The Getting Started page (April 2023) illustrates what you should experience once FSDA is installed.


FSDA TOOLBOX (Release 2023a available from April, 2023).

FSDA TOOLBOX can be directly installed via Matlab Add-ons.

For Developers. FSDA TOOLBOX is now available in Github, where we host our current code release, old releases and docs. Please report issues and submit patches.

Highlights of the last releases

FSDA follows typical MATLAB timetable in the sense that there are two releases per year. The first typically in May/June and the second around October/November.

We decided to label FSDA release with the most recent MATLAB version to which it is associated.

April 2023 Release 2023a.


Now function LTSts also accepts missing values in the response

New option Varnames in aceplot.
New option showBars in avasms

New function avasmsplot which enables: to display the solutions found using function avasms (model selection using robust avas). Using option databrush it is possible to see after interactive brushing to see the details of each solution.

New options colorBackground and typespm in spmplot.


New output in pcaFS: orthogonal distance from the principal component subspace, and score distance. A new plot which shows the orthogonal distance vs the score distance is also autoamtically produced.

 New input in pcaFS: using options bsb or bdp it is possible to have a robust estimate of the covariance matrix. New sliders snd buttons in APP biplotAPP to show how the biplot changes varying breakdown point or subset size.


The new category "Probability distribution" has been created.
This section contains the FSDA routines for  correlation coefficient, inverse gamma, mixture of non central chi-square, Tweedie, Vervaat  and Wallenius distribution


The description of the datasets (clustering, multivariate or regression) has been added inside the table. Now when a dataset in table format is loaded with DataSetName.Properties.Description it is possibile to see the description of the dataset. For example after:
load geyser.mat
the instruction
enables to see the description.

New datasets BigTradeEvents (section clsutering) and clothes33 (section multivariate) and leafpine (section regression)


Function tabledisp in order to properly display a table or an array from the command line (for example with prespecified number of decimals)

Function crosstab2datamatrix now produces in output also a table.

json function signature definitions added to subfolder clustering which allow contextual help when calling FSDA functions

New option inferential in GUIregress.m which shows the detailed calculations to compute t-statistics and confidence intervals.

New option DiscreteData in GUImad.m

New function GUIautocorr which shows the calculations to obtain the autocorrelation.

November 2022 Release 2022b.


New datasets kidney, melody and wholesale, added to the section clustering datasets. Description added to datasets inside the table format


New functions Mlocation and Mlocsca added.

Mlocation performs M estimate of location in univariate samples. Mlocsca computes simultaneously estimate of location and scale. 

New function
medcouple added. It is used to compute a robust skewness estimator. 


New functions corrpdf and corrcdf to compute the pdf and cdf of the sample correlation coefficient


tclustreg returns in output the value of the objective function for each subset after the concentration steps.


forecastTS improved to cope with autoregressive component. Decomposition of forecasts into the different underlying components when input option plots is equal to 2


LTStsVarSel.m new option firstTestLS



New function GUIcorr added to show the calculations to compute the correlation coefficient


April 2022 Release 2022a.


New option PlotGroup in scatterboxplot.m

Improved mdpattern with syncronized axes.

New options plots.ColorMapLabelRows and plots.ColorMapLabelRows  in CorAnaplot in order to have a colorbar or row or column labels depending on a particular variable such as the corresponding mass or the communaility.



Added options rob, tyinitial, trapezoid, orderR2 and scail to avas.

New function avasms, to automatically choose the best AVAS model. Added a series of options to avasms. A new graphical display to show the importance of the different options is shown in the output.


New datasets fish and Marketing_Data added to regression datasets.


Updated and improved function CreateFSDAtoolboxFile which automatizes all steps needed to create programmatically a toolbox (mltbx) file and github release

New function setToolboxStartEnd, which can set release compatibility in ToolboxPackagingConfiguration.prj file.



Improved version of ctlcurves with ordered solutions based on LR test

New options  startv1true1unitCentroid and priorSol added to tclust



New options oneplot added to aceplot.m

November 2021 Release 2021b.


