Imaging mass cytometry of full tissue samples.

Frozen tissues from a single DFU, tonsil, or prostate biopsy (n = 1 each) were sectioned serially at a thickness of 10 m using a Microm HM550 cryostat (Thermo Scientific) and thaw-mounted onto SuperFrost^TM Plus Gold charged microscopy slides (Fisher Scientific). After temperature equilibration to room temperature, tissue sections were fixed in 4% paraformaldehyde (Ted Pella) for 10 min, then rinsed 3 times with cytometry-grade phosphate-buffered saline (PBS) (Fluidigm). Unspecific binding sites were blocked using 5% bovine serum albumin (BSA) (Sigma Aldrich) in PBS including 0.3% Triton X-100 (Thermo Scientific) for 1 hour at room temperature. Metal conjugated primary antibodies (Fluidigm) at appropriately titrated concentrations were mixed in 0.5% BSA in DPBS and applied overnight at 4 °C in a humid chamber. Sections were then washed twice with PBS containing 0.1% Triton X-100 and counterstained with iridium (Ir) intercalator (Fluidigm) at 1:400 in PBS for 30 min at room temperature. Slides were rinsed in cytometry-grade water (Fluidigm) for 5 min and allowed to air dry. Data acquisition was performed using a Hyperion Imaging System (Fluidigm) and CyTOF Software (Fluidigm), in 33 channels, at a frequency of 200 pixels/second and with a spatial resolution of 1 m. Images were visualized with MCD Viewer software (Fluidigm) before exporting the data as text files for further analysis. After imaging, slides were rapidly stained with 0.1% toluidine blue solution (Electron Microscopy Sciences) to reveal gross morphology. Slides were digitized at a resolution of approximately 2.75 m/pixel using a digital camera.

Generation of mass spectrometry imaging data from full tissue samples.

Paired 10m thick sections from the same tissue blocks from DFU, tonsil, or prostate biopsy (n = 1 each) used for imaging mass cytometry were thaw mounted onto Indium-Tin-Oxide (ITO) coated glass slides (Bruker Daltonics). Tissue sections were coated with 2.5-dihydroxybenzoic acid (40 mg/mL in 50:50 acetonitrile:water including 0.1% TFA) with an automated matrix applicator (TM-sprayer, HTX imaging). Mass spectrometry imaging of sections was performed using a rapifleX MALDI Tissuetyper (Bruker Daltonics, Billerica, MA). Data acquisition was performed using FlexControl software (Bruker Daltonics, Version 4.0) with the following parameters: positive ion polarity, mass scan range (m/z) of 300–1000, 1.25 GHz digitizer, 50 m spatial resolution, 100 shots per pixel, and 10 kHz laser frequency. Regions of interest for data acquisition were defined using FlexImaging software (Bruker Daltonics, version 5.0), and individual images were visualized using both FlexImaging and SciLS Lab (Bruker Daltonics). After data acquisition, sections were washed with PBS and subjected to standard hematoxylin and eosin histological staining followed by dehydration in graded alcohols and xylene. The stained tissue was digitized at a resolution of 0.5 m/pixel using an Aperio ScanScope XT brightfield scanner (Leica Biosystems).

DFU mass spectrometry imaging data preprocessing.

Data for the DFU were processed in SciLS LAB 2018 using total ion count normalization on the mean spectra and peak centroiding with an interval width of mDa. For all analyses, a peak range of m/z 400–1,000 was used after peak centroiding, which resulted in 9,753 m/z peaks. No peak-picking was performed for presented data unless stated otherwise. Data were exported from SciLS Lab as imzML files for further analysis and processing.

Generation of prostate cancer TMA imaging data.

Serial 5-micron-thick FFPE sections were cut from a tissue microarray (TME) containing 1-millimeter cores of formalin-fixed- paraffin-embedded (FFPE) tissues of prostate cancer biopsy specimens. Sections were placed onto superfrost gold plus slides and stored under vacuum prior to processing.

Generation of prostate TMA imaging mass cytometry data.

