{"doi":"10.1007/978-3-030-46150-8_8","title":"Heavy-Tailed Kernels Reveal a Finer Cluster Structure in t-SNE Visualisations","abstract":"Abstract T-distributed stochastic neighbour embedding (t-SNE) is a widely used data visualisation technique. It differs from its predecessor SNE by the low-dimensional similarity kernel: the Gaussian kernel was replaced by the heavy-tailed Cauchy kernel, solving the ‘crowding problem’ of SNE. Here, we develop an efficient implementation of t-SNE for a t-distribution kernel with an arbitrary degree of freedom $$\\nu $$ , with $$\\nu \\rightarrow \\infty $$ corresponding to SNE and $$\\nu =1$$ corresponding to the standard t-SNE. Using theoretical analysis and toy examples, we show that $$\\nu <1$$ can further reduce the crowding problem and reveal finer cluster structure that is invisible in standard t-SNE. We further demonstrate the striking effect of heavier-tailed kernels on large real-life data sets such as MNIST, single-cell RNA-sequencing data, and the HathiTrust library. We use domain knowledge to confirm that the revealed clusters are meaningful. Overall, we argue that modifying the tail heaviness of the t-SNE kernel can yield additional insight into the cluster structure of the data.","journal":"Lecture notes in computer science","year":2020,"id":119969,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":13,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9578,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2020-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":556811,"name":"George Linderman","orcid":null,"position":1,"is_corresponding":false},{"id":556812,"name":"Stefan Steinerberger","orcid":null,"position":2,"is_corresponding":false},{"id":69468,"name":"Yuval Kluger","orcid":"0000-0002-3035-071X","position":3,"is_corresponding":false},{"id":58947,"name":"Philipp Berens","orcid":"0000-0002-0199-4727","position":4,"is_corresponding":false},{"id":58949,"name":"Dmitry Kobak","orcid":"0000-0002-5639-7209","position":0,"is_corresponding":true}],"reference_count":12,"raw_metadata":null,"created_at":"2026-07-18T23:14:13.002105Z","pmid":"33103160","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}