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Tomomi Akiyama, [Naoya Miyauchi](https://orcid.org/0000-0002-7716-3049), [Akiko N. Itakura](https://orcid.org/0000-0001-5783-141X), Takayuki Yamagishi, Satoka Aoyagi

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[Fusion data analysis of imaging data of hydrogenpermeated steel obtained by complementary methods](https://mdr.nims.go.jp/datasets/3485bda1-84ab-4830-ac75-02961ce1a6b1)

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Fusion data analysis of imaging data of hydrogen-permeated steel obtained by complementary methodsJ. Vac. Sci. Technol. B 38, 034007 (2020); https://doi.org/10.1116/6.0000009 38, 034007© 2020 Author(s).Fusion data analysis of imaging data ofhydrogen-permeated steel obtained bycomplementary methodsCite as: J. Vac. Sci. Technol. B 38, 034007 (2020); https://doi.org/10.1116/6.0000009Submitted: 21 January 2020 . Accepted: 23 March 2020 . Published Online: 14 April 2020Tomomi Akiyama,  Naoya Miyauchi,  Akiko N. Itakura, Takayuki Yamagishi, and  Satoka AoyagiCOLLECTIONSPaper published as part of the special topic on Special Topic Collection on Secondary Ion Mass Spectrometry (SIMS)ARTICLES YOU MAY BE INTERESTED INImprovement of ionization yield in sputtered neutral mass spectrometry using pulsed infraredand ultraviolet lasersJournal of Vacuum Science & Technology B 38, 034011 (2020); https://doi.org/10.1116/6.0000088Structural analysis of organic ultrathin-layer by using Ar-gas-cluster ion beam sputtercollecting methodJournal of Vacuum Science & Technology B 38, 034003 (2020); https://doi.org/10.1116/6.0000102Absorption, discharge, and internal partitioning behavior of hydrogen in the tantalum andtantalum oxide system investigated by in situ oxidation SIMS and ab initio calculationsJournal of Vacuum Science & Technology B 38, 034008 (2020); https://doi.org/10.1116/6.0000100https://images.scitation.org/redirect.spark?MID=176720&plid=1344534&setID=376421&channelID=0&CID=471725&banID=520306763&PID=0&textadID=0&tc=1&type=tclick&mt=1&hc=65f03fe99fb42a03e1a855f4f38971423ab72480&location=https://doi.org/10.1116/6.0000009https://doi.org/10.1116/6.0000009https://avs.scitation.org/author/Akiyama%2C+Tomomihttp://orcid.org/0000-0002-7716-3049https://avs.scitation.org/author/Miyauchi%2C+Naoyahttp://orcid.org/0000-0001-5783-141Xhttps://avs.scitation.org/author/Itakura%2C+Akiko+Nhttps://avs.scitation.org/author/Yamagishi%2C+Takayukihttp://orcid.org/0000-0001-7100-7179https://avs.scitation.org/author/Aoyagi%2C+Satoka/topic/special-collections/jvbsims2020?SeriesKey=jvbhttps://doi.org/10.1116/6.0000009https://avs.scitation.org/action/showCitFormats?type=show&doi=10.1116/6.0000009http://crossmark.crossref.org/dialog/?doi=10.1116%2F6.0000009&domain=avs.scitation.org&date_stamp=2020-04-14https://avs.scitation.org/doi/10.1116/6.0000088https://avs.scitation.org/doi/10.1116/6.0000088https://doi.org/10.1116/6.0000088https://doi.org/10.1116/6.0000088https://avs.scitation.org/doi/10.1116/6.0000102https://avs.scitation.org/doi/10.1116/6.0000102https://doi.org/10.1116/6.0000102https://doi.org/10.1116/6.0000102https://avs.scitation.org/doi/10.1116/6.0000100https://avs.scitation.org/doi/10.1116/6.0000100https://doi.org/10.1116/6.0000100https://doi.org/10.1116/6.0000100Fusion data analysis of imaging data ofhydrogen-permeated steel obtained bycomplementary methodsCite as: J. Vac. Sci. Technol. B 38, 034007 (2020); doi: 10.1116/6.0000009View Online Export Citation CrossMarkSubmitted: 21 January 2020 · Accepted: 23 March 2020 ·Published Online: 14 April 2020Tomomi Akiyama,1 Naoya Miyauchi,2 Akiko N. Itakura,2 Takayuki Yamagishi,1 and Satoka Aoyagi1,a)AFFILIATIONS1Faculty of Science and Technology, Seikei University, 3-3-1 Kichijoji-Kitamachi, Musashino-shi, Tokyo 180-8633, Japan2Surface Physics and Characterization Group, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047,JapanNote: