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Mixtures of spatial factor analyzers for tensor-variate data

T0 review · 2 major / 5 minor · reviewed 2026-07-10 · grok-4.5

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Pith's one-line read A mixture of spatial factor analyzers clusters high-dimensional tensor data by recovering distinct spatial decay patterns with a fixed number of parameters.

desk verdict Solid, usable method that keeps spatial covariance parameters fixed while recovering group-specific patterns; the I-spline + matrix-factor marriage works in the regimes they test. read the letter →

arxiv 2607.07887 v1 pith:RSDXFQZO submitted 2026-07-08 stat.ME stat.ML

Hanzhang Lu , Keiran Malott , Kirsty Milligan , Sanjeena Subedi , Edana Cassol , Vinita Chauhan , Connor McNairn , Prarthana Pasricha
show 4 more authors
Sangeeta Murugkar Rowan Thomson Andrew Jirasek Jeffrey L. Andrews
This is my paper
classification stat.MEstat.ML MSC 62H3062H2562M30
keywords mixturemodelsspatialcovariancefactoranalysistensor-variatedataI-splinesmodel-basedclusteringhyperspectralimaging
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

High-dimensional spatial data, such as hyperspectral images or Raman grids, arrive as matrices or tensors whose local spatial correlations and across-variable dependencies both matter for clustering. Ordinary mixture models either ignore the spatial grid or explode in parameters as the grid grows. This paper proposes mixtures of spatial factor analyzers (MSFA): each mixture component models the spatial covariance with a flexible I-spline decay that uses only a handful of free parameters no matter how large the grid is, while matrix factor analyzers compress the non-spatial dependence. Estimation proceeds by an alternating EM scheme that plugs a generalized least-squares fit for the spatial parameters into the usual factor updates. Simulations and three real applications (Raman dosimetry films, SpecTex textiles, Salinas hyperspectral patches) show that the model recovers the correct clusters and, more importantly, recovers and distinguishes the underlying spatial covariance curves of each group.

What carries the argument

The flexible spatial decay covariance Ξ = α₁J − α₂D(β|t,m) + diag(γ), where D is built from I-spline basis functions of Euclidean distance whose coefficients β lie on the probability simplex; this structure is estimated by nested GLS inside an alternating ECM algorithm and is Kronecker-coupled to a low-rank factor covariance across the non-spatial modes.

What would settle it

Generate or collect tensor data whose true spatial dependence is strongly non-monotonic or anisotropic; if MSFA then either fails to recover the correct number of clusters or produces decay curves that do not match the known ground-truth covariance while a less constrained spatial model succeeds, the central claim is refuted.

Watch

Extended reading notes

Core claim

The authors show that a coordinate-based flexible spatial decay (FSD) covariance, written as a linear combination of a ones matrix, an I-spline-transformed distance matrix, and a diagonal noise term, together with matrix factor loadings, yields a mixture model that both clusters tensor-variate observations and reconstructs distinct spatial patterns with a parameter count that does not grow with grid size.

Load-bearing premise

The true spatial covariance of each cluster is well approximated by a three-term form whose decay is a monotonic I-spline of distance, and the GLS criterion used for those spatial parameters is a reliable surrogate for the matrix-normal likelihood.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper proposes mixtures of spatial factor analyzers (MSFA) for clustering high-dimensional tensor-variate data that share a common coordinate system. Spatial dependence is modelled by a flexible spatial decay (FSD) covariance of the form Ξ = α1 J − α2 D(β|t,m) + diag(γ), where the decay function is a convex combination of I-spline basis functions (Eqs. 7–8); non-spatial dependence is captured by matrix factor analyzers (Eq. 13). Estimation proceeds via a three-stage AECM algorithm that embeds a nested GLS step (Browne 1974) for the spatial parameters (Stages 1–3, Eqs. 9–16). Six simulation designs examine parameter recovery, BIC selection of knots/degree and of (G,r), comparative performance against MCLUST/PGMM/MatrixMixtures, and TBT inversion efficiency; three real-data applications (Raman dosimetry, SpecTex textures, Salinas hyperspectral) illustrate recovery of group-specific spatial patterns and competitive ARI/BIC.

Significance. If the reported recovery and comparative results hold, MSFA supplies a practically useful, parsimonious tool for unsupervised analysis of matrix- and tensor-variate spatial data (hyperspectral images, sensor grids, Raman maps) whose dimension would otherwise render unstructured or even Kronecker-unstructured covariances infeasible. The fixed-parameter-count FSD structure, the explicit use of coordinates, and the integration with matrix factor analysis constitute a clear methodological advance over both classical spatial GMMs and existing multi-way mixtures. Strengths include systematic simulation designs that generate data from decays outside the I-spline family yet still recover the full Kronecker covariance with low entry-wise MSE (Table 1) and near-perfect ARI, transparent acknowledgement of boundary/scale ambiguity (Figs. 2–4), and public real-data demonstrations that differentiate spatial patterns beyond mean intensity. The asymptotic justification via Browne (1974) and the optional TBT inversion further support practicality.

major comments (2)
  1. Section 3.1 and Stage 2 (Eqs. 9–16): the claim that maximising the matrix-normal marginal (14) is asymptotically equivalent to the nested GLS criterion is invoked via Browne (1974), yet no finite-sample diagnostics or condition-number checks on the weight matrix V* = (Ξ̂*)−1 are reported. When V* is poorly conditioned (possible under the isotropic TBT option or near-singular sample Sg), the recovered β and α can be unstable; a short sensitivity experiment or regularisation note would strengthen the load-bearing estimation claim.
  2. Section 6 and Simulation I: the FSD form (Eq. 8) and the monotonicity axiom are acknowledged as limitations, but the manuscript never tests non-monotonic or anisotropic decays. While Simulation I shows good approximation of quadratic/sigmoid targets, a single counter-example (or an explicit statement that the method is intended only for isotropic monotonic decay) would clarify the scope of the central recovery claim.
minor comments (5)
  1. Eq. (11) and surrounding text refer to “objective function (16)” and later “objective function (16)” again; the numbering of the GLS criteria should be made consistent.
  2. Figure 5 caption and text: “30 simulated datasets” is stated, yet Table 1 reports “30 Replicates” while Simulation I used 50; a single clarifying sentence would avoid confusion.
  3. Section 3.5: the TBTMinv complexity is given as O(N2); the symbol N is elsewhere used for sample size—use p or L2 for matrix dimension.
  4. References: Lu et al. (2026) is cited as “in press”/forthcoming; ensure the final citation is complete or mark as “under review” consistently.
  5. Salinas analysis (Section 5.3): the spatially invariant mean constraint Mg = 1µ′g is introduced ad hoc; a brief justification or sensitivity check would improve transparency.

Circularity Check

1 steps flagged · score 1.0 of 10

No significant circularity: MSFA claims rest on independent AECM+GLS estimation and external simulation/real-data benchmarks; self-citation to prior SD work is background only.

  1. self citation load bearing [Section 2.4 and Introduction (citation to Lu et al. 2026)]
    "As an extension of the QD framework, Lu et al. (2026) introduced a Sigmoid Decay (SD) spatial constraint within GMM. ... To address these challenges, we propose the mixture of spatial factor analyzers (MSFA)."

