Developmentof a classification algorithm for efficient handling of multiple classes in sorting systems based on hyperspectral imaging

Correspondence

Rosalba Calvini ([email protected])

Received: 8 November 2018 Revised: 10 December 2018 Accepted: 10 December 2018 Publication: 18 December 2018 doi: 10.1255/jsi.2018.a13 ISSN: 2040-4565 Citation

R. Calvini, G. Orlandi, G. Foca and A. Ulrici, “Development of a

­classification­algorithm­for­efficient­handling­of­multiple­classes­in­­sorting­ systems­based­on­hyperspectral­imaging”,­J. Spectral Imaging7, a13 (2018). https://doi.org/10.1255/jsi.2018.a13 ©­2018­The­Authors This­licence­permits­you­to­use,­share,­copy­and­redistribute­the­paper­in­ any­medium­or­any­format­provided­that­a­full­citation­to­the­original­ ­paper­in­this­journal­is­given,­the­use­is­not­for­commercial­purposes­and­ the­paper­is­not­changed­in­any­way. In thIs Issue:

spectral preprocessing to compensate for packaging film / using neural nets to invert the PROSAIL canopy model

JOURNAL OF

SPECTRAL

IMAGING

Peer Reviewed Paper Highlighting Young Investigators openaccess

Development­of­a­classification­algorithm­for­

efficient­handling­of­multiple­classes­in­sorting­

systems­based­on­hyperspectral­imaging

Rosalba Calvini,a,_{* Giorgia Orlandi,}b _{Giorgia Foca}c _{and Alessandro Ulrici}d

Department­of­Life­Sciences,­University­of­Modena­and­Reggio­Emilia,­Padiglione­Besta,­Via­Amendola,­2,­42122­Reggio­Emilia,­Italy.­ E-mail:­[email protected]

a _{:­https://orcid.org/0000-0002-0100-8798,} b _{:­https://orcid.org/0000-0002-9116-4566} c _{:­https://orcid.org/0000-0002-4436-774X,} d _{:­https://orcid.org/0000-0002-6010-6400}

When dealing with practical applications of hyperspectral imaging, the development of efficient, fast and flexible classification algorithms is of the utmost importance. Indeed, the optimal classification method should be able, in a reasonable time, to maximise the separation between the classes of interest and, at the same time, to correctly reject possible outlier samples. To this aim, a new extension of Partial Least Squares Discriminant Analysis (PLS-DA), namely Soft PLS-DA, has been implemented. The basic engine of Soft PLS-DA is the same as PLS-DA, but class assignment is subjected to some additional criteria which allow samples not belonging to the target classes to be identified and rejected. The proposed approach was tested on a real case study of plastic waste sorting based on near infrared hyperspectral imaging. Household plastic waste objects made of the six recyclable plastic polymers commonly used for packaging were collected and imaged using a hyperspectral camera mounted on an indus-trial sorting system. In addition, paper and not recyclable plastics were also considered as potential foreign materials that are commonly found in plastic waste. For classification purposes, the Soft PLS-DA algorithm was integrated into a hierarchical classification tree for the discrimination of the different plastic polymers. Furthermore, Soft PLS-DA was also coupled with sparse-based variable selection to identify the relevant variables involved in the classification and to speed up the sorting process. The tree-structured classification model was successfully validated both on a test set of representative spectra of each material for a quantitative evaluation, and at the pixel level on a set of hyperspectral images for a qualitative assessment.

Keywords: PLS-DA, multivariate classification, hierarchical classification, sparse methods, feature selection, plastic sorting

Introduction

Over­the­past­decades,­Hyperspectral­Imaging­(HSI)­has­ gained­increasing­attention­from­industries­interested­ in­the­implementation­of­automated­sorting­systems­to­ solve­a­number­of­different­problems.­Indeed,­HSI­has­ found­a­wide­range­of­applications­in­the­food­industry,­ including­the­quality­evaluation­and­safety­assessment­

of several food products,1_{­such­as­fruits­and­vegeta}

-bles,2,3 _meat,4 _cereals5 _{and dairy products.}6 _Moreover,

other­manufacturing­environments,­such­as­the­pharma

-ceutical­industry,­have­employed­real-time­HSI­systems­ for­quality­control­and­process­monitoring­in­the­frame­ of­the­process­analytical­technology.7–9_{­Another­relevant­}

field­of­application­of­HSI­is­represented­by­the­recy -cling­industry,­where­hyperspectral­sensors­are­used­to­ separate­end-of-life­objects,­such­as­plastic,10 _paper11 _or electronic­waste,12_{­according­to­material­type.} In­these­contexts,­HSI­can­be­considered­as­a­step­ forward­with­respect­to­traditional­spectroscopic­tech -niques,­which­allow­fast­and­non-destructive­charac -terisation­of­the­chemical­properties­of­the­analysed­ samples.­In­fact,­HSI­systems­couple­these­advantages­ with­the­possibility­of­also­visualising­the­spatial­distri -bution­of­the­chemical­features­of­interest­within­the­ sample­surface.­Furthermore,­in­sorting­systems,­HSI­can­ also­be­employed­to­quickly­identify­the­chemical­compo -sition­of­homogeneous­objects­moving­on­a­conveyor­ belt,­and­to­distinguish­them­from­samples­with­different­ composition.13 In­practical­situations,­hyperspectral­imaging­can­be­ applied­to­address­complex­classification­issues,­where­ the­sorting­problem­under­investigation­requires­the­ discrimination­of­several­classes­at­the­same­time,­with­ some­classes­sharing­similar­features.­This­can­be­easily­ managed­ by­ using­ HSI­ systems,­ since­ with­ a­ single­ measurement,­i.e.­with­the­acquisition­of­a­single­hyper -spectral­image,­it­is­possible­to­have­a­wide­range­of­ information.­However,­in­order­to­meet­the­needs­of­real-time­applications,­it­is­necessary­to­identify­classification­ strategies­able­to­handle­a­huge­amount­of­spectral­data,­ providing­reliable­results­in­short­computational­times.14 When­dealing­with­multiple­classes,­this­issue­can­be­ addressed­using­a­tree-structured­classification­model,­ where­each­branching­(tree­node)­corresponds­to­a­local­ classification­model. In­this­manner,­classification­is­performed­considering­ a­top-down­approach,­where­the­samples­are­initially­ assigned­to­general­macro-categories,­and­then­each­ macro-class­is­split­into­increasingly­specific­categories,­ until­reaching­the­classes­of­interest.15–17 Another­relevant­issue­to­be­faced­in­practical­applica -tions­of­HSI­in­sorting­systems­is­related­to­the­fact­that,­ generally,­it­is­not­easy­to­have­a­strict­control­of­the­ input­stream­in­order­to­avoid­the­presence­of­foreign­ objects,­i.e.­objects­not­belonging­to­the­target­classes­of­ the­specific­application.­In­this­context,­the­availability­of­ algorithms­able­to­maximise­the­discrimination­between­ the­categories­of­interest­and,­at­the­same­time,­to­iden -tify­possible­foreign­materials­is­of­the­utmost­importance. Partial­Least­Squares­Discriminant­Analysis­(PLS-DA)­ is­one­of­the­most­widely­used­methods­for­multivariate­ classification­of­hyperspectral­data.18_{­Basically,­PLS-DA­} is­an­extension­of­the­PLS­algorithm,­which­aims­at­iden -tifying­a­new­set­of­variables,­named­Latent­Variables­ (LVs),­by­maximising­the­between-classes­variance.­Class­

membership­ is­ coded­ using­ a­ dummy­Y­ matrix,­ and­

the­assignment­of­unknown­samples­is­based­on­the­

a posteriori­probability­associated­with­the­corresponding­

Y­ predicted­ values.­The­ standard­ PLS-DA­ approach­

assigns­a­sample­to­the­class­for­which­it­has­the­higher­ a posteriori­probability,­resulting­in­unknown­samples­ always­being­assigned­to­one­of­the­target­classes.19,20 Therefore,­on­the­one­hand­PLS-DA­has­the­great­advan -tage­of­maximising­the­separation­between­the­consid -ered­classes­but,­on­the­other­hand,­it­does­not­allow­a­ straightforward­identification­of­outliers.