For imaging mass cytometry, slides were incubated for 18 hours at 60°C and cooled to room temperature. Next, wax was removed by two 3 min xylene incubations, followed by rehydration in ethanol baths (100% 1min, 100% 1 min, 95% 1 min, 70% 1 min – diluted in ddH20). Antigen retrieval was performed using Ventana CC1 buffer in a Biocare DC2012 Decloaking chamber set to 95°C for 40 min. After cooling to 70°C, tissue was incubated in PBS for 5 min three times, followed by incubation in 3% BSA for 60 min at room temperature. Tissue sections were labeled with metal-conjugated antibodies overnight at 4°C. Following incubation, the sections were incubated at room temperature in PBS 0.2% Triton X-100 for 8 min twice, followed by wash in PBS for 8 min, and then incubated with Iridium Intercalator (1:3500) for 30 min. Following a wash for 10 sec in PBS, the slide was incubated in freshly prepared 0.00025% w/v solution of RuO4 for 3 min, and washed with ddH20 for 10 sec, prior to air drying. Individual ROIs were set for each of the 30 individual cores imaged from the TMA and acquired on a Standard Biotools Hyperion system at resolution of 1μm².

Generation of prostate TMA mass spectrometry imaging data.

For MSI imaging samples, an adjacent FFPE tissue section was deparaffinized with xylene and subjected to antigen retrieval in 100 mM Tris at pH 9 for 20 min at 95 °C using a Biocare DC2012 Decloaking chamber (Biocare Medical, Pacheco, CA, USA). Using a HTX M5 Robotic sprayer, the slide was coated with trypsin and incubated for 4 h at 37 °C. Next, a matrix composed of 10 mg/mL α-cyano-4-hydroxycinnamic acid (CHCA) matrix in 70% ACN, 0.1% TFA, 10 mM ammonium phosphate was applied with the HTX Sprayer. ROIs corresponding to the same 30 biopsy cores imaged by IMC were selected and imaged using a Bruker timsTOF fleX MALDI QTOF Mass Spectrometer with a full mass spectrum collected at every position (pixel) over the surface of the tissue section at a resolution of spatial resolution 20μm². Centroid values were used to label m/z peaks.

Prostate TMA imaging data preprocessing.

For imaging processing, multi-stack TIFF image files were exported using MCD Viewer software (Standard Biotools). To remove background and folded tissue, masks were generated in ImageJ. Extraneous channels were extracted from individual image stacks, reducing the number from 64 channels to 49 channels. To identify individual cells, images were segmented with random forest pixel classifier trained in Ilastik based on cytoplasmic channels (CD45, Calretinin) and a nuclear channel (Ir193) [66]. Probability maps from Ilastik output were saved as red, green and blue tiff files and fed into CellProfiler to generate whole-cell image masks.

No noise annotations or artifact removal steps were used. Two 250 m by 250 m cropped regions for each core were required to contain more than 5% of pixels over the previously defined threshold for training. For each core and modality, a mask outlining the contours of the image was created and transformed to the final aligned image stack. Segmentation masks from the MIAAIM CellProfiler module were obtained by identifying segmented cells contained in the intersection of these contour masks with the image masks and removing those cells touching the border.

MIAAIM implementation.

MIAAIM workflows are implemented in a Docker-containerized Python package to enable reproducible workflows and eliminate any platform-specific dependencies. MIAAIM’s output interfaces with existing image analysis software tools (see S1 Note, Combining MIAAIM with existing bioimaging software).

High-dimensional image compression and pre-processing (HDIprep).

The HDIprep module is an image preprocessing pipeline to prepare multimodal images for registration. HDIprep includes dimensionality reduction for high-parameter data and filtering and morphological operations for single-channel images. Processed images were exported as 32-bit NIfTI-1 images using the NiBabel Python library. NIfTI-1 was chosen as the default file format for many of MIAAIM’s operations due to its memory mapping feature in Python and compatibility with Elastix and ImageJ.

To reduce the dimensionality of high-parameter images, HDIprep estimates an optimal UMAP embedding dimensionality for pixel-level data. Dimension reduction is initialized with optional, spatially-guided subsampling to reduce data set size (see below). Uniform Manifold Approximation and Projection (UMAP) is then used to construct a graph representing the data manifold and its underlying topological structure [34]. UMAP aims to optimize a lower-dimensional image embedding of a high-dimensional image by generating a representative fuzzy simplicial set (i.e., a weighted, undirected graph), such that the fuzzy set cross-entropy between the embedded simplicial set and the high-dimensional counterpart is minimized.