    The citation supplies the authors’ own prior SD construction as background for the new FSD/I-spline model. It is not load-bearing: the central recovery claims, AECM updates, and BIC/ARI comparisons stand independently of that paper and are validated against external synthetic truth and public datasets. Score contribution is therefore only the minor self-citation penalty.

full rationale

The derivation chain defines the FSD covariance (Eq. 8) via I-splines (Ramsay 1988) and probability-simplex coefficients, then estimates via nested GLS (Browne 1974) inside a three-stage AECM (Meng & Van Dyk 1997). Simulation I generates data from quadratic/sigmoid decays outside the I-spline family and recovers the full Kronecker covariance with low entry-wise MSE (Table 1) and near-perfect ARI; later simulations and real Raman/SpecTex/Salinas applications further compare BIC/ARI against MCLUST, PGMM and MatrixMixtures on held-out structure. No step equates a claimed prediction or first-principles result to a fitted constant by construction. The sole self-citation (Lu et al. 2026) supplies the earlier sigmoid-decay GMM as historical context for the FSD extension; it is not invoked as a uniqueness theorem or load-bearing premise for the MSFA results. Positive-definiteness, knot selection via BIC, and TBT inversion are independently justified or empirically checked. Residual modeling assumptions (monotonic radial decay, GLS–likelihood asymptotics) are limitations of scope, not circular reductions.

Assumptions & free parameters 5 free parameters · 5 assumptions · 2 invented entities

The central claim rests on standard matrix-normal and EM theory, the domain assumption that spatial correlation is a monotonic function of Euclidean distance on a shared coordinate system, and the paper-specific construction of an I-spline probability-simplex decay plus the three-term linear combination that keeps the parameter count independent of grid size. Free parameters are the usual mixture and factor quantities plus the spline coefficients and linear spatial weights; no new physical entities are postulated.

free parameters (5)
  • I-spline coefficients β_g (probability simplex)
    Estimated by projected gradient descent on the GLS criterion; control the shape of the spatial decay curve for each component.
  • Linear spatial weights α1g, α2g and diagonal noise γg
    Estimated by closed-form GLS; scale the constant, distance and residual variance terms of Ξg.
  • Number of interior knots k and spline degree m
    Selected by BIC grid search; treated as discrete free choices that affect model flexibility.
  • Number of mixture components G and latent factors r
    Selected by BIC; standard free discrete parameters of any mixture-of-factor-analyzers model.
  • Factor loadings Λg and uniquenesses Ψg
    Estimated in the third AECM stage; standard free parameters of matrix factor analysis.
assumptions (5)
  • domain assumption Observations follow a finite mixture of matrix-variate normal distributions with Kronecker covariance Ξg ⊗ Ωg
    Standard matrix-normal mixture assumption (Viroli, Gallaugher & McNicholas); invoked throughout Section 3.
  • ad hoc to paper Spatial correlation is a non-increasing function of Euclidean distance on a shared coordinate system and can be represented by a convex combination of I-spline basis functions
    Core modeling choice of the FSD structure (Eq. 7–8); not forced by first principles.
  • standard math Maximizing the matrix-normal log-likelihood for the spatial parameters is asymptotically equivalent to minimizing the GLS criterion of Browne (1974)
    Cited justification for the nested GLS updates in Stage 2 (Section 3.4).
  • standard math The AECM algorithm converges to a stationary point of the observed-data likelihood under standard regularity conditions
    Meng & Van Dyk (1997) theory assumed for the three-stage procedure.
  • domain assumption Identifiability of the Kronecker product is restored by fixing the first diagonal entry of Ωg to 1
    Standard fix used by Gallaugher & McNicholas (2018); adopted without further proof.
invented entities (2)
  • Flexible spatial decay (FSD) covariance structure
    purpose: Provides a monotonic, non-parametric, fixed-parameter-count model for spatial correlation that relaxes both quadratic and sigmoid constraints while allowing heterogeneous variances.
    Defined by Eqs. 7–8; the central modeling novelty of the paper. Independent evidence is only the empirical recovery shown in simulations and real data; no external theoretical guarantee of positive-definiteness for arbitrary β.
  • Mixture of spatial factor analyzers (MSFA)
    purpose: Unifies the FSD spatial covariance with matrix factor analysis inside a finite mixture for simultaneous clustering and spatial-pattern inference on tensor data.
    The overall model introduced in Section 3.2. Its utility is demonstrated empirically; it is not an independently observed physical object.

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Pith. "Pith review of Mixtures of spatial factor analyzers for tensor-variate data." pith.science (2026). https://pith.science/paper/RSDXFQZO

@misc{pith2026260707887,
  author       = {Pith},
  title        = {Pith review of: Mixtures of spatial factor analyzers for tensor-variate data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RSDXFQZO}},
  note         = {Machine review of arXiv:2607.07887}
}
read the original abstract

A mixture of spatial factor analyzers (MSFA) is introduced to address the challenges of clustering high-dimensional spatial data. By leveraging the underlying coordinate system, the proposed framework incorporates a flexible, spline-based spatial decay covariance structure that prevents parameter inflation as dimensionality increases. To model non-spatial dependence, matrix variate factor analyzers are employed for further dimensionality reduction. Parameter estimation is conducted via a variant of the expectation-maximization algorithm combined with a generalized least squares estimator. The proposed models are explored in the context of tensor-variate data analysis, where simulation studies and applications to Raman spectroscopy and hyperspectral texture databases demonstrate their capacity to accurately infer and differentiate distinct spatial patterns.

Figures

Figures reproduced from arXiv: 2607.07887 by the authors.

Figure 1
Figure 1. Visualization of cubic I-spline basis functions defined on the interval [0, 1]. The vertical [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Comparison of the estimated spatial decay functions against the ground truth. The red [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Evaluation of the full spatial covariance structure. Unlike the normalized decay curves, [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figures from the paper (16 more)
Figure 4
Figure 4. Figure 4: Visual comparison of the true and estimated full covariance matrices. The top row [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: Heatmap of the optimal hyperparameter selection frequencies based on the BIC criterion [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: Comparison of execution time (in seconds) between the standard R solve function (red) [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]
Figure 7
Figure 7. Figure 7: The ratio of the execution time of solve to TBTMinv across varying matrix dimensions. [PITH_FULL_IMAGE:figures/full_fig_p019_7.png]
Figure 8
Figure 8. Figure 8: Analysis of numerical precision scaling. The plot compares the MAE of the proposed [PITH_FULL_IMAGE:figures/full_fig_p019_8.png]
Figure 9
Figure 9. Figure 9: Impact of matrix conditioning on numerical stability. The curve illustrates the relation [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]
Figure 10
Figure 10. Figure 10: Raman spectra of dosimetric film at two different dose levels. [PITH_FULL_IMAGE:figures/full_fig_p020_10.png]
Figure 11
Figure 11. Figure 11: Schematic representation of the RS sampling protocol. (i) Macroscopic view of the [PITH_FULL_IMAGE:figures/full_fig_p021_11.png]
Figure 12
Figure 12. Figure 12: Visualization of a Raman peak at 2064 cm−1 , 1446 cm−1 , and 1188 cm−1 measured on a 10 × 10 grid across two dosimetric films exposed to different radiation levels (0.5 Gy bottom, 0.15 Gy top). spatial covariance structure. Subsequently, we evaluated four variations o…
Figure 13
Figure 13. Figure 13: Estimated spatial decay functions for the two radiation dosage groups. The red dashed [PITH_FULL_IMAGE:figures/full_fig_p022_13.png]
Figure 14
Figure 14. Figure 14: Visual representation of the two textile samples selected from the SpecTex database: [PITH_FULL_IMAGE:figures/full_fig_p023_14.png]
Figure 15
Figure 15. Figure 15: Clustering results for the SpecTex dataset. The maps visualize the classification assign [PITH_FULL_IMAGE:figures/full_fig_p024_15.png]
Figure 16
Figure 16. Figure 16: Estimated spatial covariance functions for the identified clusters. The curves illustrate [PITH_FULL_IMAGE:figures/full_fig_p024_16.png]
Figure 17
Figure 17. Figure 17: Mean spectral profiles of the three classes (Grapes, Corn, and Bare Soil). [PITH_FULL_IMAGE:figures/full_fig_p025_17.png]
Figure 18
Figure 18. Figure 18: Visualization of representative matrix variate observations of the three classes (Grapes, [PITH_FULL_IMAGE:figures/full_fig_p025_18.png]
Figure 19
Figure 19. Figure 19: Estimated spatial covariance functions for the three classes (Grapes, Corn, Soil). The [PITH_FULL_IMAGE:figures/full_fig_p026_19.png]