Conversely,­ the­ possibility­ of­ having­ unassigned­ samples­is­one­of­the­major­advantages­of­the­so-called­ class-modelling­techniques,­which­are­essentially­based­ on­describing­each­single­class­independently­from­the­ others,­and­then­verifying­whether­an­unknown­sample­ is­compliant­or­not­with­the­characteristics­of­each­class­ of interest.21_{­In­this­manner,­it­is­possible­that­a­new­} unknown­sample­is­rejected­from­all­the­class­models,­ resulting­in­an­unassigned­sample.­Soft­Independent­ Modelling­of­Class­Analogy­(SIMCA)­is­the­most­common­ class-modelling­ method.­ It­ calculates­ local­ Principal­ Component­Analysis­(PCA)­models­for­each­considered­ class,­which­are­used­to­define­class­boundaries­based­ on­the­distances­both­in­the­score­space­(Hotelling’s­T2₎ and­in­the­residual­space­(Q­residuals).22_{­Notwithstanding­} the­advantages­of­class-modelling­methods­like­SIMCA,­ they­can­provide­poor­classification­results­when­the­ modelled­classes­are­quite­overlapped,­since­the­model­ is­not­oriented­towards­the­discrimination­of­the­consid -ered­categories. Given­these­considerations,­it­is­reasonable­to­assume­ that­a­classification­algorithm­to­be­efficiently­employed­ in­sorting­systems­should­comprise­the­advantages­of­ both­classification­techniques­and­of­class-modelling­ methods,­i.e.­it­should­be­able­to­maximise­the­discrimi -nation­between­the­categories­of­interest­and­to­recog -nise­and­reject­outlier­samples­at­the­same­time. To­this­aim,­in­the­present­paper­a­modified­version­of­ the­PLS-DA­algorithm,­namely­Soft­PLS-DA,­is­proposed.­ The­basic­principle­of­Soft­PLS-DA­is­the­same­as­PLS-DA,­ but­class­assignment­is­performed­by­fixing­additional­ limits­ both­ on­ the­Y­ predicted­values­ and­ on­ the­ Q­ residuals.­In­this­manner,­the­classification­model­is­built­

by­maximising­the­differences­between­the­modelled­ classes;­at­the­same­time,­the­additional­limits­allow­the­ rejection­of­samples­belonging­to­unexpected­categories­ and­relegation­of­them­to­a­general­category­of­unas -signed­samples. The­effectiveness­of­Soft­PLS-DA­algorithm­was­tested­ on­a­case­study­related­to­the­implementation­of­a­near­ infrared­(NIR)­hyperspectral­imaging­system­for­plastic­ waste­sorting.­Indeed,­the­different­plastic­polymers­have­ a­specific­spectral­fingerprint­in­the­NIR­range­and­optical­ sorting­is­commonly­used­to­separate­them.23,24_{­The­goal­} of­our­study­consisted­in­the­implementation­of­a­clas -sification­method­able­to­effectively­discriminate­paper­ and­six­recyclable­plastic­polymers­commonly­used­for­ packaging,­and­to­correctly­reject­objects­belonging­to­ non-target­classes,­such­as­non-recyclable­plastics. The­present­manuscript­is­structured­as­follows: ■The­next­section­reports­the­theoretical­background­of­ the­standard­classification­approach­based­on­PLS-DA­ and­a­detailed­description­of­the­novel­Soft­PLS-DA­ algorithm. ■Material­and­methods­describes­the­plastic­dataset,­

the­ procedure­ followed­ for­ image­ acquisition­ and­ elaboration­together­with­the­different­steps­of­data­ analysis.

■Results­ shows­ the­ classification­ results­ obtained­

using­Soft­PLS-DA­algorithm­both­considering­the­full­ wavelength­range­and­sparse-based­variable­selection,­ and­also­the­results­of­the­final­implementation­of­the­ classification­tree. ■Finally,­we­report­the­general­conclusions­of­this­study.

Theory

Background

PLS-DA­is­as­an­extension­of­PLS­regression­adapted­to­ operate­in­a­classification­framework.­Similarly­to­PLS,­the­ independent­matrix­X­is­regressed­against­the­dependent­ matrix­Y­by­calculating­a­new­set­of­LVs,­which­maximise­ the­covariance­between­X and Y matrices.25,26_­In­more­

detail,­both­X and Y matrices can be decomposed as

follows:

X = TPT_{+ E (1)}

where­T, P and E­represent­the­score­matrix,­the­loading­ matrix­and­the­residuals­matrix­of­X,­respectively;

Y = UCT_{+ G (2)}

where­U­is­the­score­matrix,­C­is­the­loading­matrix­and­G

is­the­residuals­matrix­referred­to­Y.

According­to­PLS,­the­object­variation­of­the­X-block­ expressed­by­the­score­matrix­T can be used to describe

Y;­therefore­Equation­2­can­be­re-written­as­follows: Y = TCT_{+ G (3)} In­particular,­the­decomposition­of­X­has­to­be­opti -mised­in­a­manner­that­T­accounts­for­the­variation­in­X which­allows­the­best­description­of­Y.­To­this­aim,­for­ each­LV­a­weight­vector­(w)­is­calculated­which­weights­ the­original­variables­according­to­their­contribution­in­ explaining­the­Y­matrix.­Given­these­considerations,­the­ estimate­of­Y (Ŷ)­can­be­calculated­as­follows: Ŷ = XWCT_{+ F = XB + F (4)}

where­W­is­the­weights­matrix­and­B­is­the­matrix­of­

regression­coefficients. In­the­case­of­PLS-DA,­the­Y­matrix­consists­of­a­dummy­ matrix­with­as­many­rows­as­the­number­of­samples­and­ as­many­columns­as­the­number­of­considered­classes.­ This­dummy­matrix­expresses­class­membership­of­each­ sample­with­binary­coding:­a­value­equal­to­1­indicates­ that­an­object­belongs­to­the­class,­while­a­value­equal­to­ 0­refers­to­samples­not­belonging­to­the­class.19,27 Once­the­PLS­model­has­been­calibrated,­class­assign

-ment­ of­ unknown­ samples­ is­ based­ on­ the­y values

estimated­for­each­class­(ŷ).­These­values­will­not­be­ exactly­equal­to­0­or­1,­therefore­it­is­necessary­to­estab -lish­a­threshold­value­so­that­a­new­sample­is­assigned­ to­a­defined­class­only­if­its­ŷ­value­is­greater­than­the­ threshold­for­that­class.­The­threshold­is­usually­calcu -lated­using­the­Bayes­theorem­under­the­assumption­ that­the­estimated­values­for­each­class­follow­a­Gaussian­ distribution,­and­these­distributions­are­used­to­calculate­ the­a posteriori­probability­that­a­sample­belongs­to­a­ given­class.20_{­In­particular,­for­each­class­the­threshold­}

value­corresponds­to­the­ŷ­value­at­which­the­number­of­ false­positives­and­false­negatives­is­minimised,­that­is­ the­point­where­the­two­probability­distributions­cross­ (i.e.­the­point­where­the­a posteriori probability values for the­two­classes­are­the­same).

Usually,­class­assignment­of­an­unknown­sample­can­ be­done­considering­two­different­approaches:­either­ choosing­ the­ class­ with­ the­ highest­ probability,­ or­ comparing­the­predicted­ŷ­values­with­the­corresponding­ threshold­values.­The­former­strategy­represents­the­stan -dard­discriminant­approach,­where­samples­are­always­

assigned­to­one­of­the­modelled­classes.­Conversely,­if­ the­latter­approach­is­used,­a­sample­can­have­ŷ values higher­than­the­corresponding­threshold­for­more­than­ one­class,­or­lower­than­the­threshold­for­all­the­classes.­ In­both­these­cases,­the­sample­cannot­be­assigned­to­ any class.27_{­However,­in­the­case­of­only­two­classes,­}

these­two­approaches­converge­to­the­same­results­and­ standard­PLS-DA­algorithm­will­always­attribute­a­sample­ to­one­of­the­classes. The­standard­discriminant­approach­has­often­been­ criticised­due­to­its­limited­ability­to­correctly­handle­new­ objects­not­belonging­to­the­target­classes.28_{­In­order­to­} overcome­this­issue,­extensions­of­PLS-DA­have­been­ proposed­in­the­literature,­which­incorporate­a­rejection­ option­in­the­classification­rule. These­methods­usually­consist­in­considering­PLS-DA­ as­a­data­compression­method­rather­than­a­classification­ strategy,­and­class­assignment­is­performed­with­a­further­ class-modelling­step­considering­distance-based­metrics­ calculated­on­the­PLS­scores16_{­or­on­the­PCA­scores­}