Calculating cross-entropy scales quadratically with the number of data points, making its use for large data sets impractical. In contrast, UMAP does not compute the exact cross entropy when optimizing low-dimensional embeddings. Instead, it uses probabilistic edge sampling and negative sampling to reduce runtimes for large data sets [34]. To ensure accurate estimates of the embedding error, we compute landmarks on the data manifold that are representative of its global structure, and we use these in the calculation of the exact cross-entropy over a range of dimensionalities.

To identify representative landmarks on the data manifold, we use a variant of spectral clustering on the fuzzy simplicial set (detailed below). We iteratively project the spectral centroids into Euclidean spaces of increasing dimensionality using UMAP, and calculate the exact fuzzy set cross-entropy in each. To estimate the optimal embedding dimensionality, a least-squares exponential regression is fitted to the min-max normalized cross-entropy as a function of dimensionality; samples are then simulated along the regression line to find the first dimensionality falling within the 95% confidence interval of the exponential asymptote. The subsampled data is embedded into Euclidean space with this dimensionality, and out-of-sample pixels are projected into this embedding using the native nearest-neighbor based method in UMAP (transform () function). Finally, all pixels are mapped back to their original spatial coordinates to construct a “compressed” image with the number of channels equal to the indicated embedding dimensionality. These steps are summarized in the following sections and in pseudo-code below:

Algorithm 1: Image Compression.

Input: Multichannel image (), SVD dimensionality (), k-means clusters (), embedding dimensions

Output: Compressed image ()

function Compress

    {Subsample Pixels}

    {}

    {Compute Data Manifold}

    FuzzySimplicialSet () UMAP

    {Compute Spectral Centroids}

    RandomizedSVD ()

    MiniBatchKmeans ()

    {Compute Manifold Embedding Error}

    FuzzySimplicialSet ()

    for do

        EmbedSimplicialSet ()

        {Compute Fuzzy Set Cross Entropy}

        FuzzySetCrossEntropy ()

     Min-max Normalization

    {Estimate Embedding Dimensionality}

     Exponential Regression

    for do

        if do Model Gaussian Residual Process

           i

           break

    {Compute Pixel Embedding}

    for in do

         ProjectData () Project data (UMAP transform ())

    {Reconstruct Image}

    for do

    return

Image data subsampling. To reduce computational burden during dimension reduction, subsampling can be performed at the pixel level; this is optional depending on image size and available computational resources. Subsampling options include uniformly spaced grids, random coordinate selection, and random selection initialized with uniformly spaced grids (pseudo-random). HDIprep also supports restricting these subsampling approaches to masked sampling regions, which may be useful for large data sets.

By default, images with fewer than 50,000 pixels are not subsampled, images with 50,000–100,000 pixels are subsampled using 55% pseudo-random sampling initialized with 2x2 pixel uniformly spaced grids, images with 100,000–150,000 pixels are subsampled using 15% pseudo-random sampling initialized with 3x3 pixel grids, and images with over 150,000 pixels are subsampled with 3x3 pixel grids. These default values are based on empirical studies (S4, S5, and S6).

No subsampling was used for the presented MSI data from the DFU. Subsampling rates for presented IMC data from the DFU were determined on a case-by-case basis from empirical studies, and match those used in the spectral landmark sampling experiments. Subsampling with 10x10 pixel uniformly spaced grids was used for CyCIF data. All IMC and MSI data from prostate cancer biopsies in the TMA dataset were processed using the default parameters.

Landmark selection with spectral clustering. Spectral landmarks are identified using a variant of spectral clustering. Specifically, randomized singular value decomposition (SVD) followed by mini-batch k-means is used to scale spectral clustering to large data sets, following the procedure introduced in the PHATE algorithm [67]. Given a symmetric adjacency matrix representing pairwise similarities between nodes (in this context, pixels), we compute the eigenvectors corresponding to the largest eigenvalues. Mini-batch k-means is then performed on the nodes using these eigenvectors as features. Spectral landmarks are defined as the centroids of the resulting clusters in the original space.

By default, input data is reduced to 100 components using randomized SVD, then split into 3,000 clusters using mini-batch k-means. These default values are based on empirical studies (S7 Fig). Due to the suggested dimensionalities of embeddings of MSI and IMC data only being available after experimental tests, no landmark selection was used for processing or determining the optimal embedding dimensionality of these data sets. Instead, full or subsampled data sets were used. All other embeddings employing the dimensionality estimate for image data used the above default parameters.