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Reference graph

Works this paper leans on

300 extracted references · 300 canonical work pages

  1. [1]

    Medical Physics , volume=

    Exploring the potential of Raman micro-spectroscopy of radiochromic films for experimental microdosimetry , author=. Medical Physics , volume=. 2025 , publisher=

    work page 2025

  2. [2]

    Bayesian statistics , volume=

    Modelling gene expression over time: curve clustering with informative prior distributions , author=. Bayesian statistics , volume=. 2003 , publisher=

    work page 2003

  3. [3]

    Science , volume=

    The transcriptional program of sporulation in budding yeast , author=. Science , volume=. 1998 , publisher=

    work page 1998

  4. [4]

    1988 , publisher=

    Multivariate statistics: a practical approach , author=. 1988 , publisher=

    work page 1988

  5. [5]

    Statistical Papers , volume=

    Multivariate hidden Markov regression models: random covariates and heavy-tailed distributions , author=. Statistical Papers , volume=. 2021 , publisher=

    work page 2021

  6. [6]

    Longitudinal research with latent variables , pages=

    Longitudinal research using mixture models , author=. Longitudinal research with latent variables , pages=. 2010 , publisher=

    work page 2010

  7. [7]

    Journal of Business & Economic Statistics , volume=

    Model-based clustering of multiple time series , author=. Journal of Business & Economic Statistics , volume=. 2008 , publisher=

    work page 2008

  8. [8]

    Computational Statistics & Data Analysis , volume=

    Model-based time-varying clustering of multivariate longitudinal data with covariates and outliers , author=. Computational Statistics & Data Analysis , volume=. 2017 , publisher=

    work page 2017

Show all 300 references
  1. [9]

    Journal of the Royal Statistical Society: Series B (Statistical Methodology) , volume=

    Functional clustering and identifying substructures of longitudinal data , author=. Journal of the Royal Statistical Society: Series B (Statistical Methodology) , volume=. 2007 , publisher=

    2007

  2. [10]

    Computational Statistics , volume=

    KmL: k-means for longitudinal data , author=. Computational Statistics , volume=. 2010 , publisher=

    2010

  3. [11]

    Journal of Statistical Software , volume=

    Capabilities of R package mixAK for clustering based on multivariate continuous and discrete longitudinal data , author=. Journal of Statistical Software , volume=

  4. [12]

    Computational Statistics & Data Analysis , volume=

    Model-based clustering for longitudinal data , author=. Computational Statistics & Data Analysis , volume=. 2008 , publisher=

    2008

  5. [13]

    2022 , author =

    Analysis of Longitudinal Data with Examples , publisher =. 2022 , author =

    2022

  6. [14]

    Lazarsfeld , crossref =

    P.F. Lazarsfeld , crossref =

  7. [15]

    Advances in neural information processing systems , volume=

    An impossibility theorem for clustering , author=. Advances in neural information processing systems , volume=

  8. [16]

    1974 , author =

    The interpretation of multiple observations , publisher =. 1974 , author =

    1974

  9. [17]

    Journal of Computational and Graphical Statistics , volume=

    Clustering multivariate longitudinal observations: The contaminated Gaussian hidden Markov model , author=. Journal of Computational and Graphical Statistics , volume=. 2016 , publisher=

    2016

  10. [18]

    The Annals of Applied Statistics , volume=

    Dynamic mixtures of factor analyzers to characterize multivariate air pollutant exposures , author=. The Annals of Applied Statistics , volume=. 2017 , publisher=

    2017

  11. [19]

    2016 , url =

    R: A Language and Environment for Statistical Computing , author =. 2016 , url =

    2016

  12. [20]

    Biometrika , year =

    Durbin, James and Watson, Geoffrey S , title =. Biometrika , year =

  13. [21]

    , title =

    Andrews, Jeffrey L. , title =. Computational Statistics & Data Analysis , year =

  14. [22]

    Machine learning , year =

    Breiman, Leo , title =. Machine learning , year =

  15. [23]

    Journal of Computational and Graphical Statistics , year =

    Tibshirani, Robert and Knight, Keith , title =. Journal of Computational and Graphical Statistics , year =

  16. [24]

    , title =

    Rubin, Donald B. , title =. Psychometrika , year =

  17. [25]

    Journal of Statistical Software , year =

    McLachlan, Geoff J and Peel, David and Basford, Kaye E and Adams, Peter , title =. Journal of Statistical Software , year =

  18. [26]

    BOOTSTRAPPING FINITE MIXTURE MODELS , booktitle =

    Gr. BOOTSTRAPPING FINITE MIXTURE MODELS , booktitle =. 2004 , organization =

    2004

  19. [27]

    Computational Statistics & Data Analysis , year =

    Karlis, Dimitris and Xekalaki, Evdokia , title =. Computational Statistics & Data Analysis , year =

  20. [28]

    Finite mixture modeling with mixture outcomes using the EM algorithm , journal =

    Muth. Finite mixture modeling with mixture outcomes using the EM algorithm , journal =. 1999 , volume =

    1999

  21. [29]

    Biometrics , year =

    Wood, Simon N , title =. Biometrics , year =

  22. [30]

    Biometrika , year =

    Efron, Bradley , title =. Biometrika , year =

  23. [31]

    1982 , author =

    The jackknife, the bootstrap and other resampling plans , publisher =. 1982 , author =

    1982

  24. [32]

    Applied statistics , year =

    McLachlan, Geoffrey J , title =. Applied statistics , year =

  25. [33]

    1985 , author =

    Statistical analysis of finite mixture distributions , publisher =. 1985 , author =

    1985

  26. [34]

    Statistical Methods and Applications , year =

    Ingrassia, Salvatore , title =. Statistical Methods and Applications , year =

  27. [35]

    IEEE Transactions on Pattern Analysis and Machine Intelligence , year =

    Pernkopf, Franz and Bouchaffra, Djamel , title =. IEEE Transactions on Pattern Analysis and Machine Intelligence , year =

  28. [36]

    Learning mixture models using a genetic version of the EM algorithm , journal =

    Mart. Learning mixture models using a genetic version of the EM algorithm , journal =. 2000 , volume =

    2000

  29. [37]

    Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence , year =

    Attias, Hagai , title =. Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence , year =

  30. [38]

    Statistics and Computing , year =

    Robert, Christian P and Titterington, DM , title =. Statistics and Computing , year =

  31. [39]

