GraSP Gene Targets to Hierarchically Infer Sub-Classes with CuttleNet

GraSP Gene Targets to Hierarchically Infer Sub-Classes with CuttleNet | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results GraSP Gene Targets to Hierarchically Infer Sub-Classes with CuttleNet View ORCID Profile Samuel A. Budoff , View ORCID Profile Alon Poleg-Polsky doi: https://doi.org/10.1101/2024.04.26.591410 Samuel A. Budoff 1 Department of Physiology & Biophysics, University of Colorado Anschutz Medical Center , Denver, CO 80204 Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Samuel A. Budoff For correspondence: samuel.budoff{at}cuanschutz.edu Alon Poleg-Polsky 1 Department of Physiology & Biophysics, University of Colorado Anschutz Medical Center , Denver, CO 80204 Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Alon Poleg-Polsky Abstract Full Text Info/History Metrics Preview PDF Abstract This paper introduces a machine learning approach, GraSP, for retinal cell classification that addresses key challenges in spatial biology, alongside a novel neural network architecture, CuttleNet, tailored for class and subclass inference with incomplete datasets. We propose an innovative, unbiased gene selection method that utilizes simple neural networks for each target cell subclass, such that Gra dient S elected P redictors (GraSP) corresponding to gene importance are found for each. This approach significantly outperforms traditional machine learning techniques and expert-selected gene targets, reducing the necessary genes for classification from over 18k to 300 within the murine retina. Such reduction is crucial for advancing spatial biology, particularly in mapping retinal cell subclasses. Furthermore, our hierarchical architecture inspired by the organization of the cephalopod nervous system, CuttleNet, adeptly handles the pervasive issue of missing data in disjointed single-cell RNA sequencing datasets. CuttleNet operates by first classifying cell classes using consistently measured genes, then dynamically routing to subclass-specific subnetworks that leverage all available data for subclass classification. CuttleNet establishes a new standard in handling systematically missing data, offering substantial improvements over existing models in our targeted application. 1 Introduction Spatial biology, building on insights from single-cell RNA sequencing (scRNAseq), aims to place defined cell classes and subclasses into their spatial context. A key challenge is the discrepancy between the number of genes measurable in scRNAseq and spatial sequencing (spSeq), which we address by reducing predictor genes from 18k to 300 [ 1 ; 2 ; 3 ]. The complex spatial arrangement of retinal cells serves as an ideal case study. Retinal cell classes such as photoreceptors, bipolar cells (BCs), amacrine cells (ACs), and ganglion cells (RGCs) overlap in gene expression but can be distinguished. Subclasses can be as simple and obvious as the rods and cones dividing the photoreceptor class [ 4 ] or as complex as the 45 RGC subclasses identified by scRNAseq [ 2 ]. Critically, all of these subclasses perform distinct computational roles that enable vision. However, historic methods have only made limited progress mapping these subclasses, spSeq techniques promise to overcome this but currently either lack XYZ resolution or can measure only hundreds of genes. Solving this challenge is critical to understanding how and why distinct spatial arrangements of these computational cells evolved. 2 We bridge this gap by introducing: 1) A novel machine learning (ML) strategy for efficient gene target reduction, Gra dient S elected P redictors (GraSP), and 2) CuttleNet, a hierarchical NN architecture that addresses systematically missing observations in training datasets. GraSP enables a 60-fold reduction in gene targets needed to classify all subclasses in the murine retina, outperforming expert-chosen and standard ML tools. CuttleNet achieves state-of-the-art performance for hierarchical cell class and subclass inference, surpassing the best available supervised classifier [ 7 ]. 1.1 Related Work 1.1.1 Related Gene Selection Techniques Various ML-based classifiers are employed in transcriptomic studies for dimensionality reduction, from classic methods like Random Forests (RF) [ 1 ; 8 ], to more complex tools based on graph theory [ 9 ; 10 ], and many techniques in between [ 11 ; 12 ]. A foundation model for scRNAseq data is even being developed, but to date is currently limited to human data and excludes retinal cells [ 13 ]. For the retina specifically, the Model-based Analysis of Single-cell Transcriptomics (MAST) framework was first applied to BCs [ 1 ] by identifying differentially expressed genes to account for cellular detection rates [ 14 ]. These gene targets were then used for classification with both simple thresholds as is traditional in histology, as