This paper is part of the 2020 Special Topic Collection on Secondary Ion Mass Spectrometry, SIMS.a)Electronic mail: aoyagi@st.seikei.ac.jpABSTRACTChemical imaging, such as mass imaging, provides a distribution image of a particular matter and is crucial for analyzing the chemical andphysical mechanisms of a sample. However, methods that provide molecular or elemental distribution do not always have sufficiently highspatial resolution to evaluate the nanosized structures in a sample. To address this issue, a multimodal data analysis method was developedby integrating the obtained low spatial resolution chemical images with complementary methods. In this study, the hydrogen distribution ofa steel sample was measured using electron stimulated desorption (ESD) and scanning electron microscopy (SEM). ESD provided the time-course images of hydrogen distribution in the steel sample, whereas SEM provided the outline of the steel sample structure. The multimodalimages of the same sample were fused, and then all the data were analyzed together to extract detailed physical and chemical informationthat cannot be observed by only one of the methods. The alignment of the images obtained using different methods was evaluated based onthe minimization of each pixel subtraction. Three different data analysis methods, principal component analysis, least absolute shrinkageand selection operator, and autoencoder, are applied to the image fusion dataset of the ESD image and SEM images to help elucidate thehydrogen permeation behavior through the steel structure.© 2020 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1116/6.0000009I. INTRODUCTIONMultiple analysis methods such as molecular or elementalmapping and crystal structure analysis are often required to charac-terize samples that have complex structures and features. Theresults from different methods occasionally have different dataformats, which make it difficult to interpret. Therefore, it is neces-sary to develop a data analysis method for the evaluation of multi-modal datasets. In our previous study on multimodal data,1time-of-flight secondary ion mass spectrometry (TOF-SIMS) datacontaining chemical images with a resolution of several hundrednanometers and microscope image data were fused. The fusiondata were analyzed via principal component analysis (PCA) toobtain PCA score images with a higher spatial resolution and PCAloadings with detailed spectrum information. The PCA loadings ofthe image fusion data were almost the same as those of theTOF-SIMS data, which implies that the chemical information pro-vided by TOF-SIMS is preserved after the fusion of image data withother measurement method data. The analysis of the image fusiondata provides more information than that obtained using onesingle analysis method. In this study, modified image data fusionprocedures were developed, and the image fusion dataset was ana-lyzed using PCA, the least absolute shrinkage and selection opera-tor (LASSO), and autoencoder. LASSO, which is a sparse modelingmethod,2 was employed to directly search for chemical imagessimilar to a higher lateral resolution microscopic image, whileautoencoder, an unsupervised artificial neural network method,3ARTICLE avs.scitation.org/journal/jvbJ. Vac. Sci. Technol. B 38(3) May/Jun 2020; doi: 10.1116/6.0000009 38, 034007-1© Author(s) 2020https://doi.org/10.1116/6.0000009https://doi.org/10.1116/6.0000009https://www.scitation.org/action/showCitFormats?type=show&doi=10.1116/6.0000009http://crossmark.crossref.org/dialog/?doi=10.1116/6.0000009&domain=pdf&date_stamp=2020-04-14http://orcid.org/0000-0002-7716-3049http://orcid.org/0000-0001-5783-141Xhttp://orcid.org/0000-0001-7100-7179mailto:aoyagi@st.seikei.ac.jphttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/https://doi.org/10.1116/6.0000009https://avs.scitation.org/journal/jvbwas used to classify fusion data. Autoencoder is