    Computational Statistics & Data Analysis , year =

    McGrory, Clare A and Titterington, DM , title =. Computational Statistics & Data Analysis , year =

  32. [40]

    2008 , publisher=

    The EM algorithm and extensions , author=. 2008 , publisher=

    2008

  33. [41]

    2007 , author =

    The EM algorithm and extensions , publisher =. 2007 , author =

    2007

  34. [42]

    Pattern Recognition Letters , year =

    Andrews, Jeffrey L and McNicholas, Paul D , title =. Pattern Recognition Letters , year =

  35. [43]

    Advances in Data Analysis and Classification , year =

    Melnykov, Volodymyr and Melnykov, Igor and Michael, Semhar , title =. Advances in Data Analysis and Classification , year =

  36. [44]

    2015 , note =

    Weiliang Qiu and Harry Joe , title =. 2015 , note =

    2015

  37. [45]

    Lichman , title =

    M. Lichman , title =. 2013 , institution =

    2013

  38. [46]

    Choosing Starting Values for the EM Algorithm for Getting the Highest Likelihood in Multivariate Gaussian Mixture Models , journal =

    Biernacki, Christophe and Celeux, Gilles and Govaert, G. Choosing Starting Values for the EM Algorithm for Getting the Highest Likelihood in Multivariate Gaussian Mixture Models , journal =. 2003 , volume =

    2003

  39. [47]

    Lee and Geoffrey J

    Sharon X. Lee and Geoffrey J. McLachlan , title =. Journal of Statistical Software , year =

  40. [48]

    Kui Wang and Angus Ng and Geoff McLachlan , year =

  41. [49]

    Andrews and Jaymeson R

    Jeffrey L. Andrews and Jaymeson R. Wickins and Nicholas M. Boers and Paul D. McNicholas , year =

  42. [50]

    2012 , note =

    mclust Version 4 for R: Normal Mixture Modeling for Model-Based Clustering, Classification, and Density Estimation , author =. 2012 , note =

    2012

  43. [51]

    Browne and Paul D

    Ryan P. Browne and Paul D. McNicholas , year =

  44. [52]

    Benjamin Auder and Remi Lebret and Serge Iovleff and Florent Langrognet , year =

  45. [53]

    and Browne, R.P

    Franczak, B.C. and Browne, R.P. and McNicholas, P.D. , title =. IEEE Transactions on Pattern Analysis and Machine Intelligence, , year =

  46. [54]

    Computational Statistics & Data Analysis , year =

    Vrbik, Irene and McNicholas, Paul D , title =. Computational Statistics & Data Analysis , year =

  47. [55]

    Alan Genz and Frank Bretz and Tetsuhisa Miwa and Xuefei Mi and Friedrich Leisch and Fabian Scheipl and Torsten Hothorn , year =

  48. [56]

    Compstat , year =

    Leisch, Friedrich , title =. Compstat , year =

  49. [57]

    Statistics and Computing , year =

    Karlis, Dimitris and Santourian, Anais , title =. Statistics and Computing , year =

  50. [58]

    Statistics & Probability Letters , year =

    I Vrbik and PD McNicholas , title =. Statistics & Probability Letters , year =

  51. [59]

    Statistics and Computing , year =

    Lin, Tsung-I , title =. Statistics and Computing , year =

  52. [60]

    arXiv preprint arXiv:1305.4669 , year =

    Punzo, Antonio and McNicholas, Paul D , title =. arXiv preprint arXiv:1305.4669 , year =

    arXiv

  53. [61]

    Advances in Data Analysis and Classification , year =

    Browne, Ryan P and McNicholas, Paul D , title =. Advances in Data Analysis and Classification , year =

  54. [62]

    , title =

    Viroli, C. , title =. Journal of Classification , year =

  55. [63]

    and Tibshirani, R

    Witten, D.M. and Tibshirani, R. , title =. Journal of the American Statistical Association , year =

  56. [64]

    2011 , note =

    sparcl: Perform sparse hierarchical clustering and sparse k-means clustering , author =. 2011 , note =

    2011

  57. [65]

    and Viroli, C

    Montanari, A. and Viroli, C. , title =. Statistical Modelling , year =

  58. [66]

    Model-based cluster and discriminant analysis with the

    Biernacki, Christophe and Celeux, Gilles and Govaert, G. Model-based cluster and discriminant analysis with the. Computational Statistics and Data Analysis , year =

  59. [67]

    Journal of Classification , year =

    Qiu, Weiliang and Joe, Harry , title =. Journal of Classification , year =

  60. [68]

    Statistics and Computing , year =

    Bouveyron, Charles and Brunet, Camille , title =. Statistics and Computing , year =

  61. [69]

    McLachlan, G. J. and Bean, R. W. and Peel, D. , title =. Bioinformatics , year =

  62. [70]

    Andrews and Paul D

    Jeffrey L. Andrews and Paul D. McNicholas , title =. Statistics and Computing , year =

  63. [71]

    Advances in Data Analysis, Data Handling and Business Intelligence , publisher =

    Greselin, Francesca and Ingrassia, Salvatore , title =. Advances in Data Analysis, Data Handling and Business Intelligence , publisher =. 2010 , editor =

    2010

  64. [72]

    and Ingrassia, S

    Greselin, F. and Ingrassia, S. , title =. Statistics and Computing , year =

  65. [73]

    Model-based clustering with sparse covariance matrices

    Fop, Michael and Murphy, Thomas Brendan and Scrucca, Luca. Model-based clustering with sparse covariance matrices. Statistics and Computing. 2018. doi:10.1007/s11222-018-9838-y

    2018 doi

  66. [74]

    and Peterson, L

    Heinz, G. and Peterson, L. J. and Johnson, R. W. and Kerk, C. J. , title =. Journal of Statistics Education , year =

  67. [75]

    and Celeux, G

    Maugis, C. and Celeux, G. and Martin-Magniette, M.-L. , title =. Biometrics , year =

  68. [76]

    Computational Statistics and Data Analysis , year =

    Charles Bouveyron and St?phane Girard and Cordelia Schmid , title =. Computational Statistics and Data Analysis , year =

  69. [77]

    and Wasserman, Larry , title =

    Kass, Robert E. and Wasserman, Larry , title =. Journal of the American Statistical Association , year =

  70. [78]

    Statistical Science , year =

    Besag, Julian and Green, Peter and Higdon, David and Mengersen, Kerrie , title =. Statistical Science , year =

  71. [79]

    , title =

    Anderson, E. , title =. Bulletin of the American Iris Society , year =

  72. [80]

    Fisher, R. A. , title =. Annals of Eugenics , year =

  73. [81]

    Operations Research , year =

    Mangasarian, Olvi L and Street, W Nick and Wolberg, William H , title =. Operations Research , year =

  74. [82]

    Scandinavian Journal of Statistics , year =

    Sundberg, R , title =. Scandinavian Journal of Statistics , year =

  75. [83]

    Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Theory of Statistics , publisher =

    Orchard, T and Woodbury, M A , title =. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Theory of Statistics , publisher =. 1972 , editor =

    1972

  76. [84]

    Annals of Mathematical Statistics , year =

    Baum, L E and Petrie, T and Soules, G and Weiss, N , title =. Annals of Mathematical Statistics , year =

  77. [85]

    Journal of the Royal Statistical Society B , year =

    Trevor Hastie and Robert Tibshirani , title =. Journal of the Royal Statistical Society B , year =

  78. [86]

