{"doi":"10.1109/tsp.2011.2159600","title":"Uniqueness of Non-Gaussianity-Based Dimension Reduction","abstract":"Dimension reduction is a key step in preprocessing large-scale data sets. A recently proposed method named non-Gaussian component analysis searches for a projection onto the non-Gaussian part of a given multivariate recording, which is a generalization of the deflationary projection pursuit model. In this contribution, we discuss the uniqueness of the subspaces of such a projection. We prove that a necessary and sufficient condition for uniqueness is that the non-Gaussian signal subspace is of minimal dimension. Furthermore, we propose a measure for estimating this minimal dimension and illustrate it by numerical simulations. Our result guarantees that projection algorithms uniquely recover the underlying lower dimensional data signals.","journal":"IEEE Transactions on Signal Processing","year":2011,"id":3910,"datarank":0.3453877639491069,"base_score":2.302585092994046,"endowment":2.302585092994046,"self_citation_contribution":0.3453877639491069,"citation_network_contribution":0.0,"self_endowment_contribution":0.3453877639491069,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":9,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.045,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2011-09-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":39727,"name":"Motoaki Kawanabe","orcid":null,"position":1,"is_corresponding":false},{"id":57412,"name":"Klaus-Robert Müller","orcid":"0000-0002-3861-7685","position":2,"is_corresponding":false},{"id":39729,"name":"Klaus‐Robert Müller","orcid":null,"position":3,"is_corresponding":false},{"id":42,"name":"Fabian Joachim Theis","orcid":"0000-0002-2419-1943","position":0,"is_corresponding":true}],"reference_count":16,"raw_metadata":null,"created_at":"2026-03-01T18:20:47.508186Z","pmid":null,"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":[]}