capable of classify-ing fusion datasets into more detailed categories, as compared toPCA. The data analysis results of individual method data werecompared with that of the fusion data to evaluate the effects ofimage data fusion.Images obtained using various surface analysis techniques canbe integrated as one dataset. In this study, the time-course imagesof hydrogen distribution in a steel sample obtained using electronstimulated desorption (ESD),4 which is one of the desorptioninduced by electronic transition5 methods, and the same sampleimage obtained using scanning electron microscopy (SEM) werefused as one dataset. It is important to observe hydrogen adsorp-tion and permeation through the crystals in the steel sample tounderstand the hydrogen embrittlement of steels,6,7 although theobservation of hydrogen, which is the lightest element, is generallydifficult. ESD provides a two-dimensional distribution of hydrogenadsorbed on the steel surface by scanning an electron beam.8However, the spatial resolution of ESD is insufficient for observingcrystal structures in steel samples. In contrast, SEM (Ref. 9) pro-vides nanoscale distribution images and detailed crystal structures.Therefore, an image data fusion method for the multimodal data ofa hydrogen flowing steel sample obtained via ESD and SEM imageswas developed to obtain hydrogen specific distributions with suffi-ciently high spatial resolution for identifying the differencesbetween crystal structures.II. EXPERIMENTA. Electron stimulated desorptionStainless steel (SUS304) with dislocation was used as thesample for measuring the time-course images of hydrogen distribu-tion with an ESD system built in the SEM (JAMP10, JEOL, Tokyo)equipment.7 The sample SUS304 steel has an austenitic phasebefore cold-working, and a part of austenite grains is transformedinto martensite by cold-working (cold-rolled 10%). Hydrogen gas(deuterium 99.96%) at 1 atm was supplied to the backside of thesample membrane (steel with a thickness of 100 μm), which pene-trates the sample and reaches the surface. The ESD pattern ofhydrogen reflects the density of dislocations in martensite causedby lathe processing on the austenite steel surface. The electronenergies used in SEM and ESD were 3 and 1 keV, respectively.The measurement area of the sample SUS304 steel was330 μm (vertical) × 520 μm (horizontal), and the size of originalpixels for the whole measurement area was 2048 × 2048 pixels. Thepixel size of ESD hydrogen images was reduced to 64 × 64 pixels toincrease the number of ions per pixel. The time-course images ofhydrogen distribution and an SEM image were used for image datafusion. The resolution of the SEM was 2000 × 2000 pixels, whereasthe resolution of hydrogen image data was set to 64 × 64 pixels. Atotal of 13 ESD hydrogen images were obtained at the interval of5 h ranging from 0 to 65 h.B. Image data fusionThe image fusion programs were written in MATLAB(Mathworks, MA, USA). An SEM image and ESD total image(accumulating signals for 65 h) of almost the same area of the samesample were used for the image data fusion alignment. The mea-sured area of the sample was 330 μm (vertical) × 520 μm (horizon-tal). Because these two images were slightly different, the SEMimage was rotated several degrees to align with the ESD image.Next, the SEM image was trimmed so that the rotated SEM imagewas almost perfectly aligned with the ESD image. If necessary, theESD image can also be trimmed to align with the SEM imagebecause the trimmed SEM image could sometimes be smaller thanthe ESD image. Subsequently, the resolutions of the trimmed SEMand ESD images were resized to 250 × 250 pixels. The pixel sizewas changed using MATLAB (Mathworks, Inc., Natick, MA, USA)command, imresize. Finally, the intensity difference at each pixel ofthe SEM and ESD images was calculated, and the total intensitydifference was obtained. If both