obtained­from­the­decomposition­of­the­Ŷ­matrix.29_­In­

this­manner,­class­assignment­is­performed­in­a­rather­ complex­multi-step­procedure. Conversely,­an­alternative­approach­consists­in­calcu -lating­a­classification­rule­considering­confidence­inter -vals­around­the­ŷ­values­of­each­class,­and­rejecting­ samples­outside­these­intervals.30 Furthermore,­it­has­to­be­considered­that­diagnostics­ based­on­Q­residuals­can­represent­an­effective­tool­ to­ identify­ outlier­ samples,­ i.e.­ samples­with­ proper -ties­different­from­those­of­the­samples­used­for­model­ calibration.­These­diagnostics­are­widely­used­in­class-modelling,­for­example­in­the­SIMCA­algorithm.­However,­ Q­residuals­are­rarely­incorporated­in­classification­rules­ based­on­PLS-DA­algorithm,­even­if­the­computation­of­ Q­scores­from­the­outcomes­of­the­PLS­model­is­straight -forward­according­to­the­following­equation: T i i i Q=e e (5)

where­Qi­is­the­Q­score­value­of­the­ith­sample­of­matrix­X and ei­is­the­ith­row­vector­of­the­residuals­matrix­E.

Soft PLS-DA

In­the­present­study,­a­novel­algorithm­based­on­PLS-DA­ has­been­developed­in­order­to­combine­the­advantages­ of­classical­discriminant­analysis­with­those­of­class-modelling­techniques;­ for­these­reasons­it­has­been­ named­Soft­PLS-DA.­The­main­idea­behind­Soft­PLS-DA­ is­to­have­a­flexible­and­simple­classification­tool­able­to­ maximise­the­separation­between­the­considered­classes­ and,­at­the­same­time,­to­effectively­identity­possible­ outlier­objects­(i.e.­objects­that­do­not­belong­to­the­ classes­included­in­the­classification­model),­which­will­be­ automatically­not­assigned­to­any­class. In­the­same­manner­as­PLS-DA,­a­PLS­model­is­calcu

-lated­between­the­X­matrix­and­the­dummy­Y­matrix,­in­

order­to­maximise­the­differences­between­the­consid -ered­classes.­Then,­class­assignment­of­unknown­samples­ is­based­on­some­additional­criteria­which­allow­outlier­ samples­to­not­be­assigned­to­the­target­classes. According­to­the­Soft­PLS-DA­decision­rules,­class­ assignment­of­a­new­sample­to­a­defined­class­is­subjected­ to­the­following­criteria: ■having­Q­residuals­falling­inside­the­99.9 %­confidence­ limit­of­the­model.31_{­The­99.9 %­confidence­limit­has­} been­chosen­in­order­to­set­boundaries­large­enough­ to­consider­as­much­as­possible­the­variability­of­the­ different­classes­and,­at­the­same­time,­being­able­to­ exclude­samples­with­a­very­low­fit­to­the­model; ■having­ŷ­values­falling­inside­an­acceptability­range­ for­the­considered­class.­More­in­detail,­in­addition­to­ the­threshold­value­calculated­by­standard­PLS-DA­for­ each­class­g (ytsh1,g), also an upper limit (ytsh2,g)­on­the­

ŷ­values­has­been­introduced,­which­is­calculated­as­

follows:

2, ˆ, 5 ˆ,

tsh g y g y g

y =m + ´s (6)

where­my^,g and sy^,g­are­the­mean­and­the­standard­devi

-ation­of­the­ŷ values of class g­calculated­on­the­training­ set­samples.­Therefore,­in­order­to­be­assigned­to­class­g,

an­unknown­sample­must­have­a­ŷ­value­ranging­between­

ytsh1,g and ytsh2,g.­The­upper­limit­imposed­on­theŷ values

allows­objects­found­at­the­extremes­of­the­Gaussian­ probability­density­functions­(PDFs)­to­be­rejected;­these­ usually­have­low­values­in­the­PDFs­but­high­a posteriori probability­for­one­class­according­to­the­Bayes­rule.­The­ upper­limit­was­set­based­on­preliminary­tests­performed­ on­some­representative­images; ■for­classification­problems­with­more­than­two­classes,­ the­samples­must­be­unambiguously­assigned­only­to­ one class. Samples­that­do­not­match­all­the­three­criteria­are­not­ assigned­to­any­class­and­are­labelled­as­“not­assigned”­ (NA).­In­this­manner,­Soft­PLS-DA­allows­boundaries­to­ be­drawn­around­each­modelled­class­which­maximise­ the­discrimination­between­the­categories­of­interest­and­

minimise­possible­false­positives­due­to­ambiguous­clas -sifications­or­to­outlier­samples.

Material and methods

Plastic dataset

In­the­present­study,­we­have­considered­the­recyclable­ plastic­polymers­mainly­used­for­packaging,­including­ polyethylene­terephthalate­(PET),­polystyrene­(PS),­poly -vinyl­chloride­(PVC),­polypropylene­(PP)­and­polyeth -ylene­(PE),­which­in­turn­can­be­further­subdivided­in­ high-density­polyethylene­(HDPE)­and­low-density­poly -ethylene­(LDPE). Different­plastic­objects­made­of­the­considered­poly -mers­have­been­collected­form­household­waste.­In­addi -tion,­samples­composed­of­paper­and­of­other­types­ of­non-recyclable­plastics­(OTHER),­e.g.­acrylonitrile­ butadiene­styrene­(ABS)­and­polylactic­acid­(PLA),­were­ also­considered­as­possible­foreign­materials­that­can­be­ found­in­plastic­municipal­waste.

The­ different­ samples­ have­ been­ manually­ sorted­ into­the­corresponding­categories­based­on­the­Resin­ Identification­Code­(RIC)­reported­on­the­objects.32_­The­ RIC­is­an­international­coding­system­comprising­a­set­of­ symbols­(labels­and­numbers)­present­on­plastic­products­ and­indicating­the­polymer­of­which­they­are­composed.­ For­example,­according­to­RIC,­coding­number­1­is­associ -ated­to­PET,­number­2­is­associated­to­HDPE,­number­3­ is­associated­to­PVC­etc. Image­acquisition The­collected­waste­samples­have­been­acquired­with­an­ industrial­sorting­system­consisting­of­a­NIR­line­scanning­ hyperspectral­camera­(KUSTA1.9MSI,­LLA­Instruments)­ mounted­over­a­black­conveyor­belt­and­equipped­with­ an­InGaAs­detector­array­and­Zeiss­f/2.4,­10 mm­optical­ lens.­Image­acquisition­was­performed­with­a­frame­rate­ equal­to­644 Hz­and­the­speed­of­the­conveyor­belt­ was­equal­to­0.84 m s–1_{.­Illumination­was­provided­by­} halogen­light­bulbs­positioned­in­two­parallel­illumination­ rows­slightly­tilted­towards­each­other­(PMAmsi,­LLA­ Instruments).­The­hyperspectral­images­were­acquired­in­ the­NIR­range­from­1330 nm­to­1900 nm­with­a­spectral­ resolution­of­6 nm. The­samples­were­acquired­in­two­acquisition­phases­ conducted­on­different­days.­In­the­first­phase,­hyper -spectral­images­containing­objects­made­of­the­same­ material­were­acquired.­In­more­detail,­two­images­of­ different­objects­were­acquired­for­each­type­of­material,­ for­a­total­of­16­hyperspectral­images­(=­8­materials­ 2 replicated­images).­These­images­were­used­as­training­ images­in­the­subsequent­elaboration­steps,­in­order­to­ obtain­a­library­of­representative­spectra­for­each­mate -rial type.