well as RF [ 1 ]. However, MAST was replaced for the more nuanced RGCs and ACs [ 2 ; 3 ] in favor of a method of evaluating gene combinations based on the Area Under the precision-recall curve (AUCPR), emphasizing high precision to reduce false positives in cell-type labeling [ 15 ]. We show that performance relative to these classic and modern techniques can be improved upon with our GraSP algorithm and CuttleNet architecture. Other Neural Network (NN) based strategies also treat observations as matrices of gene expression values, where each vector is associated with a cell subclass label. For example, Lin et al. [ 16 ] successfully used NNs for scRNAseq data clustering. However, their dataset contained 17k genes across 16 cell classes, relative to the 300 genes we use to classify 130 subclasses. We are limited to 300 genes due to technical limitations of the 10X’s Xenium platform at the time we developed GraSP. 1.1.2 Related Hierarchical Networks Hierarchical classification embodies the Coarse-to-Fine perceptual strategy. Projects like ThalNet [ 17 ] also draw inspiration from neuroanatomy. ThalNet uses static reading weights for temporal hierarchies, which is in contrast to the more anatomic approach we pursue here. Most related to our architecture, CellTICS leverages the Reactome gene-function map for interpretability in order to also distinguish cell classes and subclasses via supervised training with pre-labeled scRNAseq data [ 7 ]. This Reactome mapping identifies marker genes from biochemical pathways for classification. In contrast, CuttleNet employs generic sub-networks without prior biological annotation, mapping cell classes-to-subclasses by leveraging knowledge of dataset specific systemic problems like imputation. The dynamic routing we employ through tentacle-like sub-networks provides resistance to imputed values, overcoming observational discrepancies in real-world scRNAseq datasets. Our benchmarking experiments demonstrate CuttleNet’s superior performance and robustness compared to CellTICS in our limited application space. 2 Materials and Methods 2.1 Computational Resources All experiments were conducted locally using consumer-grade components including an Intel i7-12700KF CPU, an NVIDIA RTX 3060 GPU with 12 GB of vRAM, and 128 GB of RAM (comprising four 32 GB Corsair CMK64GX5M2B5200C40 modules), all mounted on an MSI Z690-A Pro motherboard. The system operated on Ubuntu 22.04. All NNs and experiments were executed locally within a Python v3.9.16 Conda environment, utilizing Jupyter Notebook v6.5.4 † as an IDE or bash commands. The primary codebase was developed using NumPy v1.24.4 † , pandas v1.5.2 † , pyreadr v0.4.7 ‡ , PyTorch v2.0.0 † , scikit-learn v1.2.1 † , and tqdm v4.64.1 § . Additionally, comparisons with standard ML approaches and further data analysis and visualization were carried out in R 4.3.3 ‡ , using the RStudio 2023.03.0 IDE ¶ , employing caret v6.0-90 ‡ , e1071 v1.7-13 ‡ , gbm v2.1.9 ‡ , ggsignif v0.6.4 || , matrixStats v1.0.0 ‡ , multcomp v1.4-18 ‡ , patchwork v1.1.3 || , randomForest v4.7-1.1 ‡ , rpart v4.1.23 ‡ , Rtsne v0.16 † , tidyverse v2.0.0 || , and umap v0.2.10.0 || . Licenses: † BSD-3-Clause License; ‡ GPL-2.0 License; § MIT License; ¶ AGPL-3.0 License; ||GPL-3.0 License. Code is available upon request prior to publication. 2.1.1 Data Preparation and Preprocessing Our dataset amalgamated data from 3 scRNAseq studies of retinal cells [ 1 ; 2 ; 3 ] available open source licensed as public data in Broad Single Cell Portal (studies SCP3, SCP509, and SCP919). Integration leveraged the log-transformed, median-normalized expression matrices computed by the original authors to account for batch effects between experiments and datasets. These studies originally contained 13166, 18222, and 17429 genes measured in 27500, 35700, and 32524 cells, respectively. To enhance computational efficiency, we pre-processed the dataset by removing genes that did not contribute meaningful information, specifically those with zero expression or those consistently expressed across all cells. Using an empirically determined threshold of 0.5 for mean expression per subclass, we defined ubiquitously expressed genes and filtered them out. This process reduced the gene set by approximately ten-fold to 1642 informative genes. Missing genes in any dataset were assigned zero values to maintain matrix dimensions across samples, with the original dataset each cell was derived from stored as metadata to keep track of zero-imputations. The original subclass assignments from each study were standardized with a two-character prefix to ensure consistency across datasets, facilitating automated cell class assignments based on expert-defined rules. The categorical cell class and subclass labels were numerically transformed utilizing Scikit-learn’s LabelEncoder in Python or R’s as.factor function. Prior to