Likelihood ratio test inside ctlcurves.m and extended output which automatically detects a set of candidate solutions.


New function ctlcurvesplot.m to plot the output of the trimmed likelihood curves

New function moonplot to show the output of correspondence analysis

New function balloonplot to visualize large categorical data


New datasets oliveoil,  wine and flea added to cluster analysis section.

New datasets csdPerceptions and mobilephone added to the multivariate analysis section


New function mcdeda which monitors the output of mcd for a sequence of values of breakdown point

New option conflimMethodCramerV in  function corrNominal to compute the confidence interval of Cramer V coefficient.

New function mdpattern which finds and plots missing data patterns.


New options inside AVAS to make it robust to the presence of outliers

Sreg and MMreg with hyperbolic tangent estimator made faster.

New options inside LTSts and simulateTS that allow a customized definition of the autoregressive component



Added weights in repDupValWithMean.m

New function setdiffFS in case input arguments just contain positive integer values.

April 2021 Release 2021a.


New function pcaFS which enables to visualize both the percentage of variable explained by the different components, both the factor loadings and interactive dynmic biplot. New function biplotFS which enables to call the app biplotAPP which creates an interactive dynamic biplot.

Improvements in functions spmplot (now input can also be a table) and CorAna (now input can also be a table when optional option datamatrix is true)


A new suite of functions for robust correspondence analysis. Functions mcdCorAna, FSCorAnaeda, FSCorAnaenvmmd and mahalCorAna, extend functions mcdFSMeda, FSMenvmmd and mahalFS to the context of contingency tables. The plots produced by functions malindexplot and malfwdplot have been modified to incorporate the output of these new functions.


New function barVariableWidth which  produces a bar plot with different widths and colors for each bar

In functions mmdplot, mdrplot, mmdrsplot and mdrrsplot added the possibility of showing in output arguments the list of units brushed in each brushing operation

Option tag added to FSR, FSRmdr, FSM, FSMmmd, FSRts, FSRB, FSRr and FSRH

Option label added to malindexplot


newoption warmup in tclustICgpcm

new option commonslope in tclustreg and tclustregeda and tclustregIC


New dataset citiesItaly added to multivariate analysis section.


New options for VIOM and MSOM contamination inside function simulateLM


Added a series of routines for the estimation of integrated and instantaneous variance of a diffusion process via Fourier analysis [M.E. Mancino, M.C. Recchioni, S. Sanfelici, ``Fourier-Malliavin Volatility Estimation. Theory and Practice'', 2017, Springer - New York]

 FE_int_vol,  FE_int_vol_Fejer, FE_splot_vol, FE_spot_vol_FFT,  CEVmodel, OptimalCuttingFrequency


A new set of functions which enable to monitor  all the necessary steps to be done to obtain the main indexes of descriptve statistics. More in detail:

GUIconcentration, GUImad.html, GUIpowermean.html, GUIquantile.html, GUIskewness.html, GUIstd.html, GUItrimmean.html, GUIvar.html, GUIcov.html

October 2020 Release 2020b.


We have enriched the properties of the data transformations of the Yeo and Johnson (2000) for negative and positive responses, which we introduced in R2020a. More specifically, we intervened on the smoothness condition that the second derivative of zYJ(lambda) with respect to y be smooth at y = 0, along Atkinson et al (2019) and (2020), to allow two values of the transformations parameter: lambdaN for negative observations and lambdaP for non-negative ones. Now, function ScoreYJall computes:

1) a global t test associated with the constructed variable for lambda=lambdaP=lambdaN.

2) a t test for positive observations.

3) a t test for negative observations.

4) a F test for the joint presence of the two constructed variables described in points 2) and 3.

5) the F test based on the maximum liklihood estimate of lambdaP and lambdaN

New function ScoreYJall which computes the score tests described in points 1)-5) above.

New function scoreYJmle  which computes, in the case of extended Yeo and Johnson transformation, the likelihood ratio test of H0: lamabdaP=lamabdaP0 and lamabdaN=lambdaNeg0.