In­ the­ second­ acquisition­ phase,­ hyperspectral­ images­containing­samples­of­two­different­materials­ were­acquired­considering­all­the­possible­combinations­ between­the­material­types­under­investigation.­On­the­ whole,­56­hyperspectral­images­have­been­obtained­in­ this­phase,­resulting­from­two­replicate­images­for­each­ combination. All­the­hyperspectral­images,­acquired­on­the­objects­ positioned­on­the­moving­conveyor­belt,­have­size­equal­ to­41­row­pixels­­500­column­pixels­­96­wavelengths.­ For­each­image,­the­raw­intensity­counts­were­converted­ into­reflectance­units­by­means­of­an­internal­calibration­ procedure­based­on­the­measure­of­the­dark­current­and­ of­a­white­high­reflectance­standard.­Dark­current­was­ measured­by­closing­the­shutter­of­the­camera,­while­the­ white­reference­consisted­of­an­aluminium­frame­holding­ the­calibration­material­with­an­average­remission­factor­ equal­to­83.0 %. Image­elaboration Initially,­the­16­images­acquired­during­the­first­acquisi -tion­phase­were­analysed­by­means­of­PCA­after­mean­ centring­as­data­preprocessing,­in­order­to­segment­the­ pixels­of­the­background­(black­conveyor­belt)­from­those­ belonging­to­the­samples. After­background­segmentation,­from­each­training­ image­1000­spectra­of­the­sample­and­400­spectra­of­ the­background­were­randomly­selected.­These­spectra­ were­ used­ to­ build­ a­ training­ set­with­ size­ {22,400­ spectra ­96­wavelengths},­containing­16,000­repre -sentative­spectra­of­the­considered­materials­(2000­ spectra­for­each­material­type)­and­6400­spectra­of­the­ background.­The­average­spectra­of­each­material­type­ calculated­from­the­training­set­are­reported­in­Figure­ 1A,­while­the­average­and­standard­deviation­spectra­of­ each­class­are­shown­in­Figure­S1­of­the­Supplementary­ Material. The­images­containing­samples­of­two­different­mate -rials­were­used­as­test­images­to­obtain­both­a­quan -titative­and­qualitative­evaluation­of­the­classification­ models.­For­the­creation­of­the­test­set,­some­represen

-tative­images­have­been­chosen­in­order­to­consider­all­ the­materials,­and­Regions­of­Interest­(ROI)­were­defined­ on­these­images.­From­each­ROI,­the­corresponding­ spectra­were­extracted­to­create­a­test­set­with­size­ {21,760­spectra­­96­wavelengths},­containing­a­library­ of­spectra­with­known­assignment.­Figure­1B­shows­the­ average­spectra­of­each­considered­material­calculated­ from­the­test­set,­while­the­corresponding­average­and­

Figure 1. Average spectra of each material type calculated from training and test sets without any pre-processing (A and B), and after SNV (C and D) and detrend (E and F) as data prepre-processing.

standard­deviation­spectra­are­reported­in­Figure­S2­of­ the­Supplementary­Material.

Data analysis

The­training­set­was­initially­analysed­by­means­of­PCA­ considering­ both­ standard­ normal­variate­ (SNV)­ and­ detrend­as­row­preprocessing­methods.­This­preliminary­ analysis­ allowed­similarities­and­differences­between­ the­considered­materials­to­be­identified,­and­both­SNV­ and­detrend­gave­analogous­results.­The­clusters­of­the­ different­materials­observed­in­the­PCA­score­plots­essen -tially­reflected­similarities­and­differences­of­the­chemical­ structure­of­the­considered­polymers.­These­results­were­ used­to­develop­the­structure­of­the­tree-based­classifica -tion­model­reported­in­Figure­2.­In­particular,­PCA­high -lighted­that­the­class­corresponding­to­the­non-recyclable­ plastic­polymers­was­too­heterogenous­to­be­modelled­ into­a­single­class.­For­this­reason,­the­spectra­belonging­ to­the­OTHER­class­were­not­used­during­model­calibra -tion,­but­they­were­used­during­the­final­validation­of­the­ classification­tree­in­order­to­evaluate­the­ability­of­Soft­ PLS-DA­algorithm­to­reject­objects­belonging­to­classes­ not­considered­in­model­calibration.­The­classification­ tree­reported­in­Figure­2­is­composed­of­five­nodes,­each­ corresponding­to­a­classification­model­calculated­with­ Soft­PLS-DA­algorithm­using­the­training­set. For­each­node­of­the­tree,­the­classification­models­

have­ been­ computed­ considering­ both­SNV + mean

centring and detrend + mean centring as data prepro-cessing­methods. The­average­spectra­of­each­considered­material­type­ obtained­from­both­training­and­test­sets­preprocessed­ with­SNV­and­detrend­are­reported­in­Figures­1C–F. Classification­performances­of­each­single­class­were­ defined­using­sensitivity­(SENS),­i.e.­the­percentage­of­ objects­belonging­to­a­given­class­correctly­assigned­ to­the­corresponding­class,­specificity­(SPEC),­i.e.­the­ percentage­of­objects­correctly­rejected­from­the­class­ model,­and­efficiency­(EFF),­i.e.­the­geometric­mean­of­ sensitivity­and­specificity.­Furthermore,­for­an­overall­ evaluation­of­the­classification­quality­of­each­node,­the­ Non-Error­Rate­(NER)­was­also­considered,­which­is­ calculated­as­the­arithmetic­mean­of­the­SENS­values­of­ the­different­classes.33 The­proper­number­of­LVs­for­the­Soft­PLS-DA­models­ has­been­optimised­by­maximising­the­NER­value­in­cross-validation.­In­particular,­a­customised­cross-validation­ scheme­has­been­adopted,­consisting­of­two­deletion­ groups­(i.e.,­cross-validation­groups);­during­the­cross-validation­step­one­model­was­therefore­calculated­using­ the­spectra­of­each­deletion­group,­to­predict­the­class­of­ the­spectra­of­the­other­deletion­group. Each­deletion­group­was­defined­in­order­to­include­ the­spectra­belonging­to­all­the­considered­target­classes­ and­to­keep­together­all­the­spectra­extracted­from­the­ same­image. Furthermore,­for­each­node­of­the­classification­tree,­ the­Soft­PLS-DA­algorithm­has­also­been­coupled­with­ a­sparse-based­variable­selection­approach­in­order­to­ identify­the­relevant­variables­involved­in­the­classifica -tion.­In­more­detail,­the­outcomes­of­the­sparse­PLS-DA­ (sPLS-DA)­algorithm­proposed­by Lê Cao et al.34–36_­were­

subjected­to­the­same­constraints­for­class­assignment­ described­above­for­Soft­PLS-DA,­thus­resulting­in­a­ sparse­version­of­Soft­PLS-DA­(sparse­Soft­PLS-DA). Basically,­the­main­idea­of­sparse-based­methods­is­ to­perform­variable­selection­by­forcing­the­model­coef -ficients­not­bringing­useful­information­to­be­equal­to­ zero.­Sparse­methods­represent­an­extension­of­the­ corresponding­traditional­classification­or­regression­ methods,­where­sparsity­is­achieved­by­adding­a­penalty­ term­to­the­computation­of­the­model­coefficients.37,38_­In­ addition­to­the­number­of­model­components­(i.e.,­LVs),­ sparse­methods­also­require­the­level­of­sparsity­to­be­ optimised,­which­is­related­to­the­number­of­variables­ whose­coefficients­are­set­equal­to­zero­in­the­model.36,39 The­sparse-based­Soft­PLS-DA­models­were­optimised­ considering­a­maximum­number­of­LVs­equal­to­10­and­

a­number­of­variables­selected­for­each­LV­ranging­from­ 4­to­96­(with­a­step­equal­to­4).­For­each­node­of­the­ classification­tree,­the­best­combination­between­the­ number­of­LVs­and­the­number­of­selected­variables­ was­identified­by­maximising­the­NER­value­estimated­in­ cross-validation. Both­Soft­PLS-DA­and­sparse­Soft­PLS-DA­models­ were­validated­using­the­test­set­described­above. Image­elaboration­and­data­analysis­were­performed­ using­the­PLS_Toolbox­software­(ver.­8.5,­Eigenvector­ Research­Inc.,­USA)­and­ad hoc­routines­developed­in­the­ MATLAB­environment­(ver.­9.0,­The­MathWorks,­USA).­ The­MATLAB­routine­to­run­Soft­PLS-DA­algorithm­is­

freely­downloadable­from­http://www.chimslab.unimore.

it/downloads/.