each model training, the dataset was shuffled (using a specified random state to ensure reproducibility) and divided into input features, X , and labels y . The shuffled dataset was finally split into training (80%) and test (20%) sets. 2.2 Evaluation Criteria And Cross Validation For all ML methods evaluated, we define a subclass as satisfactorily classified if they were done so with at least a value of 0.9 for both the True Positive Rate (TPR) and Precision (Prec) computed from confusion matrices on the testing dataset. For comparisons of specific classes or subclasses the F1 statistic was evaluated, again computed from the testing set. To ensure the robustness of our findings, all models and experiments included in this work were repeated five times, each with a different random seed to initialize the shuffling and subsequent calculations. These replicates allowed ANOVA testing for statistically significant differences in the models evaluated in an experiment, followed-by post-hoc Tukey HSD testing of all pairs of models/conditions, with appropriate p-value adjustment. For all plots, * indicates p<.05, ** p<.01, and *** p<.001. Standard box-plots generated in R extend whisker to largest value ≤ 1.5 * IQR. 2.3 Traditional ML-Based Gene Reduction The MAST [ 14 ] and AUCPR [ 15 ] methods were used to propose published sets of genes for classifying the 130 cells in the retina, so we evaluated these models’ outputs [ 1 ; 2 ; 3 ]. The intended use of these genes in mapping experiments is to evaluate presence/absence to classify a given subclass. In practice, many laboratory techniques require a threshold to define said presence/absence. We simulated this for a set of RGCs’ AUCPR predictors by evaluating the F1 performance with the following thresholds for gene presence/absence: 0 expression detected, 50th greater than the 50th percentile, 75th greater than 75th percentile, and 90th greater than the 90th percentile. We evaluated the overall ability for MAST and AUCPR to classify retinal subclasses by training NNs with all of the MAST proposed BC predictors[ 1 ], the AUCPR proposed RGC [ 2 ] and AC [ 3 ] predictors, and the combination of these. The NNs were of identical architecture and training protocol as the GraSP NNs described below. We also employed several standard ML models to suggest sets of 300 genes from our scRNAseq dataset to determine how many subclasses could be accurately classified with only this reduced set of predictors by said model. The classic models we investigated included: Decision Trees (DT) [ 18 ], RF [ 19 ], Gradient Boosting Machine (GBM) [ 20 ], and Support Vector Machines (SVM) [ 21 ]. Each model was first trained on the full training split. Post training, the importance of each gene was assessed to extract the top 300 genes. For DT, RF and GBM, Gini impurity was used to define the importance of a given gene. For the SVM, importance was determined by the absolute values of the coefficients in the linear kernel. These ML models were implemented in R from standard libraries. After proposing a set of 300 genes, the training set was subset accordingly and each model was retrained. The performance of these models was evaluated by the number of subclasses classified above 0.9 TPR and Prec. 2.4 GraSP Gene Reduction 2.4.1 An Ensemble of Specialists The core of our methodology involved training an ensemble of simple NNs; f w ( x ) with weights w mapping the input gene expression vector x to the output class probabilities. Each NN is identical in architecture but trained to become a specialist for a specific cell subclass, c ∈ {1, 2, …, C }, by training on a purposefully biased training dataset. Let 𝒟 be the training dataset, where , with x i ∈ ℝ d being the input gene expression vector for the i -th sample and y i ∈ {1, 2, …, C } being the corresponding class label. 𝒟 c is the biased training dataset for class c . These training sets D c are automatically formed by combining all observations of target subclass c from 𝒟, totalling N c samples, with an equal number, N c , of randomly sampled distractors from the remaining classes, d ∈ {1, 2, …, C } − { c }. Formally, . These NNs were fully connected and had an input layer where each node represented an available predictor gene (1642 input nodes), an output layer with each node representing a subclass label (130 output nodes), and a single hidden layer with twice as many nodes as subclasses (260 nodes). ReLU non-linearities were used on the input and hidden layers, with log-softmax used on the output. Cross-entropy loss and the Adam optimizer with learning rate = 0.001 were used for training 100 epochs on batches of 32 observations. Formally, let ℒ ( f w ( x ), y ) be the loss function, which measures the discrepancy between the predicted class probabilities f w ( x ) and the true class label y . Each NN, , becomes specialized for class c by training on