UMAP embedding dimensionalities. By default, HDIprep embeds spectral landmarks into Euclidean spaces with 1–10 dimensions to identify embedding dimensionalities suggested for UMAP. Exponential regressions on the spectral landmark fuzzy set cross entropy are performed using built-in functions from the SciPy Python library. These default parameters were used for all presented data.

Image compression with UMAP parametrized by a neuronal network. We implemented parametric UMAP³⁶ using the default parameters and neural architecture with a TensorFlow backend. The default architecture was comprised of a 3-layer 100-neuron fully connected neuronal network. Training was performed using gradient descent with a batch size of 1,000 edges and the Adam optimizer with a learning rate of 0.001 [68].

Histology image preprocessing. HDIprep processing options for low-channel histological stains include image filters (e.g., median), thresholding (e.g., manually set or automated), successive morphological operations (e.g., opening and closing), and masking. Presented H&E and toluidine-blue stained images were processed using median filters to remove salt-and-pepper noise and Otsu thresholding to create a binary mask for the foreground. Sequential morphological operations were then applied to this mask, including opening to remove small, connected foreground components, closing to fill small holes, and filling to close large holes.

High-dimensional image registration (HDIreg).

HDIreg implements the open-source Elastix software [28] in conjunction with Python modules for the image resizing, padding, and trimming often applied before registration. Several different registration parameters, cost functions, and deformation models are included in Elastix; HDIreg additionally allows manual definition of point correspondences for problematic inputs, as well as composite transformations for fine-tuning (see S2 Note, Notes on the HDIreg workflow’s expected performance).

High-parameter images are registered using a manifold alignment approach, which aims to maximize image similarity. Image registration is an optimization problem to determine the smooth transformation parameters which maximize the selected similarity measure (in this case, Rényi -mutual information) between the transformed target image and a fixed reference image.

Differential geometry and manifold learning. MIAAIM’s default alignment approach uses the entropic graph-based Rényi -mutual information (-MI) [39] as similarity measure, which extends to manifold representations of images embedded in Euclidean space with potentially differing dimensionalities (e.g., UMAP pixel embeddings). This measure is justified through an intrinsic definition of the Rényi -entropy (S4 Note).

Briefly, given a Lebesgue density drawn from independent and identically distributed random vectors supported by a compact, n-dimensional Riemannian manifold, its extrinsic alpha-entropy can be approximated using continuous quasi-additive graphs, which includes k-nearest neighbor (KNN) Euclidean graphs [69], as their edge lengths asymptotically converge to the Rényi -entropy of feature distributions as the number of feature vectors increases [70].

This property leads to the convergence of KNN Euclidean edge lengths to the extrinsic Rényi -entropy of a set of random vectors with values in a compact subset of (with ) [37]. Costa and Hero [38] generalized these results to embedded manifolds by estimating an intrinsic Rényi -entropy and applied their framework along with Isomap and its variant C-Isomap for intrinsic dimensionality estimation.

In contrast to results that require all pairwise approximations for each point in the data set to estimate the -entropy, we aim to provide a similar formulation utilizing local information, following the results of our dimension reduction benchmark, which shows that local information preserving algorithms are well-suited for high-dimensional image data (see S1, S2, S3 Figs and S3 Note, HDIprep dimension reduction validation).

Entropic graph estimators on local information of embedded manifolds. Using the power-law relationship between volumes of open neighborhoods in UMAP and their embedded counterparts, we can use exponential regression to identify the dimensionality such that geodesics within open neighborhoods are preserved. KNN graph functionals calculated in this estimated embedding space provide the necessary machinery to calculate the intrinsic -entropy of embedded data manifolds in MIAAIM by applying the Beardwood-Halton-Hammersley Theorem using the induced volume measure across all coordinate patches (S4 Note, BHH).

Rényi -MI provides a quantitative measure of association between the intrinsic structure of multiple manifold embeddings constructed with the UMAP algorithm. The Rényi -MI measure extends to feature spaces of arbitrary dimensionality, which MIAAIM utilizes in combination with its image compression method to quantify similarity between optimized embeddings of image pixels in potentially differing dimensionalities.

We note that the information density of volumes of continuous regions of model families (i.e., collections of output embedding spaces or input points) have been recognized in defining an information geometry of statistical manifold learning [71]; this motivates the title of our software.