Results

Classification by Soft PLS-DA

Table­ 1­ and­ Table­ 2­ report­ the­ results­ obtained­ by­ applying­Soft­PLS-DA­algorithm­for­each­node­of­the­ classification­tree­and­considering­both­SNV­and­detrend­ as­row­preprocessing­methods.­For­each­model,­the­clas -sification­performances­have­been­evaluated­considering,­ for­each­single­class,­the­number­of­not-assigned­pixel­ spectra­and­SENS,­SPEC­and­EFF­values,­while­the­NER­ values­have­been­calculated­as­a­global­measure­over­all­ the­classes.­To­maintain­a­concise­presentation,­Table­1­ shows­only­the­NER­values­obtained­for­each­node­of­the­ classification­tree,­while­Table­2­reports­the­SENS­values­ of­all­the­considered­classes­in­each­node­of­the­tree.

SNV + mean centring Detrend + mean centring

LV CAL CV TS LV CAL CV TS NODE­1 3 91.8 87.7 98.4 5 86.1 86.0 84.9 NODE­2 2 94.3 93.6 100.0 5 93.9 92.4 91.1 NODE­3 5 94.7 89.5 100.0 2 97.0 94.7 59.6 NODE­4 4 90.3 90.2 98.9 6 87.7 83.9 98.1 NODE­5 5 90.6 82.9 100.0 2 90.7 85.1 99.9

Table 1. NER values obtained with Soft PLS-DA in calibration (CAL), cross-validation (CV) and prediction of the test set (TS) for each node of the classification tree.

SNV + mean centring Detrend + mean centring

CAL CV TS CAL CV TS NODE­1 BACKGROUND 91.6 89.7 98.1 96.9 96.6 100.0 SAMPLE 91.9 85.7 98.6 75.3 75.5 69.9 NODE­2 PAPER 98.7 98.8 100.0 100.0 99.9 100.0 PE+PVC+PP 93.5 92.9 100.0 92.3 89.5 96.6 PS+PET 90.6 89.2 100.0 80.8 76.7 50.2 NODE­3 PET 95.2 85.9 100.0 95.4 97.4 76.2 PS 94.3 93.2 100.0 98.6 92.1 43.0 NODE­4 PE 89.8 87.7 99.7 86.2 82.8 97.7 PP 89.5 91.2 97.1 91.6 86.3 99.5 PVC 91.8 91.8 100.0 85.5 82.6 97.1 NODE­5 HDPE 86.6 84.5 100.0 81.8 76.5 99.8 LDPE 94.6 81.3 100.0 99.6 93.7 100.0

Table 2. SENS values obtained with Soft PLS-DA in calibration (CAL), cross-validation (CV) and prediction of the test set (TS) for each node of the classification tree.

With­ few­ exceptions,­ SNV­ preprocessing­ method­ allowed­ better­ classification­ performances­ to­ be­ obtained­than­detrend,­both­in­cross-validation­and­in­ prediction­of­the­test­set.­Indeed,­in­Node­1,­Node­2­ and­Node­4­the­NER­values­obtained­in­cross-valida -tion­from­the­models­calculated­with­SNV­are­higher­ than­those­obtained­with­detrend,­and­these­results­ were­also­confirmed­from­the­prediction­of­the­external­ test­set.­Concerning­Node­3,­SNV­and­detrend­led­to­ similar­classification­performances­in­cross-validation,­ but­detrend­gave­a­lower­NER­value­in­prediction­of­the­ test­set;­in­particular­a­SENS­value­equal­to­43.0 %­was­ obtained­for­class­PS.­Therefore,­also­for­Node­3­SNV­ was­the­best­preprocessing­method,­since­it­resulted­ in­a­more­robust­classification­model.­Conversely,­in­ Node­5­the­two­preprocessing­methods­showed­similar­ performances­both­in­cross-validation­and­in­prediction­ of­the­test­set. Based­on­these­results,­SNV­can­be­identified­as­the­ optimal­preprocessing­method­for­all­the­five­nodes­of­ the­classification­tree.­Furthermore,­it­has­to­be­high -lighted­that­the­use­of­the­same­preprocessing­method­ for­each­node­of­the­classification­tree­represents­a­great­ advantage­from­the­computational­point­of­view.­Indeed,­ the­spectra­of­the­hyperspectral­images­can­be­row-preprocessed­only­once­after­image­acquisition,­and­the­ preprocessed­spectra­can­then­be­used­for­all­the­nodes­ of­the­classification­tree,­resulting­in­a­lower­computa -tional­effort. Figure­S3­of­the­Supplementary­Material­shows­the­ regression­vectors­of­the­classification­models­calculated­ for­each­node­of­the­tree­using­SNV­as­spectral­row­ preprocessing.­By­comparing­Figure­S3­with­Figure­1,­ which­reports­the­average­spectra­of­the­different­mate -rial­types,­it­is­possible­to­observe­that­for­each­node­ of­the­tree­the­relevant­variables,­i.e.­the­variables­with­ highest­absolute­values­of­the­regression­coefficients,­ generally­correspond­to­the­characteristic­wavelengths­ of­the­materials­considered­in­the­specific­classification­ problem.

Classification by Soft PLD-DA and

sparse-based variable selection

Since­SNV­was­the­optimal­row­preprocessing­method­

for­the­whole­classification­tree,­the­subsequent­vari

-able­selection­step­by­means­of­sparse­Soft­PLS-DA­was­ performed­considering­only­SNV + mean centring­for­each­ node. Table­3­reports­the­classification­results­obtained­for­ the­five­nodes­of­the­classification­tree­expressed­in­ terms­of­NER­vales­as­a­global­measurement­of­the­classi -fication­performances­of­each­node,­while­Table­4­shows­ the­SENS­values­of­each­modelled­class. Comparing­Table­1­with­Table­3­and­Table­2­with­Table­ 4,­it­is­possible­to­observe­that,­generally,­variable­selec -tion­improved­the­classification­performances­and,­at­the­ same­time,­considerably­reduced­the­number­of­retained­ variables. The­higher­improvement­in­classification­performances­ was­ reached­ in­ Node­ 3­ with­ a­ NER­ value­ in­ cross-­ validation­equal­to­94.3 %­with­respect­of­a­NER­value­ equal­to­89.5 %­obtained­considering­the­full­wavelength­ LV No. variables CAL CV TS NODE­1 4 62 92.7 89.1 99.2 NODE­2 2 8 95.6 95.2 100.0 NODE­3 1 20 97.8 94.3 100.0 NODE­4 4 40 90.3 90.5 98.1 NODE­5 2 6 89.6 81.9 100.0

Table 3. NER values obtained with sparse-based variable selection coupled with Soft PLS-DA in calibration (CAL), cross-validation (CV) and prediction of the test set (TS) for each node of the classification tree.

CAL CV TS NODE­1 BACKGROUND 92.5 90.5 98.9 SAMPLE 92.8 87.7 99.6 NODE­2 PAPER 100.0 99.8 100.0 PE+PVC+PP 94.6 94.6 100.0 PS+PET 92.3 91.3 100.0 NODE­3 PET 97.4 92.5 100.0 PS 98.2 96.1 100.0 NODE­4 PE 88.4 87.2 94.7 PP 91.9 93.1 99.5 PVC 90.7 91.3 100.0 NODE­5 HDPE 92.9 82.6 100.0 LDPE 86.3 81.3 100.0

Table 4. SENS values obtained with sparse-based variable selection coupled with Soft PLS-DA in calibration (CAL), cross-validation (CV) and prediction of the test set (TS) for each node of the classification tree.

range.­In­addition,­by­considering­only­the­20­selected­ variables­in­Node­3,­all­the­test­set­spectra­were­correctly­ assigned. Node­2­is­the­node­with­the­lower­number­of­selected­ variables,­retaining­only­8­variables­out­of­the­96­original­ wavelengths.­Such­a­small­number­of­variables­enabled­ an­increase­in­the­classification­performances­for­all­the­ three­classes­modelled­in­Node­2­(PAPER,­PE+PVC+PP­ and­PS+PET),­maintaining­at­the­same­time­the­100.0 % of­correct­assignments­for­the­test­set. Conversely,­in­Node­5­variable­selection­led­to­a­slight­ decrease­of­the­classification­performances­in­cross-­ validation;­in­particular,­the­SENS­value­for­class­HDPE­is­ lower­than­what­obtained­with­the­full­wavelength­range­ (82.6 % vs 84.5 %).­Actually,­it­should­be­considered­that­ Node­5­deals­with­the­classification­of­HDPE­and­LDPE,­ which­are­derived­from­the­same­monomer,­and­the­ difference­between­these­two­polymers­is­only­related­ to­the­degree­of­branching.­Therefore,­it­is­reasonable­to­ assume­that,­for­the­discrimination­between­HDPE­and­ LDPE,­the­full­wavelength­range­provides­more­complete­ information.