images were exactly the same, thetotal intensity difference should be zero. Thus, the rotation andtrimming procedures were repeated until the smallest total differ-ence was obtained. This was the final image that had the smallesttotal intensity difference at every pixel.C. Principal component analysisAutoscaling (the dataset is initially mean-centered and subse-quently divided by the standard deviation) was applied to theimage fusion data before PCA. PLS Toolbox (Eigenvector ResearchInc., WA, USA)10 working on MATLAB (Mathworks, MA, USA) wasused for PCA. The intensity of the SEM or the fluorescent micro-scopic image was added as a new variable to the variables of theESD hydrogen time-course image data. PCA was performed usingthe matrix data of the ESD and the fusion data of ESD and SEM.D. Least absolute shrinkage and selection operatorLASSO (Ref. 2) was used to identify appropriate solutions byminimizing the error between a target and solutions. Moreover, theL1 norm (sum of the absolute values of the intensity) of the solu-tions was used. The solutions were obtained by minimizing E, asexpressed in the following equation:E ¼ kY –Axk2 þ λXjxij: (1)In this equation, the vector Y is the target. The vector Y corre-sponds to the SEM image that is exactly aligned with the targetdata A, the ESD hydrogen time-course images. The vector x, whichprovides the minimum value of E in Eq. (1), was identified usingLASSO.2The first term in the right-hand side of Eq. (1) is the squareerror between Y and candidate solutions, and the second term con-tains an L1 norm and a hyper parameter λ, which depends on thesparsity contribution. The greater the value of λ, the more impor-tant is the sparsity. This parameter controls whether to prioritizethe reduction of the square error or the L1 norm. For example, inmatrix A (the ESD time-course images), the number of rows is thenumber of observation points (pixels), and the number of columnsis the number of time-courses. For the analysis, the machine learn-ing package for group LASSO11–13—PYTHON 3—was employed.ARTICLE avs.scitation.org/journal/jvbJ. Vac. Sci. Technol. B 38(3) May/Jun 2020; doi: 10.1116/6.0000009 38, 034007-2© Author(s) 2020https://avs.scitation.org/journal/jvbE. AutoencoderThe autoencoder system by Deep Learning Toolbox forMATLAB (Mathworks, MA, USA) has three layers comprising aninput layer, a hidden layer, and an output layer. Log-sigmoid wasemployed as a transfer function. The input data were encoded tothe hidden layer to extract the essential features of the input data.The size of the hidden layer was set by an analyst. Both datasets ofthe ESD images and the fusion of the ESD and the SEM imageswere analyzed by the autoencoder, and the extracted featuresdescribed in the hidden layer were compared with PCA results.III. RESULTS AND DISCUSSIONA. Image data fusion and PCAThe ESD image of hydrogen permeating through the steelsample for 65 h was used for the image data fusion with an SEMimage. The resolution of both images was adjusted to 250 × 250pixels, and the final size of the SEM image fused with the ESDimages was 316 μm (vertical) × 480 μm (horizontal). Table I liststhe principal component loadings and times of the ESD data indescending order, and Fig. 1 shows the principal component scoreimages. In the PCA results of ESD time-course hydrogen imagedata, the contribution ratios for principal components (PCs) 1, 2,and 3 are 61.02%, 7.79%, and 4.63%, respectively, which indicatesthat PC1 has the most information on the ESD data. The brightdistributions in the PC1 score image in Fig. 1(a) correspond to thehydrogen distribution at the final time, and the bright distributionsin the PC2 score image in Fig. 1(b) correspond to the hydrogendistribution at the initial time. Useful information was not obtainedfrom PC3.In the PCA results of ESD and SEM fusion data, as shown inTable II and Fig. 2, the contribution