    Andrews and Paul D

    Jeffrey L. Andrews and Paul D. McNicholas , title =. Journal of Statistical Planning and Inference , year =

  79. [87]

    Andrews, J. L. and McNicholas, P. D. and Subedi, S. , title =. Computational Statistics and Data Analysis , year =

  80. [88]

    Andrews, J. L. and McNicholas, P. D. , title =. Statistics and Computing , year =

  81. [89]

    Edwards, A. W. F. and Cavalli-Sforza, L. L. , title =. Biometrics , year =

  82. [90]

    1981 , author =

    Classification , publisher =. 1981 , author =

    1981

  83. [91]

    Gormley, I. C. and Murphy, T. B. , title =. The Annals of Applied Statistics , year =

  84. [92]

    Fraley and A

    C. Fraley and A. E. Raftery , title =. 2006 , type =

    2006

  85. [93]

    1992 , author =

    Discriminant Analysis and Statistical Pattern Recognition , publisher =. 1992 , author =

    1992

  86. [94]

    1982 , author =

    The classification and mixture maximum likelihood approaches to cluster analysis , publisher =. 1982 , author =

    1982

  87. [95]

    , title =

    Scrucca, L. , title =. Statistics and Computing , year =

  88. [96]

    and Cook, D

    Swayne, D.F. and Cook, D. and Buja, A. and Lang, D.T. and Wickham, H. and Lawrence, M. , title =. 2006 , note =

    2006

  89. [97]

    1992 , author =

    Numerical Recipies in C --- The Art of Scientific Computation , publisher =. 1992 , author =

    1992

  90. [98]

    2002 , author =

    Categorical Data Analysis , publisher =. 2002 , author =

    2002

  91. [99]

    1994 , author =

    Elementary Linear Algebra , publisher =. 1994 , author =

    1994

  92. [100]

    and Imielinski, T

    Agrawal, R. and Imielinski, T. and Swami, A. , title =. ACM SIGMOD International Conference on Management of Data , year =

  93. [101]

    and Srikant, R

    Agrawal, R. and Srikant, R. , title =. 20th International Conference on Very Large Data Bases , year =

  94. [102]

    Aitken, A. C. , title =. Proceedings of the Royal Society of Edinburgh , year =

  95. [103]

    and Bruzzese, D

    Balbi, S. and Bruzzese, D. and Scepi, G. , title =. 15th CompStat Conference , year =

  96. [104]

    and Raftery, Adrian E

    Banfield, Jeffrey D. and Raftery, Adrian E. , title =. Biometrics , year =

  97. [105]

    Bartholomew, D. J. and Schuessler, K. F. , title =. Sociological Methodology , year =

  98. [106]

    Bartholomew, D. J. , title =. Sankhy\=a. The Indian Journal of Statistics. Series A , year =

  99. [107]

    Bartholomew, D.J. and. Latent trait and latent class models applied to survey data , booktitle =. 1997 , editor =

    1997

  100. [108]

    1999 , author =

    Latent Variable Models and Factor Analysis , publisher =. 1999 , author =

    1999

  101. [109]

    Note sur une m\'

    Beno\^. Note sur une m\'. Bulletin G\'. 1924 , volume =

    1924

  102. [110]

    and Celeux, G

    Biernacki, C. and Celeux, G. and Govaert, G. , title =. IEEE Transactions on Pattern Analysis and Machine Intelligence , year =

  103. [111]

    Binder, D. A. , title =. Biometrika , year =

  104. [112]

    The Distribution of the Likelihood Ratio for Mixtures of Densities from the One-Parameter Exponential Family , journal =

    B\". The Distribution of the Likelihood Ratio for Mixtures of Densities from the One-Parameter Exponential Family , journal =. 1994 , volume =

    1994

  105. [113]

    , title =

    Bonferroni, C. , title =. Studi in Onore del Professore Salvatore Ortu Carboni , year =

  106. [114]

    and Kruse, R

    Borgelt, C. and Kruse, R. , title =. 15th COMPSTAT Conference , year =

  107. [115]

    , title =

    Borgelt, C. , title =. Workshop of Frequent Item Set Mining Implementations , year =

  108. [116]

    1973 , author =

    Algorithms for Minimization without Derivatives , publisher =. 1973 , author =

    1973

  109. [117]

    and Davino, C

    Bruzzese, D. and Davino, C. , title =. Computational Statistics , year =

  110. [118]

    Campbell, N. A. and Mahon, R. J. , title =. Australian Journal of Zoology , year =

  111. [119]

    and Feelders, A

    Castelo, R. and Feelders, A. and Siebes, A. , title =. Proceedings of 4th International Symposium on Intelligent Data Analysis , year =

  112. [120]

    Gaussian Parsimonious Clustering Models , journal =

    Celeux, Gilles and Govaert, G\'. Gaussian Parsimonious Clustering Models , journal =. 1995 , volume =

    1995

  113. [121]

    A Classification

    Gilles Celeux and G\'. A Classification. Computational Statistics and Data Analysis , year =

  114. [122]

    Applied Statistics , year =

    Chang, Wei Chien , title =. Applied Statistics , year =

  115. [123]

    2001 , author =

    College Entry in Focus: a fourth national survey of access to higher education , publisher =. 2001 , author =

    2001

  116. [124]

    , title =

    Cohen, J. , title =. Educational and Psychological Measurement , year =

  117. [125]

    2007 , author =

    Interactive and Dynamic Graphics for Data Analysis: With R and GGobi (Use R) , publisher =. 2007 , author =

    2007

  118. [126]

    1991 , author =

    Elements of Information Theory , publisher =. 1991 , author =

    1991

  119. [127]

    1990 , author =

    Analysis of repeated measures , publisher =. 1990 , author =

    1990

  120. [128]

    and Raftery, A

    Dasgupta, A. and Raftery, A. E. , title =. Journal of the American Statistical Association , year =

  121. [129]

    Day, N. E. , title =. Biometrika , year =

  122. [130]

    Dawid, A. P. , title =. Journal of the Royal Statistal Society. Series B , year =

  123. [131]

    2006 , note =

    The clustvarsel Package , author =. 2006 , note =

    2006

  124. [132]

    and Murphy, T

    Dean, N. and Murphy, T. B. and Downey, G. , title =. Journal of the Royal Statistical Society. Series C , year =

  125. [133]

    Dempster, A. P. and Laird, N. M. and Rubin, D. B. , title =. Journal of the Royal Statistical Society. Series B , year =

  126. [134]

    1996 , volume =

    New developments in latent structure analysis applied to social attitudes , journal =. 1996 , volume =

    1996

  127. [135]

    1994 , author =

    Analysis of Longitudinal Data , publisher =. 1994 , author =

    1994

  128. [136]

    and Li, J

    Dong, G. and Li, J. , title =. Pacific-Asia Conference on Knowledge Discovery and Data Mining , year =

  129. [137]

    2006 , author =

    Facing Extinction? Why Men are not Attracted to Primary Teaching , publisher =. 2006 , author =

    2006

  130. [138]

    2002 , author =

    GNU Octave Manual , publisher =. 2002 , author =

    2002

  131. [139]

    , title =

    Fisher, R.A. , title =. Journal of the Royal Statistical Society , year =

  132. [140]

    and Tiscornia, E

    Forina, M. and Tiscornia, E. , title =. Annali di Chimica , year =

  133. [141]

    and Armanino, C

    Forina, M. and Armanino, C. , title =. Annali di Chimica , year =

  134. [142]

    and Armanino, C

    Forina, M. and Armanino, C. and Lanteri, S. and Tiscornia, E. , title =. Food Research and Data Analysis , publisher =. 1983 , editor =

