Finite mixtures, projection pursuit and tensor rank: a triangulation View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-03

AUTHORS

Nicola Loperfido

ABSTRACT

Finite mixtures of multivariate distributions play a fundamental role in model-based clustering. However, they pose several problems, especially in the presence of many irrelevant variables. Dimension reduction methods, such as projection pursuit, are commonly used to address these problems. In this paper, we use skewness-maximizing projections to recover the subspace which optimally separates the cluster means. Skewness might then be removed in order to search for other potentially interesting data structures or to perform skewness-sensitive statistical analyses, such as the Hotelling’s T2 test. Our approach is algebraic in nature and deals with the symmetric tensor rank of the third multivariate cumulant. We also derive closed-form expressions for the symmetric tensor rank of the third cumulants of several multivariate mixture models, including mixtures of skew-normal distributions and mixtures of two symmetric components with proportional covariance matrices. Theoretical results in this paper shed some light on the connection between the estimated number of mixture components and their skewness. More... »

PAGES

1-29

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11634-018-0336-z

DOI

http://dx.doi.org/10.1007/s11634-018-0336-z

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1106803959


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0104", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Statistics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of Urbino", 
          "id": "https://www.grid.ac/institutes/grid.12711.34", 
          "name": [
            "Dipartimento di Economia, Societ\u00e0 e Politica, Universit\u00e0 degli Studi di Urbino \u201cCarlo Bo\u201d, Via Saffi 42, Urbino, PU, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Loperfido", 
        "givenName": "Nicola", 
        "id": "sg:person.07507272505.84", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07507272505.84"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/j.jmva.2008.03.009", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1001239893"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/3-540-28084-7_15", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1001242173", 
          "https://doi.org/10.1007/3-540-28084-7_15"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/1351847x.2012.720269", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002743026"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11634-013-0137-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002987272", 
          "https://doi.org/10.1007/s11634-013-0137-3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1111/j.1467-9868.2009.00706.x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003264105"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1111/j.1467-9868.2009.00706.x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003264105"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1111/j.1751-5823.2007.00016.x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004737747"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.laa.2014.05.043", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006578866"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s13571-011-0008-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008022257", 
          "https://doi.org/10.1007/s13571-011-0008-x"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0167-7152(03)00121-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1013941022"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0167-7152(03)00121-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1013941022"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.spl.2012.08.032", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1015995010"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.spl.2015.01.018", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1018776913"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1019492299", 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-4-431-55459-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019492299", 
          "https://doi.org/10.1007/978-4-431-55459-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-4-431-55459-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019492299", 
          "https://doi.org/10.1007/978-4-431-55459-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-4-431-55459-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019492299", 
          "https://doi.org/10.1007/978-4-431-55459-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00357-016-9211-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019839337", 
          "https://doi.org/10.1007/s00357-016-9211-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00357-016-9211-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019839337", 
          "https://doi.org/10.1007/s00357-016-9211-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1093/biostatistics/kxp062", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020133500"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1093/biostatistics/kxp062", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020133500"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00477-009-0341-z", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020774605", 
          "https://doi.org/10.1007/s00477-009-0341-z"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00477-009-0341-z", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020774605", 
          "https://doi.org/10.1007/s00477-009-0341-z"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00477-009-0341-z", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020774605", 
          "https://doi.org/10.1007/s00477-009-0341-z"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11222-009-9138-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020996016", 
          "https://doi.org/10.1007/s11222-009-9138-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11222-009-9138-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020996016", 
          "https://doi.org/10.1007/s11222-009-9138-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10260-013-0237-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025298908", 
          "https://doi.org/10.1007/s10260-013-0237-4"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1111/1467-9868.00391", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025959631"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jsc.2012.11.005", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030191032"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1201/9780203492000.ch4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032761221"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11634-013-0147-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035052974", 