the biased training dataset 𝒟 c by minimizing the loss function over the biased dataset: 2.4.2 Gradient Selected Predictors To identify the most relevant genes for cell subclass classification, we devised a gradient-based feature importance statistic. After training each specialist NN with the respective biased datasets, the gradients of the loss with respect to the input predictors, which in our case, were gene expression levels, were calculated. Formally, for each sample ( x , y ) ∈ 𝒟 c , we computed the gradients of the loss function with respect to the input gene expression vector x : The mean absolute value of these gradients across the batch dimension was used as a measure of each gene’s importance in classification. To calculate the mean absolute value of the gradients across all samples in 𝒟 c for each gene j ∈ {1, 2, …, d }: The gene importance scores represent the sensitivity of the loss function to changes in the expression level of gene j for classifying class c . Higher values indicate that the gene is more important for discriminating class c from other classes. This method captures the network’s sensitivity to changes in gene expression levels, ranking the genes’ influence for classification of c . The feature importance calculation was performed for each subclass-specialized network, providing a rank order in descending order according to their importance scores for each class c . The rank order of all predictors relative to all subclasses was then compiled into a list by iterating through each subclass’ individual list and storing novel genes j as they were encountered. A final NN model with the above architecture (except only 300 input nodes) was trained using the selected gene set. This model was evaluated on the test set to assess its classification performance. 2.4.3 Ablation Study ML models may take advantage of the zero-imputation we used to maintain matrix dimensionality. On the other-hand, discarding such predictors is not desirable when they are truly informative. To test this we performed an ablation study by comparing the classification performance of specific classes and subclasses predicted by a given model trained with or without zero-imputed genes. A paired T-test was used to test for changes caused by this manipulation. 2.5 CuttleNet - Hierarchical Network Architecture To avoid such cheating without deleting real data, we developed a novel two-tier NN, CuttleNet, designed to hierarchically classify cell classes followed by cell subclasses. CuttleNet consists of a primary class classifier NN and multiple subclass classifier NNs, the general architecture of each is identical to the fully-connected network described above for GraSP, see Fig. 3A . Class Classifier The first stage predicts cell classes with input consisting of data common to all studies, and the output layer size corresponds to the number of classes. Non-linearity is introduced via ReLU activation functions, and a softmax layer generates a probability distribution over classes. Subclass Classifiers Each subclass classifier, stored in a PyTorch ModuleDict for dynamic selection, is tasked with identifying subclasses within a predicted class. These networks take concatenated inputs of class-specific gene expression data and the class classifier’s output. They are uniquely configured to output predictions for the number of subclasses they represent, based on a predefined class-to-subclass mapping. The class-specific genes are simply those free of zero-imputation and thus correct the main methodological compromises in the dataset merging. 2.5.1 Benchmarking To assess the performance of CuttleNet relative to the best available model for this hierarchical task, 1 layer and 5 layer CellTICS models were trained with and without access to imputed data. We first optimized the CuttleNet performance at classifying the maximum number of subclasses via a systematic grid search varying epochs, early stopping, and L1 regularization: Number of Epochs: Tested across 10, 25, 50, 100 epochs to assess the impact on model convergence. Early Stopping: Implemented with 0, 5, 10 epochs to prevent overfitting. L1 Regularization: Applied with 0.0, 0.001, 0.005, 0.01, aiding in feature selection and robustness. Each hyperparameter combination was evaluated across multiple seeds (18 to 108, in increments of 18) for robustness and reproducibility. The model’s performance was assessed on a test set following training with the specified configurations. 