Added option usefmin in funtion  boxcoxR. This option uses the solver (fminsearch or fminunc) to find MLE of the two transformation parameters for extended Yeo and Johnson family (Atkinson et al. 2020).

New function fanBIC which takes in input the output of FSRfan and using BIC and smoothness index enables to automatically choose in an effcieint and robust way, the best value of the transformation parameter.

New function fanBICpn which enables to automatically choose the best values of the transformation parameters for positive and negative observations

New function normYJpn which extends the companion functions normBoxCox and normYJ to the case of extended Yeo and Johnson transformation.


New function SETARX which implements Threshold autoregressive models with two regimes


New tools for dealing with the 14 Gaussian parsimonious clustering models (GPCM).

In function genSigmaGPCM new option pa.exactrestriction has been added. If pa.exactrestriction is true the covariance matrices are  generated with the exact values of the restrictions specified in pa.cdet, pa.shw and pa.swb. In function MixSim optional input structure sph now can be called with field  sph.exactrestriction

In function tclust the fourth input restrfactor can be a structure which can contain the type of Gaussian Parsimonious Clustering Model - GPCM (, the
scalars in the interval [1 Inf) which specifies the
the restriction which have to be applied to the determinants (restrfactor.cdet), to the to the elements of the shape matrices inside each group (restrfactor.shw) and across groups (restrfactor.shb).

New functions tclustICgpcm, tclustICsolGPCM, tclustICplotGPCM, and  carbikeplotGPCM which extend functions tclustIC, tclustICsol, tclustICplot and carbikeplot to the case of the 14 GPCM.


New plots waterfallchart (which implements the waterfall chart (see and new function funnelchart which implements the funnel chart (see

new function scatterboxplot (which creates scatter diagram with marginal boxplots).

Improvment to functions

Now spmplot accepts as input a table. In the case the names of the tables are automatically added at the marings. Similarly, in function corrNominal when option datamatrix is true it is possible to supply as first argument a table.



New datasets balancesheets and facemasks added in the datasets regression section and datasets clustering section respectively

April 2020 Release 2020a.


New set of routines for minimum density power divergence estimators (mdpd, mdpdR, mdpdReda, PDrho, PDpsi, PDwei, PDpsider, PDpsix, PDbdp, PDeff, PDc), discussed in

New function simulateLM to simulate linear regression data with prespecified value of R2, prespecified correlation among the explanatory variables and type of distribution.

New function VIOM which computes weights estimates under a Variance-Inflation Outlier Model using MLE or Restricted MLE (REMLE).


New function tclustregeda which enables to monitor the regression clustering classification for different levels of trimming.

Improved function tclustregIC which enables to compute the BIC (and other information criteria) for different values of restriction factors and different number of groups, for classification or mixture likelihood and regression clustering.

Modified function tclustICsol now accepts input from tclustregIC to show the yXplot of the best solutions.

New function ctlcurves to select the appropriate number of groups in robust clustering.

New function mdrrsplot which plots the random starts trajectories and enables to brush them. The companion function mmdrsplot referred to multivariate analysis has been improved.


New function boxcoxR which computes the profile log Likelihood for a range of values of the transforamtion parameter (lambda) and computes the MLE of lambda in the supplied range. Supported families Box Cox, Yeo and Johnson and extended Yeo and Johnson (Atkinson et al. 2020).


Improved menu for the automatic installation of the FSDA html help files.


New function exactcdf for finding the exact cdf of each element in a vector x with respect to the empirical distribution, represented by another vector.

New functions twdpdf and twdrnd to compute the pdf of the Tweedie distribution and generate random numbers from it.

October 2019 Release 2019b.

This is the first release which is distributed from Mathworks marketplace and from github platform.


New function tBothSides which enables to transform both sides of a (nonlinear) regression model. New function boxcoxR which finds MLE of lambda in linear regression (and confidence interval) using Box Cox or Yeo and Johnson family.

New function boxcoxR which finds MLE of lambda in linear regression (and confidence interval) using Box Cox or Yeo and Johnson family.