          "https://doi.org/10.1007/s11634-013-0147-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jmva.2014.04.018", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038046160"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/9780470012505.tac046", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040314627"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.neuropsychologia.2009.11.016", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040876634"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.csda.2012.12.008", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1045792756"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/cjs.11166", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1046701086"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1006/jmva.2000.1960", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047563666"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1111/j.1354-7798.2006.00309.x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048522846"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1111/j.1354-7798.2006.00309.x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048522846"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0167-9473(02)00177-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1053580480"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0167-9473(02)00177-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1053580480"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0167-6687(99)00006-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1054621131"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/01621459.1987.10478427", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058303404"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1093/biomet/57.3.519", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059417944"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/msp.2014.2298533", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1061424127"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/t-c.1974.224051", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1061456026"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/060661569", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062849432"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/1138055", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062868764"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1177/1471082x0800800204", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064025714"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1177/1471082x0800800204", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064025714"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1198/016214501753382345", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064197915"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1198/1061860031374", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064199363"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1198/106186004x12740", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064199443"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1214/09-ss053", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064391086"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1214/15-sts520", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064395478"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/16m1067457", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1083507905"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/03461238.2017.1306795", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1084160551"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.csda.2017.11.001", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1092830470"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1142/3599", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1098973722"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2019-03", 
    "datePublishedReg": "2019-03-01", 
    "description": "Finite mixtures of multivariate distributions play a fundamental role in model-based clustering. However, they pose several problems, especially in the presence of many irrelevant variables. Dimension reduction methods, such as projection pursuit, are commonly used to address these problems. In this paper, we use skewness-maximizing projections to recover the subspace which optimally separates the cluster means. Skewness might then be removed in order to search for other potentially interesting data structures or to perform skewness-sensitive statistical analyses, such as the Hotelling\u2019s T2 test. Our approach is algebraic in nature and deals with the symmetric tensor rank of the third multivariate cumulant. We also derive closed-form expressions for the symmetric tensor rank of the third cumulants of several multivariate mixture models, including mixtures of skew-normal distributions and mixtures of two symmetric components with proportional covariance matrices. Theoretical results in this paper shed some light on the connection between the estimated number of mixture components and their skewness.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s11634-018-0336-z", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1045303", 
        "issn": [
          "1862-5347", 
          "1862-5355"
        ], 
        "name": "Advances in Data Analysis and Classification", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "13"
      }
    ], 
    "name": "Finite mixtures, projection pursuit and tensor rank: a triangulation", 
    "pagination": "1-29", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "1896bf4a5ba3daeea788dc0418623817bdb07e96293a857d4d005972087617d5"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s11634-018-0336-z"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1106803959"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s11634-018-0336-z", 
      "https://app.dimensions.ai/details/publication/pub.1106803959"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T14:00", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000371_0000000371/records_130826_00000006.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2Fs11634-018-0336-z"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s11634-018-0336-z'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s11634-018-0336-z'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s11634-018-0336-z'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s11634-018-0336-z'