Multimodal image registration studies. Custom Python scripts were used to propagate alignment across imaging modalities. Manual landmark correspondences were used in all pairwise registrations, including full tissue alignments and within IMC-derived ROIs for the DFU, as well as for the PC TMA dataset. Using landmarks during the registration processes imparts bias to the alignment, as compared to fully unsupervised registration, by ensuring images more closely adhere to manually set correspondences across modalities. However, landmark overlap is a penalty in the optimization, rather than a strict constraint. Consequently, they guide the registration rather than forcing it to match potentially imperfect human input. All registrations involving MSI or IMC data were conducted using KNN -MI, with and 15 nearest neighbors (S4 Note, α-entropy). All registrations aligning low-channel slides (toluidine blue IMC reference and H&E) were conducted using histogram-based MI after grayscale conversion for rapid processing. All data that underwent image registration were exported and stored as 32-bit NIfTI-1 images. IMC data were not transformed and were kept in 16-bit OME-TIF (F) format.

As data acquisition removed tissue context at regions of interest on the IMC full-tissue reference image, we first aligned full tissue sections, then used the coordinates of IMC regions to extract data from all modalities for fine-tuning. Manual landmarks were used to guide both registration steps. We accounted for alignment errors around IMC regions following full-tissue registration by padding regions prior to cropping. For full-tissue images in the DFU dataset, a two-step registration process was implemented by aligning images first using an affine model, and then with a nonlinear model parametrized by B-splines. Hierarchical Gaussian smoothing pyramids were used to account for resolution differences between image modalities, and stochastic gradient descent with random coordinate sampling was used for optimization. We additionally optimized final control point grid spacings for B-spline models (MSI to H&E alignment) and the number of hierarchical levels to include in pyramidal smoothing (MSI and IMC to H&E) (S1, S2, and S3 Figs). A final control point spacing of 300 pixels for nonlinear B-spline registrations of MSI data to corresponding H&E was found to balance correct alignment with unrealistic warping, which we identified visually and by inspecting the determinants of the spatial Jacobian matrices for values that deviated substantially from 1. H&E and IMC reference tissue registrations utilized a final grid spacing of 5 pixels.

For PC TMA cores, alignment was performed similarly, with grid spacing optimized for minimal warping. Manual landmark correspondences of at least 4 set points were used to guide the registration of each modality for each core.

Benchmark study to manual alignment. MIAAIM benchmarking was performed by comparing the improvement in -MI between the IMC and MSI modalities for each prostate cancer TMA core relative to manual landmark alignment using Elastix (S9 Fig). The same set of landmarks were used in both conditions (MIAAIM versus manual landmarking alone). Manual landmark registration was performed using a multiresolution, local-to-global alignment workflow in the same fashion as MIAAIM registration, where, for each TMA core, the IMC data was registered to the corresponding H&E data and then propagated to the IMC coordinate system by composition. The optimization and alignment were performed by first aligning modalities using a rigid transformation, followed by an affine transformation, and a final B-spline alignment. The -MI was quantified on the registered IMC and MSI modalities using the KNN graph-based estimator with and 15 nearest neighbors on a 10x10 uniformly spaced grid. Pixels were only sampled from the nonzero intersection of TMA core masks after alignment with both approaches to reduce edge artifacts. The nearest-neighbor graph used to compute the -MI was built after principal component analysis (PCA) dimensionality reduction on each separate modality. The embedding dimensionality of each was determined by keeping 99% of the variation in the respective dataset.

Microenvironmental correlation network analysis.

To calculate associations across MSI and IMC modalities, we used Spearman’s correlation coefficient in the Python Scipy library. m/z peaks from MSI data with no correlations to IMC data with Bonferroni corrected P-values above 0.001 were removed from the analysis. Correlation modules were formed with hierarchical Louvain community detection using the Scikit-network package. The resolution parameter used for community detection was chosen based on the elbow point of a graph plotting resolution vs. modularity of community detection results. UMAP’s simplicial set, created with 5 nearest neighbors and the Euclidean metric, was used as input for community detection after inverse cosine transformation of Spearman’s correlation coefficients to form metric distances [72]. Line plots to visualize the average trends of MSI correlation modules to IMC parameters were computed using exponential-weighted moving averages in the Pandas library in Python after standard scaling of IMC and MSI single-cell data. MSI moving averages were additionally min-max scaled to a range of 0–1 for plotting purposes. Differential correlations of variables from MSI data and from IMC data between conditions and were weighted by the maximal absolute correlation coefficient among both conditions and then ranked, following the method of Hsu et al [73]. Statistical significance levels of differential correlations were calculated using one-sided, Bonferroni corrected z-statistics after Fisher transformation.