    1983

  135. [143]

    and Armanino, C

    Forina, M. and Armanino, C. and Castino, M. and Ubigli, M. , title =. Vitis , year =

  136. [144]

    and Raftery, A

    Fraley, C. and Raftery, A. E. , title =. The Computer Journal , year =

  137. [145]

    1990 , author =

    Calculus with Analytic Geometry , publisher =. 1990 , author =

    1990

  138. [146]

    and Raftery, A

    Fraley, C. and Raftery, A. E. , title =. Journal of Classification , year =

  139. [147]

    , title =

    Fraley, Chris and Raftery, Adrian E. , title =. Journal of the American Statistical Association , year =

  140. [148]

    Fraley and A

    C. Fraley and A. E. Raftery , title =. 2002 , type =

    2002

  141. [149]

    Sur les tableaux de corr

    Fr. Sur les tableaux de corr. Annales de l'Universit. 1951 , volume =

    1951

  142. [150]

    Fr. G. Fundamenta Mathematica , year =

  143. [151]

    2006 , author =

    Finite Mixture and Markov Switching Models , publisher =. 2006 , author =

    2006

  144. [152]

    Proceedings of 2005 International Conference on Machine Learning and Cybernetics , year =

    Min Gan and Ming-Yi Zhang and Shen-Wen Wang , title =. Proceedings of 2005 International Conference on Machine Learning and Cybernetics , year =

    2005

  145. [153]

    and Hinton, G

    Ghahramani, Z. and Hinton, G. E. , title =. 1997 , number =

    1997

  146. [154]

    Gormley, I. C. and Murphy, T. B. , title =. Journal of the Royal Statistical Society. Series A , year =

  147. [155]

    Gower, J. C. , title =. Psychometrika , year =

  148. [156]

    and Orlowska, M

    Gray, B. and Orlowska, M. , title =. Pacific-Asia Conference on Knowledge Discovery and Data Mining , year =

  149. [157]

    1983 , author =

    Matrices with Applications in Statistics , publisher =. 1983 , author =

    1983

  150. [158]

    and Hornik, K

    Hahsler, M. and Hornik, K. and Reutterer, T. , title =. Research Report Series, Department of Statistics and Mathematics, Wirtschaftsuniversitat Wien , year =

  151. [159]

    Hartigan, J. A. and Kleiner, B. , title =. 13th Symposium on the Interface Between Computer Science and Statistics , year =

  152. [160]

    2005 , note =

    arules: Mining Association Rules and Frequent Itemsets , author =. 2005 , note =

    2005

  153. [161]

    2001 , author =

    The Elements of Statistical Learning , publisher =. 2001 , author =

    2001

  154. [162]

    and Siebes, A

    Hofmann, H. and Siebes, A. , title =. ACM SIGKDD Conference , year =

  155. [163]

    and Wilhelm, A

    Hofmann, H. and Wilhelm, A. , title =. Computational Statistics , year =

  156. [164]

    Data Mining of Association Rules and the Process of Knowledge Discovery in Databases , booktitle =

    Jochen Hipp and Ulrich G\". Data Mining of Association Rules and the Process of Knowledge Discovery in Databases , booktitle =. 2002 , pages =

    2002

  157. [165]

    and Arabie, P

    Hubert, L. and Arabie, P. , title =. Journal of Classification , year =

  158. [166]

    Hunter, D. L. and Lange, K. , title =. Journal of Computational and Graphical Statistics , year =

  159. [167]

    Hunter, D. L. and Lange, K. , title =. The American Statistician , year =

  160. [168]

    Catherine Hurley , year =

  161. [169]

    Journal of Computational and Graphical Statistics , year =

    Hurley, Catherine , title =. Journal of Computational and Graphical Statistics , year =

  162. [170]

    Final Report and Recommendations , publisher =

    Commission on the Points System. Final Report and Recommendations , publisher =. 1999 , author =

    1999

  163. [171]

    Jensen, J. L. W. V. , title =. Acta Mathematica , year =

  164. [172]

    and Raftery, Adrian E

    Kass, Robert E. and Raftery, Adrian E. , title =. Journal of the American Statistical Association , year =

  165. [173]

    and Schl\"

    Keller, R. and Schl\". 2002 , note =

    2002

  166. [174]

    Comptes Rendus de l'Acad\'emie des Sciences

    Keribin, Christine , title =. Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I. Math\'ematique , year =

  167. [175]

    , title =

    Keribin, C. , title =. Sankhy\=a. The Indian Journal of Statistics. Series A , year =

  168. [176]

    1987 , author =

    Soziale Empfindungen: ein interkultureller Skalenvergleich bei. 1987 , author =

    1987

  169. [177]

    1788 , author =

    M\'. 1788 , author =

  170. [178]

    1812 , author =

    Theorie Analytique des Probabilites , publisher =. 1812 , author =

  171. [179]

    Lawley, D. N. and Maxwell, A. E. , title =. The Statistician , year =

  172. [180]

    1971 , author =

    Factor Analysis as a Statistical Method , publisher =. 1971 , author =

    1971

  173. [181]

    Leroux, B. G. , title =. The Annals of Statistics , year =

  174. [182]

    Lindsay, B. G. , title =. NSF-CBMS Regional Conference Series in Probability and Statistics , publisher =. 1995 , volume =

    1995

  175. [183]

    Statistica Sinica , year =

    Hedibert Freitas Lopes and Mike West , title =. Statistica Sinica , year =

  176. [184]

    , title =

    Lubischew, Alexander A. , title =. Biometrics , year =

  177. [185]

    and Hsu, W

    Lui, B. and Hsu, W. and Ma, Y. , title =. ACM SIGKDD Conference , year =

  178. [186]

    1996 , author =

    Handbook of Matrices , publisher =. 1996 , author =

    1996

  179. [187]

    Research paper no

    Commission on the points system. Research paper no. 4. Points and performance in higher education: A study of the predictive validity of the points system , publisher =. 1999 , author =

    1999

  180. [188]

    Lynch, C. D. and McConnell, R. J. and Hannigan, A. , title =. European Journal of Dental Education , year =

  181. [189]

    1999 , author =

    Matrix Differential Calculus with Applications in Statistics and Econometrics , publisher =. 1999 , author =

    1999

  182. [190]

    McLachlan, G. J. and Peel, D. , title =. Lecture Notes in Computer Science , publisher =. 1998 , volume =

    1998

  183. [191]

    McLachlan, G. J. and Peel, D. , title =. Proceedings of the Seventh International Conference on Machine Learning , year =

  184. [192]

    McLachlan, G. J. and Peel, D. , title =. Journal of Computational Statistics , year =

  185. [193]

    McLachlan, G. J. and Peel, D. and Bean, R. W. , title =. Computational Statistics & Data Analysis , year =

  186. [194]

    McLachlan, G. J. and Bean, R. W. and Jones, L. Ben-Tovim , title =. Computational Statistics and Data Analysis , year =

  187. [195]

    McNicholas, P. D. , title =. Journal of the Statistical & Social Inquiry Society of Ireland , year =

  188. [196]

    McNicholas, P. D. and Murphy, T. B. , title =. Statistics and Computing , year =

  189. [197]

    McNicholas, P. D. and Murphy, T. B. and McDaid, A. F. and Frost, D. , title =. Computational Statistics and Data Analysis , year =