Final implementation of the classification tree

Based­on­the­results­obtained­from­the­optimisation­of­ each­single­node,­the­different­classification­models­have­ been­assembled­together­in­order­to­obtain­the­final­ implementation­of­the­classification­tree,­which­is­sche -matised­in­Figure­3. The­proposed­tree-structured­classification­model­was­ applied­to­the­test­set­in­order­to­obtain­a­quantitative­ assessment­of­its­classification­performances.­During­the­ final­validation­of­the­model,­the­spectra­belonging­to­ the­other­types­of­non-recyclable­plastics­(class­OTHER)­ were­also­included­in­the­test­set­to­evaluate­the­ability­ of­Soft­PLS-DA,­and­of­its­sparse-based­extension,­to­ correctly­reject­spectra­not­belonging­to­the­modelled­ classes. The­results­are­summarised­in­Figure­4,­which­can­be­ seen­as­a­kind­of­graphical­representation­of­the­confu -sion­matrix­obtained­by­applying­the­classification­tree­to­ the­test­set.­Indeed,­each­point­in­the­graph­represents­ a­spectrum­of­the­test­set­and­it­is­coloured­according­to­ the­corresponding­actual­class,­while­the­position­of­the­ points­on­the­y-axis­is­based­on­the­class­predicted­from­ the­tree-structured­classification­model. The­same­results­are­also­reported­in­Table­5­in­terms­ of­SENS­and­SPEC­values­for­each­considered­class,­and­ of­NER­of­the­overall­tree-structured­model. Generally,­satisfactory­classification­results­have­been­ obtained­for­all­the­modelled­classes,­resulting­in­a­NER­ value­equal­to­98.4 %.­The­SENS­values­are­always­greater­ than­90 %,­and­for­PS­and­PVC­all­the­test­set­spectra­ have­been­correctly­predicted.

Figure 3. Final implementation of the tree-structured classification model for plastic waste sorting.

Concerning­the­results­expressed­in­terms­of­speci -ficity,­for­all­the­classes,­SPEC­values­close­to­1­were­ obtained,­indicating­that­the­classification­tree­correctly­ rejected­ the­ great­ part­ of­ spectra­ not­ belonging­ to­ the­considered­class.­Indeed,­Figure­4­shows­that­the­ majority­of­the­test­set­spectra­belonging­to­the­category­ of­other­plastics­(OTHER),­which­was­not­included­in­the­ classification­tree,­was­correctly­rejected­from­all­the­ considered­classes­and­thus­labelled­as­“not-assigned”­ (NA).­In­more­detail,­70.9 %­of­spectra­belonging­to­ class­OTHER­was­predicted­as­NA,­while­only­a­minority­ of­these­spectra­from­other­plastics­was­erroneously­ assigned­to­PET­and­PS­classes­(12.4 %­and­14.7 %, respectively). These­results­confirm­that­the­proposed­tree-­structured­ classification­model­is­able­to­effectively­recognise­the­ spectra­of­the­analysed­materials,­minimising­at­the­same­ time­possible­false­positives­due­to­spectra­belonging­to­ materials­that­were­not­considered­during­model­calibra -tion. Furthermore,­the­classification­tree­was­applied­to­the­ test­images,­i.e.­to­the­images­containing­objects­of­two­ different­materials,­in­order­to­evaluate­the­classification­ performances­at­the­pixel­level.­As­an­example,­Figure­5­ shows­the­prediction­images­obtained­from­the­hyper -spectral­images­containing­PP­+­PVC­(Figure­5A),­PAPER­ +­HDPE­(Figure­5B),­LDPE­+­OTHER­(Figure­5C)­and­PET­ +­PS­(Figure­5D).­In­order­to­facilitate­the­interpretation­ of­the­results,­the­RGB­images­of­the­corresponding­ waste­samples­have­also­been­included­together­with­the­ prediction­images.­In­the­prediction­images,­all­the­pixels­ predicted­as­belonging­to­a­defined­class­have­been­ coloured­according­to­the­legend.­In­particular,­grey­is­ associated­with­those­pixels­that­have­not­been­assigned­ to any class.

Based­ on­ the­ prediction­ images,­ it­ is­ possible­ to­ observe­that­the­majority­of­the­pixels­of­each­single­

object­are­correctly­assigned­to­the­corresponding­mate

-rial­type.­Misclassifications­mainly­occur­at­the­edges­of­ the­objects­or­in­some­areas­of­the­background,­due­to­

Figure 4. Prediction results obtained from the final implementation of the tree-structured classification model.

HDPE LDPE PAPER PET PP PS PVC BACK

SENS­% 99.9 92.1 96.7 99.8 99.5 100.0 100.0 98.9

SPEC­% 100.0 100.0 100.0 97.7 100.0 97.4 100.0 99.2

NER­% 98.4

Table 5. Results in prediction obtained by applying the classification tree to the test set. BACK is the abbre-viation for background.

the­noise­caused­by­specular­reflections­of­the­conveyor­ belt. In­more­detail,­in­Figure­5A­and­Figure­5D­all­the­pixels­ of­the­objects­depicted­in­the­images­are­correctly­classi -fied,­while­in­Figure­5B­the­pixels­of­the­larger­HDPE­bottle­ located­at­its­upper­edge­are­not­assigned.­Considering­ Figure­5C,­the­majority­of­the­pixels­of­the­LDPE­object­ are­correctly­assigned,­while­some­of­them­are­classified­ as­HDPE­or­not­assigned.­In­the­same­image,­the­objects­ made­of­plastic­polymers­not­included­in­the­classifica -tion­model­have­been­globally­not­assigned­to­any­class.

Conclusions

In­ practical­ applications­ of­ hyperspectral­ imaging­ to­ classification­aims,­e.g.­in­sorting­plants,­it­is­necessary­ to­implement­classification­methods­able­to­effectively­ handle­a­large­number­of­classes,­to­correctly­classify­ samples­belonging­to­the­considered­categories,­and­to­ correctly­recognise­and­reject­possible­foreign­objects. The­present­study­was­aimed­at­the­development­of­ a­classification­rule­for­the­discrimination­of­multiple­ categories­through­a­tree-structured­model,­in­which­ the­classification­at­each­node­was­performed­by­Soft­ PLS-DA,­an­extension­of­the­PLS-DA­algorithm.­The­ basic­engine­of­Soft­PLS-DA­is­the­same­as­PLS-DA,­but­ class­assignment­is­subjected­to­some­additional­criteria­ involving­the­calculation­of­further­thresholds­based­on­ Q­residuals­and­on­y­predictions.­These­additional­thresh -olds­allow­the­rejection­of­unknown­samples­which­are­ not­compliant­with­the­classes­of­interest. The­proposed­approach­was­tested­on­a­case­study­ related­to­the­discrimination­of­the­different­recyclable­

Figure 5. Prediction images and corresponding RGB images of the samples: PP+PVC (A), PAPER+HDPE (B), LDPE+OTHER (C) and PET+PS (D).

plastic­polymers­that­are­commonly­used­for­packaging.­ On­the­one­hand,­the­use­of­a­tree-structured­classifica -tion­model­allowed­eight­different­classes­to­be­efficiently­ handled,­a­situation­in­which­a­single­discrimination­step­ would­rarely­give­satisfactory­results.­On­the­other­hand,­ Soft­PLS-DA­proved­to­be­a­flexible­algorithm­thanks­to­ the­possibility­of­rejecting­foreign­objects,­whose­pres -ence­is­a­plausible­situation­in­recycling­plants,­since­it­is­ not­possible­to­completely­control­the­incoming­materials.­ Furthermore,­coupling­Soft-PLS-DA­with­a­sparse-based­ variable­selection­allowed­us­to­improve­the­classification­ performances­and­to­decrease­the­number­of­spectral­ variables,­reducing­at­the­same­time­the­computational­ efforts. The­external­validation­of­the­classification­tree­demon -strated­ the­ effectiveness­ of­ the­ proposed­ approach,­ reaching­a­NER­value­equal­to­98.4 %.­These­satisfactory­ results­were­also­confirmed­by­the­pixel-level­prediction­ performed­on­a­set­of­test­images. A­further­improvement­of­this­application­will­consist­ in­the­extension­of­the­prediction­from­a­pixel-level­to­an­ object-level­approach,­by­assigning­each­plastic­sample­ to­a­defined­class­based­on­the­class­attribution­of­the­ majority­of­its­pixels.­In­the­specific­case­under­inves -tigation,­this­task­can­be­accomplished­by­coupling­the­ hyperspectral­camera­with­an­RGB­camera­for­object­ shape­detection.­Indeed,­the­much­higher­spatial­reso -lution­of­RGB­imaging­could­allow­to­better­define­the­ edges­of­each­imaged­object,­to­identify­labels­partly­ covering­the­samples,­and­to­further­classify­the­samples­ of­a­given­plastic­material­based­on­its­colour.