ratios of PCs 1, 2, and 3 were57.16%, 7.62%, and 6.29%, respectively. PC1 has most of the datainformation as well. The bright distributions in the PC1 scoreTABLE I. PCA loadings of ESD data.PC1 (61.02%) PC2 (7.79%) PC3 (4.63%)LoadingTime ofESDdata (h) LoadingTime ofESDdata (h) LoadingTime ofESDdata (h)0.304 31 60–65 0.635 88 0–5 0.735 60 0–50.302 90 50–55 0.487 12 5–10 0.119 02 60–650.302 04 45–50 0.304 75 10–15 0.092 01 45–500.300 8 40–45 0.196 98 15–20 0.078 74 55–600.300 06 55–60 0.041 50 20–25 0.063 04 40–450.298 60 35–40 −0.000 51 25–30 0.062 11 35–400.296 89 30–35 −0.063 53 30–35 0.058 84 50–550.285 65 25–30 −0.089 53 35–40 −0.015 04 30–350.282 60 20–25 −0.168 03 40–45 −0.017 31 25–300.263 50 15–20 −0.198 14 45–50 −0.047 11 20–250.238 95 10–15 −0.206 55 50–55 −0.211 72 15–200.215 82 5–10 −0.212 92 60–65 −0.397 33 5–100.178 98 0–5 −0.239 64 55–60 −0.461 87 10–15FIG. 1. PCA score images of ESD data: (a) PC1, (b) PC2, and (c) PC3. The color scale bars show the PCA scores.TABLE II. PCA loadings of fusion data.PC1 (57.16%) PC2 (7.62%) PC3 (6.29%)LoadingTime ofESD data(h) LoadingTime ofESD data LoadingTime ofESD data(h)0.3024 60–65 h 0.5363 0–5 h 0.8357 SEM0.3010 50–55 h 0.5329 SEM 0.1155 55–60 h0.3003 45–50 h 0.4045 5–10 h 0.0845 45–50 h0.2990 40–45 h 0.2183 10–15 h 0.0801 60–65 h0.2984 55–60 h 0.1450 15–20 h 0.0712 50–55 h0.2972 35–40 h 0.0218 20–25 h 0.0544 40–45 h0.2955 30–35 h −0.0065 25–30 h 0.0439 35–40 h0.2844 25–30 h −0.0605 30–35 h 0.0286 30–35 h0.2813 20–25 h −0.0821 35–40 h −0.0035 25–30 h0.2624 15–20 h −0.1638 40–45 h −0.0416 20–25 h0.2378 10–15 h −0.1825 45–50 h −0.1444 15–20 h0.2154 5–10 h −0.1980 50–55 h −0.2463 10–15 h0.1790 0–5 h −0.2012 60–65 h −0.2677 5–10 h0.0989 SEM −0.2130 55–60 h −0.3301 0–5 hARTICLE avs.scitation.org/journal/jvbJ. Vac. Sci. Technol. B 38(3) May/Jun 2020; doi: 10.1116/6.0000009 38, 034007-3© Author(s) 2020https://avs.scitation.org/journal/jvbimage correspond to the hydrogen distribution at the final time,the same as the PCA results of the ESD data, and the dark distribu-tions in the PC2 score image correspond to the SEM image. ThePCA score images of the fusion data have a higher spatial resolu-tion compared with the ESD data. The bright distributions in PC2correspond to the SEM image and the hydrogen distribution at theinitial time. In PC3, the PCA score image of the fusion data has ahigher spatial resolution than that of the ESD data and more usefulinformation than that of the ESD data. The bright distributions inthe PC3 score image (Fig. 2) correspond to the SEM image and thehydrogen distribution at the final time, and the dark distributionsin the PC3 score image correspond to the times when the ring-shape prominently appears at the left side.B. LASSO and autoencoderIn LASSO, the solution Y in Eq. (1) was the SEM image witha higher spatial resolution than the ESD images. The same ESDtime-course images for PCA, with resolution adjusted to 250 × 250pixels, were used as the data matrix X in Eq. (1). Group LASSOwas employed in this study because a conventional LASSO methodsometimes excludes some important variables. All the variables inthe ESD time-course images were separately classified for groupLASSO to select every single variable if necessary. When the regula-tion parameter λ in Eq. (1) was 2.8 and the learning rate for thegradient method was 0.03, LASSO suggested that the ESD imagesFIG. 3. SEM image (a) and hydrogen distribution images at 30–35 h (b), 35–40 h (c), and 25–30 h (d), as chosen by LASSO.FIG. 2. PCA score images of ESD and SEM fusion data: (a) PC1, (b) PC2, and (c) PC3. The color scale bars show the PCA scores.FIG. 4. Autoencoder results of ESD data: (a) encoder weight No. 1, (b) encoder weight No. 2, (c) encoder weight No. 3, (d) encoder weight No. 4, and (e) encoder weightNo. 