Single-cell segmentation (MIAAIM Probabilities and Segmentation modules).

To quantify parameters of single cells in IMC and registered MSI data within the DFU dataset, we performed cell segmentation on IMC ROIs using the pixel classification module in Ilastik (version 1.3.2) [30], which utilizes a random forest classifier for semantic segmentation. Ilastik is included in the MIAAIM software along with CellProfiler [31]. In addition, the following workflow is included outside of the noise-removal steps.

For each ROI, two 250 m by 250 m areas were cropped from IMC data and exported in the HDF5 format for use in supervised training. To ensure cropped areas were representative training samples, a global foreground threshold was calculated using Otsu thresholding on the Iridium (nuclear) stain with the Scikit-image Python library separately for each such region. Cropped regions were required to contain over 30% of pixels above their respective threshold.

Training regions were annotated for “background”, “membrane”, “nuclei”, and “noise”. Random forest classification incorporated Gaussian smoothing features, edges features (including Laplacian of Gaussian features, Gaussian gradient magnitude features, and difference of Gaussian features), and texture features (including structure tensor eigenvalues, and Hessian of Gaussian eigenvalues). The trained classifier was used to predict each pixels’ probability of assignment to the four classes in the full images, and predictions were exported as 16-bit TIFF stacks.

To remove artifacts in cell staining, noise prediction channels were Gaussian blurred with a sigma of 2 and then subjected to Otsu thresholding with a correction factor of 1.3, which created a binary mask separating foreground (high pixel probability to be noise) from background (low pixel probability to be noise). The noise mask was used to assign zero values to the other three Ilastik probability channels (nuclei, membrane, background) to all pixels that were considered foreground in the noise channel. Noise-removed, three-channel probability images of nuclei, membrane, and background were used for single-cell segmentation in CellProfiler.

Single-cell parameter quantification.

Single-cell parameter quantification for IMC and MSI data were performed using an in-house modification of the quantification (MCQuant) module in the multiple-choice microscopy software (MCMICRO) [22] to accept NIfFTI-1 files after cell segmentation. This modification is the default in MIAAIM. IMC single-cell measures were transformed using 99^th percentile normalization prior to downstream analysis. MSI data for the prostate cancer TMA were similarly transformed prior to analysis.

Imaging mass cytometry cluster analysis.

Cluster analysis was performed in Python using the Leiden community detection algorithm with the leidenalg Python package. UMAP’s simplicial set (weighted, undirected graph) created with 15 nearest neighbors and Euclidean metric was used as input to community detection.

Single-cell spatial features.

Using each segmented cell’s centroid as its spatial coordinates and Euclidean distances between cells as weights, a spatial nearest-neighbor graph was generated using Squidpy [74] by connecting each cell to its neighbors within a radius of 75 m. A Gaussian kernel over the edges of this graph was then used to normalize the weights of edges starting from each cell to the standard deviation of the distances between that cell and all its connected neighbors. To produce single-cell neighborhood scores, i.e., spatial features, normalized weights were then summed across connected cells separately for each feature in the segmented cell-by-feature matrix. This can be viewed as a spatial smoothing operator over the feature matrix for each core. These features were built for both the IMC and MSI parameters for each cell in each core.

Logistic regression and feature selection of integrated multimodal data.

Single cell MSI/IMC profiles were normalized to a mean of 0 and a standard deviation of 1 prior to analysis. Multi-class logistic regression using a one-vs-rest approach (i.e., one model trained per class) was performed with elastic net regularization using the scikit-learn package. Regularization parameters were tuned using a grid search approach. To ensure a generalizable model and reduce overfitting due to unique signatures per TMA core, we performed three-fold cross validation on the set of TMA cores instead of the set of single cells. Model performance was evaluated using class balanced accuracy. Since the input data are normalized, model coefficients for each predictor represent the contribution of that predictor on the model’s final output. This allows us to use the magnitude of model coefficients as a measure of feature importance and thereby rank the predictors. With this ranking, we trained and tested new models on subsets of ranked predictors from the single most important predictors to all predictors in increments of 50. To further refine the list of parameters, we used leave-one-out analysis to generate a set of generalized features based on accuracy degradation from the full model.