Acknowledgements

The­ authors­ acknowledge­ financial­ support­ for­ this­ research­by­CNIGROUP­–­Vision­systems­business­unit­ through­the­POR-FESR­2014-2020­project­RICIPLA.­The­ authors­also­wish­to­thank­Philipp­Haumann­and­Edoardo­ Covertino­(CNIGROUP­–­Vision­systems­business­unit,­ Alfonsine,­Italy)­for­the­help­during­image­acquisition­and­ for­technical­support.

References

1.­ A.­Gowen,­C.­O’Donnell,­P.J.­Cullen,­G.­Downey­ and­J.M.­Frias,­“Hyperspectral­imaging–an­emerging­ process­analytical­tool­for­food­quality­and­safety­ control”,­Trends Food Sci. Technol.18(12),­590­(2007).­ doi:­https://doi.org/10.1016/j.tifs.2007.06.001

2.­ Y.Y.­Pu,­Y.Z.­Feng­and­D.W.­Sun,­“Recent­progress­ of­hyperspectral­imaging­on­quality­and­safety­ inspection­of­fruits­and­vegetables:­a­review”,­

Compr. Rev. Food Sci F.14(2),­176­(2015).­doi:­

https://doi.org/10.1111/1541-4337.12123

3. C. Ferrari, G. Foca, R. Calvini and A. Ulrici, “Fast exploration­and­classification­of­large­hyperspectral­ image­datasets­for­early­bruise­detection­on­apples”,­

Chemometr. Intell. Lab. Syst.146,­108­(2015).­doi:­

https://doi.org/10.1016/j.chemolab.2015.05.016

4.­ G.­ElMasry,­F.D.­Barbin,­D.W.­Sun­and­ P.­Allen,­“Meat­quality­evaluation­by­hyper -spectral­imaging­technique:­an­overview”,­Crit. Rev. Food Sci. Nutr.52(8),­689­(2012).­doi:­

https://doi.org/10.1080/10408398.2010.507908

5.­ K.­Sendin,­P.J.­Williams­and­M.­Manley,­“Near­ infrared­hyperspectral­imaging­in­qual -ity­and­safety­evaluation­of­cereals”,­Crit. Rev. Food Sci. Nutr.58(4),­575­(2018).­doi:­

https://doi.org/10.1080/10408398.2016.1205548

6.­ E.­Dufour,­“Recent­advances­in­the­analy -sis­of­dairy­product­quality­using­methods­ based­on­the­interactions­of­light­with­mat -ter”,­Int. J. Dairy Technol.64(2),­153­(2011).­doi:­

https://doi.org/10.1111/j.1471-0307.2010.00665.x

7.­ Y.­Roggo,­A.­Edmond,­P.­Chalus­and­

M.­Ulmschneider,­“Infrared­hyperspectral­imag

-ing­for­qualitative­analysis­of­pharmaceutical­ solid­forms”,­Anal. Chim. Acta535,­79­(2005).­doi:­

https://doi.org/10.1016/j.aca.2004.12.037

8.­ A.A.­Gowen,­C.P.­O’Donnell,­P.J.­Cullen­and­ S.E.J.­Bell,­“Recent­applications­of­chemical­imaging­ to­pharmaceutical­process­monitoring­and­quality­ control”,­Eur. J. Pharm. Biopharm.69(1), 10 (2008).

doi:­https://doi.org/10.1016/j.ejpb.2007.10.013

9.­ J.M.­Amigo,­“Practical­issues­of­hyperspec -tral­imaging­analysis­of­solid­dosage­forms”,­

Anal. Bioanal. Chem.398,­93­(2010).­doi:­

https://doi.org/10.1007/s00216-010-3828-z

10.­A.­Ulrici,­S.­Serranti,­C.­Ferrari,­D.­Cesare,­

G.­Foca­and­G.­Bonifazi,­“Efficient­chemomet

-ric­strategies­for­PET–PLA­discrimination­in­ recycling­plants­using­hyperspectral­imaging”,­

Chemometr. Intell. Lab. Syst.122,­31­(2013).­doi:­

11.­P.­Tatzer,­M.­Wolf­and­T.­Panner,­“Industrial­appli -cation­for­inline­material­sorting­using­hyperspec -tral­imaging­in­the­NIR­range”,­Real-Time Imaging 11(2),­99­(2005).­doi:­https://doi.org/10.1016/j.

rti.2005.04.003

12. ­R.­Palmieri,­G.­Bonifazi­and­S.­Serranti,­“Recycling-oriented­characterization­of­plastic­frames­and­

printed­circuit­boards­from­mobile­phones­by­elec

-tronic­and­chemical­imaging”,­Waste Manag.34(11),

2120­(2014).­doi:­https://doi.org/10.1016/j.was -man.2014.06.003

13.­J.M.­Amigo,­H.­Babamoradi­and­S.­Elcoroaristizabal,­ “Hyperspectral­image­analysis.­A­tutorial”,­Anal. Chim.

Acta896,­34­(2015).­doi:­https://doi.org/10.1016/j.

aca.2015.09.030

14.­P.­Paclik,­R.­Leitner­and­R.P.W.­Duin,­“A­study­on­ design­of­object­sorting­algorithms­in­the­industrial­ application­using­hyperspectral­imaging”,­J. Real-Time Image Proc.1(2),­101­(2006).­doi:­https://doi. org/10.1007/s11554-006-0018-5

15.­L.­Eriksson,­J.­Trygg­and­S.­Wold,­“PLS‐trees®_{, a}

top‐down­clustering­approach”,­J. Chemometr.23(11),

569­(2009).­doi:­https://doi.org/10.1002/cem.1254

16.­K.H.­Liland,­A.­Kohler­and­V.­Shapaval,­“Hot­PLS—a­ framework­for­hierarchically­ordered­taxonomic­ classification­by­partial­least­squares”,­Chemometr. Intell. Lab. Syst.138,­41­(2014).­doi:­https://doi. org/10.1016/j.chemolab.2014.07.010

17.­W.­Song,­H.­Wang,­P.­Maguire­and­O.­Nibouche,­

“Nearest­clusters­based­partial­least­squares­discrimi -nant­analysis­for­the­classification­of­spectral­data”,­

Anal. Chimica Acta1009,­27­(2018).­doi:­https://doi. org/10.1016/j.aca.2018.01.023

18.­S.­Chevallier,­D.­Bertrand,­A.­Kohler­and­P.­Courcoux,­ “Application­of­PLS‐DA­in­multivariate­image­analy

-sis”,­J. Chemometr.20(5),­221­(2006).­doi:­https://doi. org/10.1002/cem.994

19.­M.­Barker­and­W.­Rayens,­“Partial­least­squares­for­ discrimination”,­J. Chemometr.17(3),­166­(2003).­doi:­

https://doi.org/10.1002/cem.785

20.­N.F.­Pérez,­J.­Ferré­and­R.­Boqué,­“Calculation­of­ the­reliability­of­classification­in­discriminant­par -tial­least-squares­binary­classification”,­Chemometr. Intell. Lab. Syst.95(2),­122­(2009).­doi:­https://doi. org/10.1016/j.chemolab.2008.09.005

21.­P.­Oliveri,­“Class-modelling­in­food­analytical­

chemistry:­Development,­sampling,­optimisa

-tion­and­validation­issues–A­tutorial”,­Anal. Chim.