5. The color scale bars show the intensity of the encoded ESD data images.ARTICLE avs.scitation.org/journal/jvbJ. Vac. Sci. Technol. B 38(3) May/Jun 2020; doi: 10.1116/6.0000009 38, 034007-4© Author(s) 2020https://avs.scitation.org/journal/jvbobserved in 30–35 h, 35–40 h, and 25–30 h (Fig. 3) corresponded tothe SEM image. It can be inferred that in these intermediate timeshydrogen was stably flowing through the steel structures, asroughly shown by SEM. This information is useful for estimatinghydrogen diffusion mechanisms in a sample having multiple crystalstructures.The ESD and SEM fusion data were also analyzed using theautoencoder. Figure 4 and Table III summarize the autoencoderresults of ESD data, and Fig. 5 and Table IV summarize the resultsof the ESD and SEM fusion data. The variables in Tables III and IV,such as time and SEM intensity, corresponding to each encoderweight were sorted in descending order. In both cases of the ESDdata analysis and fusing data analysis, additional information wasextracted by autoencoder than by PCA. The features of the imagedata were extracted with a higher spatial resolution by the image datafusion with SEM. For example, although PCA indicated the uniquering-shape hydrogen distribution on the left side of PC1 images inFigs. 1 and 2, the times specific to this distribution could not be sug-gested because PC1 also includes other factors. In contrast, theimages of encoder weight No. 5 in Fig. 5 clearly show the ring-shapehydrogen distribution without other factors and indicate that theinitial times, from 0 to 10 h, are directly related to this distribution.This suggests that hydrogen from this area permeates more rapidlythan from other areas.All trends obtained from the PCA results were also obtainedusing the autoencoder; however, the PCA results did not containall information indicated by the autoencoder. For example, thefactors regarding the ring-shape distribution were specified only bythe autoencoder. While PCA extracted the rough features of thedatasets, the autoencoder extracted additional specific features. Inaddition, the times corresponding to the prominent features of thesample were shown directly so that more detailed interpretationcould be possible by the autoencoder.From these results suggested by the PCA and autoencoder ofthe fusion data, it is evident that the image fusion data analysis canprovide information on hydrogen permeation, depending on theparticular structure of the steel. Although further studies areneeded to characterize the detailed structure of the ring-shape area,the fusion data clearly indicate important areas for clarifyinghydrogen permeation through steel. In the absence of this type ofinformation, it is difficult to determine the areas that need to beanalyzed in detail. The measurement area for the method providingnanoscale crystal structures is limited; therefore, it is important toidentify important areas for further investigation.TABLE III. Encoder weights for ESD data analysis by the autoencoder.No. 1 No. 2 No. 3 No. 4 No. 5EncoderweightTime(h)EncoderweightTime(h)EncoderweightTime(h)EncoderweightTime(h)EncoderweightTime(h)0.972 60–65 1.326 55–60 0.545 10–15 0.913 35–40 0.923 40–450.651 45–50 0.594 25–30 0.499 5–10 0.883 50–55 0.353 25–300.560 50–55 0.539 40–45 0.293 0–5 0.528 55–60 0.167 35–40−0.196 40–45 0.224 35–40 0.237 30–35 0.217 40–45 0.142 15–20−0.249 30–35 0.039 60–65 0.220 45–50 0.129 15–20 0.133 0–5−0.339 25–30 −0.050 20–25 0.056 20–25 −0.032 30–35 0.099 60–65−0.346 55–60 −0.071 0–5 0.054 15–20 −0.197 10–15 0.093 20–25−0.460 20–25 −0.319 5–10 −0.040 55–60 −0.351 5–10 0.0706 5–10−0.491 0–5 −0.332 15–20 −0.130 25–30 −0.388 0–5 −0.164 50–5−0.692 10–15 −0.341 10–15 −0.404 60–65 −0.423 20–25 −0.189 10–15−0.702 15–20 −0.667 45–50 −0.459 50–55 −0.899 45–50 −0.334 30–35−0.778 5–10 −0.782 30–35 −0.960 35–40 −1.135 25–30 −0.668 45–50−0.821 35–40 −2.232 50–55 −1.662 40–45 −1.707 60–65 −2.158 55–60FIG. 5. Autoencoder results of ESD and SEM fusion data: (a) encoder