 

This table displays all metadata directly associated to this object as RDF triples.

210 TRIPLES      21 PREDICATES      74 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s11634-018-0336-z schema:about anzsrc-for:01
2 anzsrc-for:0104
3 schema:author N69e0dd357a3d4eb183fe8ad061c3273c
4 schema:citation sg:pub.10.1007/3-540-28084-7_15
5 sg:pub.10.1007/978-4-431-55459-2
6 sg:pub.10.1007/s00357-016-9211-9
7 sg:pub.10.1007/s00477-009-0341-z
8 sg:pub.10.1007/s10260-013-0237-4
9 sg:pub.10.1007/s11222-009-9138-7
10 sg:pub.10.1007/s11634-013-0137-3
11 sg:pub.10.1007/s11634-013-0147-1
12 sg:pub.10.1007/s13571-011-0008-x
13 https://app.dimensions.ai/details/publication/pub.1019492299
14 https://doi.org/10.1002/9780470012505.tac046
15 https://doi.org/10.1002/cjs.11166
16 https://doi.org/10.1006/jmva.2000.1960
17 https://doi.org/10.1016/j.csda.2012.12.008
18 https://doi.org/10.1016/j.csda.2017.11.001
19 https://doi.org/10.1016/j.jmva.2008.03.009
20 https://doi.org/10.1016/j.jmva.2014.04.018
21 https://doi.org/10.1016/j.jsc.2012.11.005
22 https://doi.org/10.1016/j.laa.2014.05.043
23 https://doi.org/10.1016/j.neuropsychologia.2009.11.016
24 https://doi.org/10.1016/j.spl.2012.08.032
25 https://doi.org/10.1016/j.spl.2015.01.018
26 https://doi.org/10.1016/s0167-6687(99)00006-2
27 https://doi.org/10.1016/s0167-7152(03)00121-4
28 https://doi.org/10.1016/s0167-9473(02)00177-9
29 https://doi.org/10.1080/01621459.1987.10478427
30 https://doi.org/10.1080/03461238.2017.1306795
31 https://doi.org/10.1080/1351847x.2012.720269
32 https://doi.org/10.1093/biomet/57.3.519
33 https://doi.org/10.1093/biostatistics/kxp062
34 https://doi.org/10.1109/msp.2014.2298533
35 https://doi.org/10.1109/t-c.1974.224051
36 https://doi.org/10.1111/1467-9868.00391
37 https://doi.org/10.1111/j.1354-7798.2006.00309.x
38 https://doi.org/10.1111/j.1467-9868.2009.00706.x
39 https://doi.org/10.1111/j.1751-5823.2007.00016.x
40 https://doi.org/10.1137/060661569
41 https://doi.org/10.1137/1138055
42 https://doi.org/10.1137/16m1067457
43 https://doi.org/10.1142/3599
44 https://doi.org/10.1177/1471082x0800800204
45 https://doi.org/10.1198/016214501753382345
46 https://doi.org/10.1198/1061860031374
47 https://doi.org/10.1198/106186004x12740
48 https://doi.org/10.1201/9780203492000.ch4
49 https://doi.org/10.1214/09-ss053
50 https://doi.org/10.1214/15-sts520
51 schema:datePublished 2019-03
52 schema:datePublishedReg 2019-03-01
53 schema:description Finite mixtures of multivariate distributions play a fundamental role in model-based clustering. However, they pose several problems, especially in the presence of many irrelevant variables. Dimension reduction methods, such as projection pursuit, are commonly used to address these problems. In this paper, we use skewness-maximizing projections to recover the subspace which optimally separates the cluster means. Skewness might then be removed in order to search for other potentially interesting data structures or to perform skewness-sensitive statistical analyses, such as the Hotelling’s T2 test. Our approach is algebraic in nature and deals with the symmetric tensor rank of the third multivariate cumulant. We also derive closed-form expressions for the symmetric tensor rank of the third cumulants of several multivariate mixture models, including mixtures of skew-normal distributions and mixtures of two symmetric components with proportional covariance matrices. Theoretical results in this paper shed some light on the connection between the estimated number of mixture components and their skewness.
54 schema:genre research_article
55 schema:inLanguage en
56 schema:isAccessibleForFree false
57 schema:isPartOf N31b2cc21df2b4e9f87d4dd73759e3e01
58 Neeb5f4bf51714abf8376075081c4dba6
59 sg:journal.1045303
60 schema:name Finite mixtures, projection pursuit and tensor rank: a triangulation
61 schema:pagination 1-29
62 schema:productId N883d0634b6c74c1bbc1d9bd851c4c925
63 Nbdfc2f5ea95d45c5895f961392b001c6
64 Nd9a7727588a24f6e938ffcf406829639
65 schema:sameAs https://app.dimensions.ai/details/publication/pub.1106803959
66 https://doi.org/10.1007/s11634-018-0336-z
67 schema:sdDatePublished 2019-04-11T14:00
68 schema:sdLicense https://scigraph.springernature.com/explorer/license/
69 schema:sdPublisher N3d1f4f774a2b4ca68afdb1e42d3ee579
70 schema:url http://link.springer.com/10.1007%2Fs11634-018-0336-z
71 sgo:license sg:explorer/license/