  190. [198]

    McNicholas, P. D. and Murphy, T. B. , title =. The Canadian Journal of Statistics , year =

  191. [199]

    McNicholas, P. D. , title =. Journal of Statistical Planning and Inference , year =

  192. [200]

    Meng, X-L and Rubin, D. B. , title =. Biometrika , year =

  193. [201]

    Journal of the Royal Statistical Society Series B , year =

    Meng, X-L and van Dyk, D , title =. Journal of the Royal Statistical Society Series B , year =

  194. [202]

    Moran, M. A. and Crowley, M. J. , title =. Journal of the Statistical and Social Inquiry Society of Ireland , year =

  195. [203]

    2006 , author =

    Who went to college in 2004? A national survey of new entrants to higher education , publisher =. 2006 , author =

    2004

  196. [204]

    , title =

    Ooche, W., and Kastelijn, H., and DeWaele, A. , title =. Annales des Falsifications et de l'Expertise Chimique , year =

  197. [205]

    1970 , author =

    Iterative Solutions of Nonlinear Equations in Several Variables , publisher =. 1970 , author =

    1970

  198. [206]

    Biometrika , year =

    Pan, Jianxin and MacKenzie, Gilbert , title =. Biometrika , year =

  199. [207]

    Statistical Modelling , year =

    Pan, Jianxin and MacKenzie, Gilbert , title =. Statistical Modelling , year =

  200. [208]

    and Bastide, Y

    Pasquier, N. and Bastide, Y. and Taouil, R. and Lakhal, L. , title =. Seventh International Conference on Database Theory , year =

  201. [209]

    and Han, J

    Pei, J. and Han, J. and Mao, R. , title =. Proceedings of ACM-SIGMOD International Workshop on Data Mining and Knowledge Discovery , year =

  202. [210]

    Plackett, R. L. , title =. Applied Statistics , year =

  203. [211]

    Biometrika , year =

    Pourahmadi, Mohsen , title =. Biometrika , year =

  204. [212]

    and Park,T

    Pourahmadi, Mohsen and Daniels,M. and Park,T. , title =. Journal of Multivariate Analysis , year =

  205. [213]

    Rand, W. M. , title =. Journal of the American Statistical Association , year =

  206. [214]

    Raftery, A. E. and Dean, N. , title =. Journal of the American Statistical Association , year =

  207. [215]

    1996 , author =

    Pattern Recognition and Neural Networks , publisher =. 1996 , author =

    1996

  208. [216]

    , title =

    Savasere, A., and Omiecinski, E., and Navathe, S. , title =. Proceedings 14th International Conference on Data Engineering , year =

  209. [217]

    1982 , author =

    Measuring Social Life Feelings , publisher =. 1982 , author =

    1982

  210. [218]

    , title =

    Schwarz, G. , title =. The Annals of Statistics , year =

  211. [219]

    Pattern Recognition , year =

    Shy Shoham , title =. Pattern Recognition , year =

  212. [220]

    and Tuzhilin, A

    Silberschatz, A. and Tuzhilin, A. , title =. Knowledge Discovery and Data Mining , year =

  213. [221]

    Data Mining and Knowledge Discovery , year =

    Silverstien, Craig, and Brin, Sergey, and Motwani, Rajeev , title =. Data Mining and Knowledge Discovery , year =

  214. [222]

    , title =

    Spearman, C. , title =. American Journal of Psychology , year =

  215. [223]

    Association Scientifique Internationale pour le Caf\'

    Streuli, Hans , title =. Association Scientifique Internationale pour le Caf\'. 1973 , pages =

    1973

  216. [224]

    2006 , author =

    Introduction to Data Mining , publisher =. 2006 , author =

    2006

  217. [225]

    R., and Webb, G

    Thiruvady, D. R., and Webb, G. I. , title =. Pacific-Asia Conference on Knowledge Discovery and Data Mining , year =

  218. [226]

    Tipping, T. E. and Bishop, C. M. , title =. Neural Computation , year =

  219. [227]

    Tipping, T. E. and Bishop, C. M. , title =. Journal of the Royal Statistical Society. Series B , year =

  220. [228]

    1998 , author =

    Commission on the points system. 1998 , author =

    1998

  221. [229]

    2003 , author =

    Uncertainty Handling and Quality Assessment in Data Mining , publisher =. 2003 , author =

    2003

  222. [230]

    1999 , author =

    Modern Applied Statistics with S-PLUS , publisher =. 1999 , author =

    1999

  223. [231]

    , title =

    Wilhelm, A. , title =. Computational Statistics: 15th Symposium , year =

  224. [232]

    1990 , author =

    Graphical Models on Applied Multivariate Statistics , publisher =. 1990 , author =

    1990

  225. [233]

    Wolfe, J. H. , title =. 1963 , address =

    1963

  226. [234]

    Wolfe, J. H. , title =. 1965 , note =

    1965

  227. [235]

    Wolfe, J. H. , title =. Multivariate Behavioral Research , year =

  228. [236]

    1950 , author =

    Inverting modified matrices , publisher =. 1950 , author =

    1950

  229. [237]

    19th International Conference on Machine Learning , year =

    Xindong Wu and Chengqi Zhang and Shichao Zhang , title =. 19th International Conference on Machine Learning , year =

  230. [238]

    ACM Transactions on Information Systems , year =

    Xindong Wu and Chengqi Zhang and Shichao Zhang , title =. ACM Transactions on Information Systems , year =

  231. [239]

    Undy , title =

    Yule, G. Undy , title =. Biometrika , year =

  232. [240]

    and Hsiao, C

    Zaki, M. and Hsiao, C. , title =. 2nd SIAM International Conference on Data Mining , year =

  233. [241]

    and Jiang, Q

    Zhao, J. and Jiang, Q. , title =. Neurocomputing , year =

  234. [242]

    2008 , author =

    The. 2008 , author =

    2008

  235. [243]

    Raftery and Luca Scrucca , year =

    Chris Fraley and Adrian E. Raftery and Luca Scrucca , year =

  236. [244]

    McNicholas, P. D. and Murphy, T. B. , title =. Bioinformatics , year =

  237. [245]

    McNicholas, P. D. and Murphy, T. B. , title =. 2005 , number =

    2005

  238. [246]

    Artificial Intelligence Review , year =

    Karaboga, Dervis and Gorkemli, Beyza and Ozturk, Celal and Karaboga, Nurhan , title =. Artificial Intelligence Review , year =

  239. [247]

    Applied soft computing , year =

    Karaboga, Dervis and Ozturk, Celal , title =. Applied soft computing , year =

  240. [248]

    Applied mathematics and computation , year =

    Karaboga, Dervis and Akay, Bahriye , title =. Applied mathematics and computation , year =

  241. [249]

    Journal of global optimization , year =

    Karaboga, Dervis and Basturk, Bahriye , title =. Journal of global optimization , year =

  242. [250]

    Swarm and Evolutionary Computation , year =

    Zhou, Aimin and Qu, Bo-Yang and Li, Hui and Zhao, Shi-Zheng and Suganthan, Ponnuthurai Nagaratnam and Zhang, Qingfu , title =. Swarm and Evolutionary Computation , year =

  243. [251]

    Encyclopedia of machine learning , publisher =

    Kennedy, James , title =. Encyclopedia of machine learning , publisher =. 2011 , pages =

    2011

  244. [252]

    Machine Learning , year =

    Martens, David and Baesens, Bart and Fawcett, Tom , title =. Machine Learning , year =