New functions LTStsVarSel which enables to perform variable selection in the robust time series model LTSts. In functions LTSts.m, simulateTS and forecastTS it is now possible to add an autoreressive component.


New function existFS which checks whether a file exists and puts the answer in a cached persistent variable


Added file getting_started.mlx in subfolder doc of the main root of FSDA for packaging the FSDA toolbox.

May 2019 Release 2019a.


Function tclustreg has been considerably enhanced. Now the function includes: (i) robust BIC, (ii) possibility of constraining the determinants of the covariance matrices of the explanatory variables, (iii) options for treating datasets with concentrated noise, making use of concentration steps appropriately modified using observation weighting and thinning methods.

New function tclustregIC which (if present) uses the Parallel Computing toolbox to compute robust BIC  for mixture and classification likeilhood for different values of k (number of groups) and different values of c (restriction factor for the variances of the residuals), for a prespecified level of trimming.

New function  for constraining the determinants  restrdeter. This function has its own interest but is called in every  concentration step of function tclust in case determinant restriction is needed.

Routines for constraining the determinants (restrdeterGPCM), the shape matrices (restrshapeGPCM) and to impose common rotation matrices (common principal components) in presense of equal shape (cpcE.m) or varying shape (cpcV.m) and a general routine to impose constraints in the family of the 14 Gaussian Parsimonious Clustering Models (restrSigmaGPCM).

Routine to generate data based on the 14 Gaussian Parsimonious Clustering Models (genSigmaGPCM). This routine can be called directly from function MixSim in order to generate each of the 14 Gaussian Parsimonious Clustering Models with a prespecified level of overlap (see option sph inside MixSim).

Routine GowerIndex to compute matrix of similarity indexes using Gower metric.


New datasets added to the collection:

animals, P12119085, P17049075, fondi_large, JohnDraper data, gasoline data, ms212. See pages datasets_reg and datasets_mult for a description of these datasets.


Possibility of brushing using rownames. Rownames also appear in the associated scatter plot matrix, both for regression and multivariate analysis: se new examples in resfwdplot and malfwdplot.

New function aceplot to visualize the results of the output produced by functions ace and avas.

Option RowNamesLabels has been added to add2spm and to add2yX to label the units.


Funciton FSMeda is now much faster; the original function FSMeda has been kept, renamed FSMedaeasy, because the algorithm is much easier to follow.


New functions: (i) ace which implements the alternating conditional expectations algorithm to find the transformations of y and X that maximise the proportion of variation in y explained by X and (ii) avas which uses a (nonparametric) variance-stabilizing transformation for the response variable.

New function smothr to smooth values imposing variour constraints (e.g. monotonicity, circularity,..). This function calls the supersmoother routine of Friedman.

New function rlssmo to compute a running line smoother with global cross validation.

New function supsmu to smooth scatterplots using Friedman's supersmoother algorithm.

Function RobCov now includes the estimator covrobc (a corrected version of the covariance matrix of  robust beta coefficients). A new motivating example  shows a case why covrobc should be always used.


New function repDupValWithMean that enable to replace values of y including non unique elements in vector x with local means.


Function publishFS is fourthly improved. This function automatically transforms structuerd .m files into MATLAB pure style files. In the HTML help files now the right click of the mouse (similarly to pure Mathworks pages) enables to execute, select or find help (F1 key) for all the versions of MATLAB starting from 2017a.



New function genr8 to generate random numbers which are coherent across different software platforms.

New function exactcdf to find exact cdf values of each element of an input vector x with respect to an empirical distribution.

New function wthin which thins a uni/bi-dimensional dataset.

New function ctsub which computes numerical integrarion from x(1) to z(i) of y=f(x)

New functions (i) vervaatsim (to simulate precisely from a Vervaat perpetuity
distribution)  (ii) vervaarxdf (to obtain the pdf or the cdf of a Vervaat perpetuity distribution) and (iii) vervaatrnd (to simulate random variates from the Vervaat perpetuity distribution).