72 sgo:sdDataset articles
73 rdf:type schema:ScholarlyArticle
74 N31b2cc21df2b4e9f87d4dd73759e3e01 schema:issueNumber 1
75 rdf:type schema:PublicationIssue
76 N3d1f4f774a2b4ca68afdb1e42d3ee579 schema:name Springer Nature - SN SciGraph project
77 rdf:type schema:Organization
78 N69e0dd357a3d4eb183fe8ad061c3273c rdf:first sg:person.07507272505.84
79 rdf:rest rdf:nil
80 N883d0634b6c74c1bbc1d9bd851c4c925 schema:name readcube_id
81 schema:value 1896bf4a5ba3daeea788dc0418623817bdb07e96293a857d4d005972087617d5
82 rdf:type schema:PropertyValue
83 Nbdfc2f5ea95d45c5895f961392b001c6 schema:name doi
84 schema:value 10.1007/s11634-018-0336-z
85 rdf:type schema:PropertyValue
86 Nd9a7727588a24f6e938ffcf406829639 schema:name dimensions_id
87 schema:value pub.1106803959
88 rdf:type schema:PropertyValue
89 Neeb5f4bf51714abf8376075081c4dba6 schema:volumeNumber 13
90 rdf:type schema:PublicationVolume
91 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
92 schema:name Mathematical Sciences
93 rdf:type schema:DefinedTerm
94 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
95 schema:name Statistics
96 rdf:type schema:DefinedTerm
97 sg:journal.1045303 schema:issn 1862-5347
98 1862-5355
99 schema:name Advances in Data Analysis and Classification
100 rdf:type schema:Periodical
101 sg:person.07507272505.84 schema:affiliation https://www.grid.ac/institutes/grid.12711.34
102 schema:familyName Loperfido
103 schema:givenName Nicola
104 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07507272505.84
105 rdf:type schema:Person
106 sg:pub.10.1007/3-540-28084-7_15 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001242173
107 https://doi.org/10.1007/3-540-28084-7_15
108 rdf:type schema:CreativeWork
109 sg:pub.10.1007/978-4-431-55459-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019492299
110 https://doi.org/10.1007/978-4-431-55459-2
111 rdf:type schema:CreativeWork
112 sg:pub.10.1007/s00357-016-9211-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019839337
113 https://doi.org/10.1007/s00357-016-9211-9
114 rdf:type schema:CreativeWork
115 sg:pub.10.1007/s00477-009-0341-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1020774605
116 https://doi.org/10.1007/s00477-009-0341-z
117 rdf:type schema:CreativeWork
118 sg:pub.10.1007/s10260-013-0237-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025298908
119 https://doi.org/10.1007/s10260-013-0237-4
120 rdf:type schema:CreativeWork
121 sg:pub.10.1007/s11222-009-9138-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020996016
122 https://doi.org/10.1007/s11222-009-9138-7
123 rdf:type schema:CreativeWork
124 sg:pub.10.1007/s11634-013-0137-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002987272
125 https://doi.org/10.1007/s11634-013-0137-3
126 rdf:type schema:CreativeWork
127 sg:pub.10.1007/s11634-013-0147-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035052974
128 https://doi.org/10.1007/s11634-013-0147-1
129 rdf:type schema:CreativeWork
130 sg:pub.10.1007/s13571-011-0008-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1008022257
131 https://doi.org/10.1007/s13571-011-0008-x
132 rdf:type schema:CreativeWork
133 https://app.dimensions.ai/details/publication/pub.1019492299 schema:CreativeWork
134 https://doi.org/10.1002/9780470012505.tac046 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040314627
135 rdf:type schema:CreativeWork
136 https://doi.org/10.1002/cjs.11166 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046701086
137 rdf:type schema:CreativeWork
138 https://doi.org/10.1006/jmva.2000.1960 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047563666
139 rdf:type schema:CreativeWork
140 https://doi.org/10.1016/j.csda.2012.12.008 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045792756
141 rdf:type schema:CreativeWork
142 https://doi.org/10.1016/j.csda.2017.11.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1092830470
143 rdf:type schema:CreativeWork
144 https://doi.org/10.1016/j.jmva.2008.03.009 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001239893
145 rdf:type schema:CreativeWork
146 https://doi.org/10.1016/j.jmva.2014.04.018 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038046160
147 rdf:type schema:CreativeWork
148 https://doi.org/10.1016/j.jsc.2012.11.005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030191032
149 rdf:type schema:CreativeWork
150 https://doi.org/10.1016/j.laa.2014.05.043 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006578866