Acta982,­9­(2017).­doi:­https://doi.org/10.1016/j.

aca.2017.05.013

22.­S.­Wold,­“Pattern­recognition­by­means­of­disjoint­

principal­components­models”,­Pattern Recognit.

8(3),­127­(1976).­doi:­https://doi.org/

10.1016/0031-3203(76)90014-5

23.­Y.­Zheng,­J.­Bai,­J.­Xu,­X.­Li­and­Y.­Zhang,­“A­dis -crimination­model­in­waste­plastics­sorting­using­

NIR­hyperspectral­imaging­system”,­Waste Manag.

72,­87­(2018).­doi:­https://doi.org/10.1016/j.was -man.2017.10.015 24.­G.­Bonifazi,­G.­Capobianco­and­S.­Serranti,­“A­hier -archical­classification­approach­for­recognition­ of­low-density­(LDPE)­and­high-density­polyeth -ylene­(HDPE)­in­mixed­plastic­waste­based­on­ short-wave­infrared­(SWIR)­hyperspectral­imaging”,­

Spectrochim. Acta A198,­115­(2018).­doi:­https://doi. org/10.1016/j.saa.2018.03.006

25.­P.­Geladi­and­B.R.­Kowalski,­“Partial­least-squares­ regression:­a­tutorial”,­Anal. Chim. Acta185, 1 (1986).­doi:­https://doi.org/

10.1016/0003-2670(86)80028-9

26.­A.­Höskuldsson,­“PLS­regression­methods”,­

J. Chemometr.2(3),­211­(1988).­doi:­https://doi. org/10.1002/cem.1180020306

27.­D.­Ballabio­and­V.­Consonni,­“Classification­tools­ in­chemistry.­Part­1:­linear­models.­PLS-DA”,­

Anal. Methods5,­3790­(2013).­doi:­https://doi. org/10.1039/c3ay40582f

28.­O.Y.­Rodionova,­A.V.­Titova­and­A.L.­Pomerantsev,­ “Discriminant­analysis­is­an­inappropriate­method­

of­authentication”,­TrAC Trends Anal. Chem. 78,­17­(2016).­doi:­https://doi.org/10.1016/j. trac.2016.01.010

29.­A.L.­Pomerantsev­and­O.Y.­Rodionova,­“Multiclass­

partial­least­squares­discriminant­analysis:­Taking­ the­right­way—A­critical­tutorial”,­J. Chemometr.32,

3030­(2018).­doi:­https://doi.org/10.1002/cem.3030

30.­C.­Botella,­J.­Ferré­and­R.­Boqué,­“Classification­ from­microarray­data­using­probabilis

-tic­discriminant­partial­least­squares­with­ reject­option”,­Talanta80,­321­(2009).­doi:­

https://doi.org/10.1016/j.talanta.2009.06.072

31.­J.E.­Jackson­and­G.S.­Mudholkar,­“Control­proce -dures­for­residuals­associated­with­principal­com -ponent­analysis”,­Technometrics21,­341­(1979).­doi:­

32.­ASTM­D7611­/­D7611M-13e1,­Standard Practice for Coding Plastic Manufactured Articles for Resin Identification.­ASTM­International,­ West­Conshohocken,­PA,­USA­(2013).­

https://www.astm.org

33.­D.­Ballabio,­F.­Grisoni­and­R.­Todeschini,­ “Multivariate­comparison­of­classifica

-tion­performance­measures”,­Chemometr.

Intell. Lab. Syst.174,­33­(2018).­doi:­

https://doi.org/10.1016/j.chemolab.2017.12.004

34.­K.A.­Lê­Cao,­S.­Boitard­and­P.­Besse,­“Sparse­PLS­ discriminant­analysis:­biologically­relevant­feature­ selection­and­graphical­displays­for­multiclass­ problems”,­BMC bioinformatics12,­253­(2011).­doi:­

https://doi.org/10.1186/1471-2105-12-253

35.­E.­Szymańska,­E.­Brodrick,­M.­Williams,­A.N.­Davies,­

H.J.­van­Manen­and­L.M.­Buydens,­“Data­size­reduc

-tion­strategy­for­the­classification­of­breath­and­air­ samples­using­multicapillary­column-ion­mobility­ spectrometry”,­Anal. Chem.87(2),­869­(2015).­doi:­

https://doi.org/10.1021/ac503857y

36.­R.­Calvini,­A.­Ulrici­and­J.M.­Amigo,­“Practical­ comparison­of­sparse­methods­for­classifica -tion­of­Arabica­and­Robusta­coffee­species­ using­near­infrared­hyperspectral­imaging”,­

Chemometr. Intell. Lab. Syst.146,­503­(2015).­doi:­

https://doi.org/10.1016/j.chemolab.2015.07.010

37.­P.­Filzmoser,­M.­Gschwandtner­and­V.­Todorov,­

“Review­of­sparse­methods­in­regression­and­ classification­with­application­to­chemo -metrics”,­J. Chemometr.26,­42­(2012).­doi:­

https://doi.org/10.1002/cem.1418

38.­M.A.­Rasmussen­and­R.­Bro,­“A­tutorial­on­ the­Lasso­approach­to­sparse­modeling”,­

Chemometr. Intell. Lab. Syst.119,­21­(2012).­doi:­

https://doi.org/10.1016/j.chemolab.2012.10.003

39.­R.­Calvini,­J.M.­Amigo­and­A.­Ulrici,­“Transferring­ results­from­NIR-hyperspectral­to­NIR-multispectral­ imaging­systems:­a­filter-based­simulation­applied­to­ the­classification­of­Arabica­and­Robusta­green­cof -fee”,­Anal. Chimica Acta967,­33­(2017).­doi:­https:// doi.org/10.1016/j.aca.2017.03.011

Highlighting­Young­Investigators

In­this­series­we­are­highlighting­the­contributions­of­young­researchers­who­are­leading­exciting­new­research­ paths­in­Spectral­Imaging.­Contributors,­primarily­PhD­students­or­Postdoctoral­researchers­under­the­age­of­40,­ are­selected­by­the­editorial­board,­based­on­having­published­or­presented­substantially­novel­research­in­Spectral­ Imaging.­Nominations­will­be­accepted­and­should­include­a­statement­(no­longer­than­one­page)­on­the­researcher’s­

novel­research­in­Spectral­Imaging,­along­with­a­CV.­Please­send­nominations­to­JSI’s­Editor-in-Chief,­Aoife­Gowen­

([email protected]).

Dr Rosalba Calvini­was­born­in­Genova­(Italy)­in­1988.­She­obtained­her­PhD­(cum­laude)­

in­Agri-Food­Sciences­Technologies­and­Biotechnologies­in­2017,­defending­a­thesis­titled­ “Chemometric­tools­for­food­characterization­through­RGB­and­hyperspectral­imaging”.­ Since­2017,­she­has­been­a­post-doctoral­researcher­at­the­Department­of­Life­Sciences,­ University­of­Modena­and­Reggio­Emilia. Her­research­interests­include­the­application­and­development­of­chemometric­algo -rithms­for­hyperspectral­and­digital­image­analysis­with­a­focus­on­variable­selection­and­ data­dimensionality­reduction,­the­use­of­spectroscopy­(mainly­NIR­spectroscopy)­for­the­ characterisation­of­raw­materials­or­complex­food­matrices,­and­the­application­of­data­fusion­strategies­for­the­joint­ analysis­of­data­deriving­from­different­analytical­instrumentations. She­has­co-authored­multiple­papers­in­international­peer-reviewed­scientific­journals­and­presented­the­results­of­ her­research­activities­in­several­national­and­international­conferences.­She­has­been­involved­in­teaching­chemo -metrics­applied­to­image­analysis­in­PhD­and­professional­courses.­She­has­been­co-supervisor­of­multiple­thesis­for­ the­MSc­in­Food­Control­and­Security­(University­of­Modena­and­Reggio­Emilia)­and­of­one­PhD­thesis­in­Agri-Food­ Sciences,­Technologies­and­Biotechnologies.