September 2018 Release 2018b

(1) New function qqplotFS that enables to create a qqplot of residuals with confidence bands

(2) New function  mtR which generates the same random numbers produced by R software with Mersenne Twister mt19937ar

(3) New functions associated with Rocke biweght estimator. See for example RKrho, RKpsi, RKpsider, RKwei, RKbdp, RKeff.

(4) Routines FSR, FSRmdr, FSRbsb extended to time series (see new functions FSRts, FSRtsmdr, FSRtsbsb and regressts)

(5) New function verlessthanFS.  It is a faster version of MATLAB function verlessthan.

(6) New datasets added to the collection.

(7) New routine publishBibliography to create in a automatic way the bibliography from the citations present inside the .m files.

June 2018 Release 2018a

(1) New function tclusteda that helps choosing the best tclust model. It computes tclustfor different values of the trimming factor and produces plots that allow to find the optimal level of trimming. This function uses the parallel processing toolbox, if available. 

(2) Extension of the score test. New function ScoreYJpn  that computes the score test for Yeo Johnson transformation separately for positive and negative observations. FSRfan now accepts the new option family "YJpn" and it is possible to monitor the score test for both positive and negative observations (output arguments out.Scorep and out.Scoren).

(4) New functions for time series analysis. simulateTS simulates a time series with trend (up to third order), seasonality (constant or of varying amplitude) with a different number of  harmonics and a level shift. forecastTS produces forecasts with confidence bands for a time series estimated with function LTSts.   

(4) CorAna has an improved display of results. New function CorAnaplot draws a rich Correspondence Analysis graph with different types of confidence ellipses for selected rows and columns.

(5) New function verlessthanExt.  It is a faster version of MATLAB function verlessthan.

(6) Documentation of yXplot considerably improved. New options added (xlimx, ylimy, namey, nameX).

(7) MixSimreg extended to account for multiple parameter distribution (betadistrib option) 

(8) histFS has a new optional argument (weights) for plotting a weighted histogram.

(9) options labenv has been added to mmdrsplot.

(10) option axesellipse added to ellipse

(11) New output argument OldAndNewIndexes used in function UnitsSameCluster, to track the indexes permutations used to rearch a desired cluster labelling.


November 2017 Release 2017b.

Major statistical release. Highlights:

FSDA has introduced two new categories of tools, one for (robust) time series analysis; another for analyzing categorical data and contingency tables. More precisely:

(1) Function LTSts  extends LTS estimator to time series. A related new graphical plot associated to a time series, wedgeplot, provides information on the presence of outliers and level shifts.

(2) CorAna performs correspondence analysis; SparseTableTest computes independence test for large and sparse contingency tables; CressieRead computes the power divergence family of tests, to check the discrepancy/distance between observed and expected frequencies in a contingency table; rcontFS generates a random two-way table with given marginal totals; barnardtest computes the Barnard test,  corrNominal measures strength of association between two unordered (nominal) categorical variables. Similarly for ordinal data with corrOrdinal. crosstab2datamatrix recreates the original data matrix X from contingency table N. This group of functions is complemented by file examples_categorical.m as in style of FSDA.

The two categories of functions will be progressively enriched.

Other new functions which are included are boxtest (test of equality of covariance matrices used for example in tkmeans), GYfilt (Gervini and Yohai, univariate outlier identifier), mmdrsplot (interactive plot of the trajectories of minimum Mahalanobis distances from different starting points), overlapmap to plot the ordered pairwise overlap values between components, dempk to perform a merging of components found by tkmeans, ncpci to compute a non centrality parameter confidence interval. 

Finally, spmplot has been enriched to superimpose ellipses, density and contour functions to data and extract single panels from the scatter matrix.

May 2017 Release 2017a.

Major statistical release. Highlights:
    Function tclustreg now includes trimmed Cluster Weighted Restricted Models.
    New function tclustIC for the automatic selection of the best number of groups.
    New function tlclustICsol to extract a set of relevant solutions (and associated tclustICplot).
    New function UnitsSameCluster to to control the labels of the clusters which contain predefined units.
    New function to compare two partitions (Fowlkes and Mallows index)
    Updated routine simdatasetreg to generate new outlier patterns


    New routines for density estimation and thinning, for univariate and bivariate data (used in tclustreg).
    bwe, rthin, wthin, WNChygepdf.