151 rdf:type schema:CreativeWork
152 https://doi.org/10.1016/j.neuropsychologia.2009.11.016 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040876634
153 rdf:type schema:CreativeWork
154 https://doi.org/10.1016/j.spl.2012.08.032 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015995010
155 rdf:type schema:CreativeWork
156 https://doi.org/10.1016/j.spl.2015.01.018 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018776913
157 rdf:type schema:CreativeWork
158 https://doi.org/10.1016/s0167-6687(99)00006-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054621131
159 rdf:type schema:CreativeWork
160 https://doi.org/10.1016/s0167-7152(03)00121-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013941022
161 rdf:type schema:CreativeWork
162 https://doi.org/10.1016/s0167-9473(02)00177-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053580480
163 rdf:type schema:CreativeWork
164 https://doi.org/10.1080/01621459.1987.10478427 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058303404
165 rdf:type schema:CreativeWork
166 https://doi.org/10.1080/03461238.2017.1306795 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084160551
167 rdf:type schema:CreativeWork
168 https://doi.org/10.1080/1351847x.2012.720269 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002743026
169 rdf:type schema:CreativeWork
170 https://doi.org/10.1093/biomet/57.3.519 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059417944
171 rdf:type schema:CreativeWork
172 https://doi.org/10.1093/biostatistics/kxp062 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020133500
173 rdf:type schema:CreativeWork
174 https://doi.org/10.1109/msp.2014.2298533 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061424127
175 rdf:type schema:CreativeWork
176 https://doi.org/10.1109/t-c.1974.224051 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061456026
177 rdf:type schema:CreativeWork
178 https://doi.org/10.1111/1467-9868.00391 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025959631
179 rdf:type schema:CreativeWork
180 https://doi.org/10.1111/j.1354-7798.2006.00309.x schema:sameAs https://app.dimensions.ai/details/publication/pub.1048522846
181 rdf:type schema:CreativeWork
182 https://doi.org/10.1111/j.1467-9868.2009.00706.x schema:sameAs https://app.dimensions.ai/details/publication/pub.1003264105
183 rdf:type schema:CreativeWork
184 https://doi.org/10.1111/j.1751-5823.2007.00016.x schema:sameAs https://app.dimensions.ai/details/publication/pub.1004737747
185 rdf:type schema:CreativeWork
186 https://doi.org/10.1137/060661569 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062849432
187 rdf:type schema:CreativeWork
188 https://doi.org/10.1137/1138055 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062868764
189 rdf:type schema:CreativeWork
190 https://doi.org/10.1137/16m1067457 schema:sameAs https://app.dimensions.ai/details/publication/pub.1083507905
191 rdf:type schema:CreativeWork
192 https://doi.org/10.1142/3599 schema:sameAs https://app.dimensions.ai/details/publication/pub.1098973722
193 rdf:type schema:CreativeWork
194 https://doi.org/10.1177/1471082x0800800204 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064025714
195 rdf:type schema:CreativeWork
196 https://doi.org/10.1198/016214501753382345 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064197915
197 rdf:type schema:CreativeWork
198 https://doi.org/10.1198/1061860031374 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064199363
199 rdf:type schema:CreativeWork
200 https://doi.org/10.1198/106186004x12740 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064199443
201 rdf:type schema:CreativeWork
202 https://doi.org/10.1201/9780203492000.ch4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032761221
203 rdf:type schema:CreativeWork
204 https://doi.org/10.1214/09-ss053 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064391086
205 rdf:type schema:CreativeWork
206 https://doi.org/10.1214/15-sts520 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064395478
207 rdf:type schema:CreativeWork
208 https://www.grid.ac/institutes/grid.12711.34 schema:alternateName University of Urbino
209 schema:name Dipartimento di Economia, Società e Politica, Università degli Studi di Urbino “Carlo Bo”, Via Saffi 42, Urbino, PU, Italy
210 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...