weight No. 1, (b) encoder weight No. 2, (c) encoder weight No. 3, (d) encoder weight No. 4, and(e) encoder weight No. 5. The color scale bars show the intensity of the encoded ESD and SEM fusion data images.ARTICLE avs.scitation.org/journal/jvbJ. Vac. Sci. Technol. B 38(3) May/Jun 2020; doi: 10.1116/6.0000009 38, 034007-5© Author(s) 2020https://avs.scitation.org/journal/jvbIV. SUMMARY AND CONCLUSIONSIn conclusion, it has been demonstrated that different types ofinformation can be extracted depending on the data analysismethod, although all the methods employed in this study, such asPCA, LASSO, and autoencoder, were useful for interpreting thetime-course images of the hydrogen distribution in the steel sampleobtained by the ESD. The analysis results obtained from LASSOindicated the dependence of hydrogen permeation on the steelcrystal structure as shown by SEM, and the fusion data analysis byautoencoder indicated unique areas for hydrogen permeation. Theimage data fusion of multiple methods is powerful for the extrac-tion of additional information, as compared to a single method.ACKNOWLEDGMENTSThis work was partly supported by a JSPS KAKENHI (GrantNo. JP 18H03849) and JST-Mirai Program (Grant No. JPMJMI18A3).REFERENCES1K. Takahashi, T. Yamagishi, S. Aoyagi, D. Aoki, K. Fukushima, and Y. Kimura,J. Vac. Sci. Technol. B 36, 03F113 (2018).2I. Rish and G. Ya. Grabarnik, Sparse Modeling (CRC, Boca Raton, 2015).3S. A. Thomas, A. M. Race, R. T. Steven, I. S. Gilmore, and J. Bunch,“Dimensionality reduction of mass spectrometry imaging data using autoen-coders,” in 2016 IEEE Symposium Series on Computational Intelligence (SSCI)(IEEE, New York, 2016).4T. E. Madey and J. T. Yates, Jr, J. Vac. Sci. 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Encoder weights of ESD and SEM fusion data.No. 1 No. 2 No. 3 No. 4 No. 5EncoderweightTime (h)or SEMEncoderweightTime (h)or SEMEncoderweightTime (h)or SEMEncoderweightTime (h)or SEMEncoderweightTime (h)or SEM1.094 5–10 1.608 5–10 1.706 10–15 0.318 55–60 0.913 0–50.191 10–15 1.021 0–5 0.957 0–5 0.270 60–65 0.820 5–100.101 15–20 0.076 45–50 0.236 15–20 0.267 50–55 0.713 10–15−0.027 50–55 0.065 60–65 0.134 5–10 0.201 45–50 0.563 15–20−0.042 40–45 0.044 40–45 −0.157 20–25 0.058 40–45 0.362 20–25−0.051 55–60 −0.094 55–60 −0.195 SEM 0.025 35–40 0.353 50–55−0.095 30–35 −0.160 50–55 −0.271 25–30 −0.059 0–5 0.306 60–65−0.154 45–50 −0.168 35–40 −0.515 30–35 −0.086 30–35 0.280 35–40−0.196 60–65 −0.443 30–35 −0.719 35–40 −0.099 25–30 0.276 45–50−0.277 25–30 −0.529 SEM −0.901 50–55 −0.183 20–25 0.259 55–60−0.302 35–40 −0.675 20–25 −0.936 60–65 −0.294 10–15 0.256 30–35−0.384 20–25 −0.684 25–30 −0.967 40–45 −0.844 SEM 0.217 40–45−0.562 SEM −0.722 15–20 −1.019 55–60 −1.071 15–20 0.186 25–30−5.025 0–5 −3.883 10–15 −1.047 45–50 −4.549 5–10 −3.764 SEMARTICLE avs.scitation.org/journal/jvbJ. Vac. Sci. Technol. B 38(3) May/Jun 2020; doi: 10.1116/6.0000009 38, 034007-6© Author(s) 2020https://doi.org/10.1116/1.5013218https://doi.org/10.1116/1.1315200https://doi.org/10.1016/j.apsusc.2019.06.172https://doi.org/10.1038/s41529-019-0074-5https://doi.org/10.1038/s41529-019-0074-5https://doi.org/10.1016/j.scriptamat.2017.09.026https://doi.org/10.3131/jvsj2.57.23https://doi.org/10.3131/jvsj2.57.23https://doi.org/10.1088/1742-6596/644/1/012016https://doi.org/10.1002/sia.5731https://doi.org/10.1002/sia.5731https://doi.org/10.1111/j.1467-9868.2005.00532.xhttps://doi.org/10.1111/j.1467-9868.2007.00627.xhttps://avs.scitation.org/journal/jvb Fusion data analysis of imaging data of  hydrogen-permeated steel obtained by complementary methods I. INTRODUCTION II. EXPERIMENT A. Electron stimulated desorption B. Image data fusion C. Principal component analysis D. Least absolute shrinkage and selection operator E. Autoencoder III. RESULTS AND DISCUSSION A. Image data fusion and PCA B. LASSO and autoencoder IV. SUMMARY AND CONCLUSIONS References