    New functions wraptextFS, removeextraspacesLF

    New functions mveeda, MMmulteda
    Smulteda, Sregeda

     New function ScoreYJ which implements the score test for the Yeo and Johnson transformation. This new transformation has also been embedded inside function FSRfan.

    updated functions randsampleFS and subsets.
    New routines for thinning.

  • NEW mlx files
    .mlx files introduced for examples_MixSim

    New function to create the car-bike plot to find the most relevant solutions (carbikeplot).
    Functions resfwdplot, malfwdplot generalized in order to take as input the output of procedures which monitor robust estimators.

  • The FSDA help folder now contains XML files associated to the functions documentation. This is in view of generating/updating automatically or using a GUI the functions documentation, in html as well as in the function head


October 2016 Release 2016b.

Major statistical release. Highlights:
  • New functions for  bivariate density estimation and random thinning (kdebiv.m, rthin.m) used to extend tclustreg.m features.
  • The FSDA help folder now contains XML files associated to the functions documentation. This is in view of generating/updating automatically or using a GUI the functions documentation, in html as well as in the function head


June 2016 Release 2016a.

Major statistical release. Highlights:
  • New features added to the tclust function, including determinant restriction and new adjusted BIC criterion for the estimation of the number of groups.
  • Added functions for reweighting FSR and FSRB (FSRr and FSRBr).
  • Functions FSR, FSRB and FSRH redesigned; a routing implementing the core of the Forward Search algorithm (FSRcore) introduced to avoid code redundancies.
  • New function, winsor, to winsor data.
  • New function FSMbsb, which will replace FSMbbm.
  • New function randindexFS, to evaluate the quality of different clusterings.
  • New routines poolClose and poolPrepare introduced to conveniently open and close a pool of parallel workers.
  • Several new robust functions to generate, for example, the Tukey Biweigh rho function (HUrho), the tuning constant associated to a certain efficiency (HUeff), the psi functions (HUpsi), its derivative (HUpsider), etc. For a full list, see functions under utilities_stats folder.

Major highlights in the documentations and examples:

  • New function, publishFS, introduced to generate documentation pages directly from the .m files.
  • New function, makecontentsfileFS, introduced to create a the list of files present in a FSDA folder and/or subfolders. It extends MATLAB function makecontentsfile.
  • .mlx files introduced for examples_multivariate and examples_regression

September 2015 Release 2015b.

  • Function simdataset.m modified to allow the user to simulate outliers from different distributions and contamination schemes and/or contaminate existing datasets.
  • New Bayesian regression analysis routines: FSRB.m, FSRBeda.m, FSRBmdr.m, regressB.m.
  • In FSReda.m: monitoring of confidence intervals of beta and sigma2.
  • In FSRBeda.m: monitoring of HPD (highest posterior density regions) of beta and sigma2.
  • New functions for inverse gamma computation: inversegampdf.m, inversegamcdf.m, inversegaminv.m.
  • Added functions to monitor units forming subset in heterosckedastic and Bayesian regression: FSRHbsb.m, FSRBbsb.m.
  • Added new datasets for Bayesian examples.
  • Added option for the robust transformation in the Yeo-Johnson family.
  • addFSDA2path.m: modified for compatibility with unix platforms and to address changes in the folder organization of FSDA functions.
  • Added routines to compute and visualize robust bivariate boxplot (function boxplotb.m).
  • New routine for automatic outlier detection in heteroskedastic regression (FSRH.m).

Please, do not hesitate to contact us for any bug you might find and for any suggestion you might have!!! Thanks to all those who have already contacted us and have helped us to correct several bugs and improve the performance of the code.

Marco Riani, Andrea Cerioli and Aldo Corbellini (University of Parma)

Domenico Perrotta and Francesca Torti (EC, Joint Research Centre)

Patrizia Calcaterra, Andrea Cerasa, Emmanuele Sordini, Daniele Palermo (EC, Joint Research Centre)