  245. [253]

    Mathematical Problems in Engineering , year =

    Zhang, Yudong and Wang, Shuihua and Ji, Genlin , title =. Mathematical Problems in Engineering , year =

  246. [254]

    Complete gradient clustering algorithm for features analysis of x-ray images , booktitle =

    Charytanowicz, Ma. Complete gradient clustering algorithm for features analysis of x-ray images , booktitle =. 2010 , pages =

    2010

  247. [255]

    Python Language Reference , howpublished =

    Python. Python Language Reference , howpublished =

  248. [256]

    IEEE computational intelligence magazine , year =

    Dorigo, Marco and Birattari, Mauro and Stutzle, Thomas , title =. IEEE computational intelligence magazine , year =

  249. [257]

    2004 , author =

    Finite mixture models , publisher =. 2004 , author =

    2004

  250. [258]

    1988 , author =

    Mixture Models: Inference and applications to clustering , publisher =. 1988 , author =

    1988

  251. [259]

    1990 , author =

    Finding Groups in Data , publisher =. 1990 , author =

    1990

  252. [260]

    Biometrics , year =

    Gower, John C , title =. Biometrics , year =

  253. [261]

    Journal of Statistics Education , year =

    Kim, Albert Y and Escobedo-Land, Adriana , title =. Journal of Statistics Education , year =

  254. [262]

    1966 , publisher =

    Stroud, Arthur H and Secrest, Don , title =. 1966 , publisher =

    1966

  255. [263]

    Statistical Methods & Applications , year =

    Subedi, Sanjeena and Punzo, Antonio and Ingrassia, Salvatore and McNicholas, Paul D , title =. Statistical Methods & Applications , year =

  256. [264]

    Psychometrika , year =

    Gibson, WILFRED A , title =. Psychometrika , year =

  257. [265]

    1950 , author =

    Measurement and prediction , publisher =. 1950 , author =

    1950

  258. [266]

    Psychometric monographs , year =

    Lord, Frederic , title =. Psychometric monographs , year =

  259. [267]

    1996 , author =

    Handbook of modern item response theory , publisher =. 1996 , author =

    1996

  260. [268]

    2008 , author =

    Longitudinal analysis of labor market data , publisher =. 2008 , author =

    2008

  261. [269]

    1997 , author =

    Applications of latent trait and latent class models in the social sciences , publisher =. 1997 , author =

    1997

  262. [270]

    Advances in Data Analysis and Classification , year =

    Hennig, Christian , title =. Advances in Data Analysis and Classification , year =

  263. [271]

    Browne, R. P. and McNicholas, P. D. and Sparling, M. D. , title =. IEEE Transactions on Pattern Analysis and Machine Intelligence , year =

  264. [272]

    Journal of Statistical Planning and Inference , year =

    Browne, Ryan P and McNicholas, Paul D , title =. Journal of Statistical Planning and Inference , year =

  265. [273]

    McNicholas and Sanjeena Subedi , title =

    Paul D. McNicholas and Sanjeena Subedi , title =. Journal of Statistical Planning and Inference , year =

  266. [274]

    Journal of the Royal Statistical Society

    Aitkin, Murray and Anderson, Dorothy and Hinde, John , title =. Journal of the Royal Statistical Society. Series A , year =

  267. [275]

    Statistics Surveys , year =

    Volodymyr Melnykov and Ranjan Maitra , title =. Statistics Surveys , year =

  268. [276]

    2011 , note =

    pgmm: Parsimonious Gaussian Mixture Models , author =. 2011 , note =

    2011

  269. [277]

    1996 , author =

    Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms , publisher =. 1996 , author =

    1996

  270. [278]

    2001 , author =

    Multi-Objective Optimization Using Evolutionary Algorithms , publisher =. 2001 , author =

    2001

  271. [279]

    Statistics and Computing , year =

    Christophe Biernacki , title =. Statistics and Computing , year =

  272. [280]

    Neural Networks , year =

    Naonori Ueda and Ryohei Nakano , title =. Neural Networks , year =

  273. [281]

    2004 , author =

    Evolutionary Computation for Modeling and Optimization , publisher =. 2004 , author =

    2004

  274. [282]

    , title =

    McNicholas, Paul D. , title =. Journal of the Iranian Statistical Society , year =

  275. [283]

    Martinez and Jordi Vitria , title =

    Aleix M. Martinez and Jordi Vitria , title =. Pattern Recognition Letters , year =

  276. [284]

    2011 , author =

    Latent variable models and factor analysis: A unified approach , publisher =. 2011 , author =

    2011

  277. [285]

    The American Journal of Psychology , year =

    Spearman, Charles , title =. The American Journal of Psychology , year =

  278. [286]

    2015 , note =

    MixGHD: Model Based Clustering, Classification and Discriminant Analysis Using the Mixture of Generalized Hyperbolic Distributions , author =. 2015 , note =

    2015

  279. [287]

    A. C. Aitken , title =. Proceedings of the Royal Society of Edinburgh , year =

  280. [288]

    Canadian Journal of Statistics , year =

    Ryan P Browne and Paul D McNicholas , title =. Canadian Journal of Statistics , year =

  281. [289]

    2016 , author =

    Mixture Model-Based Classification , publisher =. 2016 , author =

    2016

  282. [290]

    Journal of Classification , year =

    Irene Vrbik and Paul D McNicholas , title =. Journal of Classification , year =. doi:10.1007/s00357-015-9188-9 , publisher =

    doi

  283. [291]

    Computing in Science & Engineering , year =

    Oliphant, Travis E , title =. Computing in Science & Engineering , year =

  284. [292]

    Neurocomputing , year =

    Naldi, Murilo Coelho and Campello, Ricardo JGB , title =. Neurocomputing , year =

  285. [293]

    Applied Soft Computing , year =

    Niknam, Taher and Amiri, Babak , title =. Applied Soft Computing , year =

  286. [294]

    Open Computer Science , year =

    Karol, Stuti and Mangat, Veenu , title =. Open Computer Science , year =

  287. [295]

    Computational Science and Engineering (CSE), 2013 IEEE 16th International Conference on , year =

    Tran, Khoa Anh and Vo, Nhat Quang and Lee, Gueesang , title =. Computational Science and Engineering (CSE), 2013 IEEE 16th International Conference on , year =

    2013

  288. [296]

    Artificial Intelligence and Robotics (IRANOPEN), 2017 , year =

    Kebriaei, Emad and Bijari, Kayvan and Zare, Hadi , title =. Artificial Intelligence and Robotics (IRANOPEN), 2017 , year =

    2017

  289. [297]

    Applied Intelligence , year =

    Shin, Kyoung Seok and Jeong, Young-Seon and Jeong, Myong K , title =. Applied Intelligence , year =

  290. [298]

    A comparison of heuristic and model-based clustering methods for dietary pattern analysis , journal =

    Greve, Benjamin and Pigeot, Iris and Huybrechts, Inge and Pala, Valeria and B. A comparison of heuristic and model-based clustering methods for dietary pattern analysis , journal =. 2016 , volume =

    2016

  291. [299]

    Handbook of nature-inspired and innovative computing , publisher =

    Kennedy, James , title =. Handbook of nature-inspired and innovative computing , publisher =. 2006 , pages =

    2006

  292. [300]

    1999 , author =

    Swarm intelligence: from natural to artificial systems , publisher =. 1999 , author =

    1999

Pith tools

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