in recent years (McInnes et al. [2020], Sainburg et al. [2021], Amid and Warmuth [2022], Wang et al. [2021]). Only equiped with a comprehensive understanding of these DR methods, can make informed decision based on data visualization from them, can substantially improve upon them. The state of the art for unsupervised DR relies on the stochastic neighbor embedding (SNE) framework (Hinton and Roweis [2002]), where t-SNE (van der Maaten and Hinton [2008], van der Maaten [2014]), UMAP (McInnes et al. [2020], Sainburg et al. [2021]) are two most popular example methods with impressive visualization performance on real-word data.

Exploratory data analysis (EDA) is a vital procedure for data science projects. In this work, we introduce a stable equilibrium point (SEP) - based framework for improving the efficiency and solution quality of EDA. By exploiting the SEPs to be the representative points, our approach aims to generate high-quality clustering and data visualization for large-scale data sets. A very unique property of the proposed method is that the SEPs will directly encode the clustering properties of data sets. Compared with prior state-of-the-art clustering and data visualization methods, the proposed methods allow substantially improving computing efficiency and solution quality for large-scale data analysis tasks.

We describe a probabilistic approach to the task of placing objects, de- scribed by high-dimensional vectors or by pairwise dissimilarities, in a low-dimensional space in a way that preserves neighbor identities. A Gaussian is centered on each object in the high-dimensional space and the densities under this Gaussian (or the given dissimilarities) are used to define a probability distribution over all the potential neighbors of the object. The aim of the embedding is to approximate this distribu- tion as well as possible when the same operation is performed on the low-dimensional "images" of the objects. A natural cost function is a sum of Kullback-Leibler divergences, one per object, which leads to a simple gradient for adjusting the positions of the low-dimensional im- ages. Unlike other dimensionality reduction methods, this probabilistic framework makes it easy to represent each object by a mixture of widely separated low-dimensional images.

Stochastic Neighbor Embedding (SNE) has shown to be quite promising for data visualization. Currently, the most popular implementation, t-SNE, is restricted to a particular Student t-distribution as its embedding distribution. Moreover, it uses a gradient descent algorithm that may require users to tune parameters such as the learning step size, momentum, etc., in finding its optimum. In this paper, we propose the Heavy-tailed Symmetric Stochastic Neighbor Embedding (HSSNE) method, which is a generalization of the t-SNE to accommodate various heavy-tailed embedding similarity functions. With this generalization, we are presented with two difficulties.

We propose a unified view on two widely used data visualization techniques: Self-Organizing Maps (SOMs) and Stochastic Neighbor Embedding (SNE). We show that they can both be derived from a common mathematical framework. Leveraging this formulation, we propose to compare SOM and SNE quantitatively on two datasets, and discuss possible avenues for future work to take advantage of both approaches.

Stochastic Neighbor Embedding (SNE) is a manifold learning and dimensionality reduction method with a probabilistic approach. In SNE, every point is consider to be the neighbor of all other points with some probability and this probability is tried to be preserved in the embedding space. SNE considers Gaussian distribution for the probability in both the input and embedding spaces. However, t-SNE uses the Student-t and Gaussian distributions in these spaces, respectively. In this tutorial and survey paper, we explain SNE, symmetric SNE, t-SNE (or Cauchy-SNE), and t-SNE with general degrees of freedom. We also cover the out-of-sample extension and acceleration for these methods. Some simulations to visualize the embeddings are also provided.

Multimodal relational data analysis has become of increasing importance in recent years, for exploring across different domains of data, such as images and their text tags obtained from social networking services (e.g., Flickr). A variety of data analysis methods have been developed for visualization; to give an example, t-Stochastic Neighbor Embedding (t-SNE) computes low-dimensional feature vectors so that their similarities keep those of the observed data vectors. However, t-SNE is designed only for a single domain of data but not for multimodal data; this paper aims at visualizing multimodal relational data consisting of data vectors in multiple domains with relations across these vectors. By extending t-SNE, we herein propose Multimodal Relational Stochastic Neighbor Embedding (MR-SNE), that (1) first computes augmented relations, where we observe the relations across domains and compute those within each of domains via the observed data vectors, and (2) jointly embeds the augmented relations to a low-dimensional space. Through visualization of Flickr and Animal with Attributes 2 datasets, proposed MR-SNE is compared with other graph embedding-based approaches; MR-SNE demonstrates the promising performance.

Stochastic Neighbor Embedding (SNE) has shown to be quite promising for data visualization. Currently, the most popular implementation, t-SNE, is restricted to a particular Student t-distribution as its embedding distribution. Moreover, it uses a gradient descent algorithm that may require users to tune parameters such as the learning step size, momentum, etc., in finding its optimum. In this paper, we propose the Heavy-tailed Symmetric Stochastic Neighbor Embedding (HSSNE) method, which is a generalization of the t-SNE to accommodate various heavy-tailed embedding similarity functions. With this generalization, we are presented with two difficulties.

Imagine you get a dataset with hundreds of features (variables) and have little understanding about the domain the data belongs to. You are expected to identify hidden patterns in the data, explore and analyze the dataset. And not just that, you have to find out if there is a pattern in the data – is it signal or is it just noise? Does that thought make you uncomfortable? It made my hands sweat when I came across this situation for the first time. Do you wonder how to explore a multidimensional dataset?