3 Results 3.1 Gene Selection spSeq promises to comprehensively map retinal cells, but to facilitate this it is necessary to determine a much smaller set of genes capable of effectively and reliably clustering cell subclasses. Traditionally, biologists rely on expert selected “gold-standard” targets to classify cells in their native spatial positions [ 4 ; 5 ; 22 ; 23 ; 24 ; 25 ; 26 ]. scRNAseq allowed for experts to propose not only novel cell subclasses, but also predictors identified by much more powerful statistical techniques, such as MAST [ 1 ; 14 ] or AUCPR [ 2 ; 15 ]. These small sets of genes, relevant for traditional experimental mapping methods, are typically limited to ≤ 3 per subclass where a binary assessment of presence or absence is used for classification. While spSeq cannot make use of the > 10 4 genes available to scRNAseq, it can use many more than 3 genes at a time, and in a more nuanced manner than presence or absence. To test if published gene sets proposed by statistical methods including PCA and AUCPR [ 2 ; 15 ] could be useful to spSeq we evaluated the proposals of 10 RGCs by setting a variety of thresholds, as one would do in an experimental setting, and performed classification. The F1 performance of such small gene sets indicated that neither expert-chosen genes nor traditional thresholding strategies can be relied upon for spSeq, as shown in Fig. 1A and Sup. Fig. A.5 . 3 . Download figure Open in new tab Figure 1. GraSP performance relative to: A) Published gene targets proposed by AUCPR with classification thresholds simulating laboratory practice; B) Traditional ML methods used for selecting 300 genes as well as a NN trained on the published AUCPR set of genes for classifying all 130 retinal subclasses with classification defined by subclass performance above 90% TPR and Prec. To identify gene sets more purposefully designed for spSeq we explored traditional ML methods for dimensionality reduction. The most commonly used embedding tools, like UMAP, t-SNE and PCA projections do not explicitly preserve the importance of individual predictors so were not relevant. Methods which do, such as RF and SVM, however, did not perform as well as we expected, or simply failed to converge, as was the case for genetic evolutionary algorithms. While exploring, we observed that very simple feed-forward NNs could be trained via back-propagation to predict subclasses in a supervised manner with superior performance to these methods. This inspired us to interrogate the gradients computed by these NNs from a given subclass back to its predictors. In so doing we devised an importance statistic that could rank order these genes for a given subclass. As our dataset is skewed over 4 orders of magnitude ( Sup. Fig. A.4 ) we decided to create biased training datasets for each subclass, to train an ensemble of NNs where each was a specialist at its respective subclass. Computing and combining the predictors selected by the gradients’ importance score produced our GraSP algorithm for gene selection. GraSP significantly outperformed published predictor gene sets, Fig. 1A , ANOVA results indicate a significant difference in F1 scores among different gene thresholds ( F (4, 45) = 42.07, p = 0). Post-hoc Tukey’s HSD test revealed that the network chosen gene thresholds significantly outperformed the human chosen thresholds, with p = 0 for all comparisons. Practically, the GraSP chosen genes demonstrate superior performance, with average F1 performance at least 60% better than the best thresholded published gene sets. Even when all predicted genes from AUCPR, and MAST are used to train NNs identically to the final NN containing GraSP predictors, they fail to satisfactorily classify the potential set of subclasses Sup. Fig. A.5 . This highlights the efficacy of the GraSP approach over published retinal classification schemes in the context of spSeq. To evaluate our novel algorithm relative to traditional ML methods, we defined subclasses as being correctly classified with the selected predictors if they were classified with a TPR and Precision both above 90%. Using the GraSP, DT, RF, GBM, and SVM we asked how many subclasses could be classified with 300 genes. We also combined all AUCPR and MAST published predictors for the retina and used them to train a NN identically to the final network proposed by GraSP. ANOVA results indicate a significant difference in the number of subclasses classified by the different methods ( F (4, 20) = 2770, p = 0). Post-hoc Tukey’s HSD test revealed that GraSP significantly outperformed each method with p = 0. Practically, GraSP demonstrated a substantial advantage in classifying subclasses. Specifically, GraSP identified an average of 15.4 more subclasses than RandomForest, 81.0 more than SVM, 91.6 more than DecisionTree, and 77.4 more than the AUCPR and MAST published predictors - highlighting its superior performance compared to traditional machine learning methods, see Fig. 1B . For completeness, we also evaluated the individual sets of MAST, AUCPR, and historical expert selected predictors for the respective subclasses they targeted by again using them to train NNs and evaluated them on the percent of applicable subclasses classified above the 0.9 TPR and Prec threshold, Sup. Fig. A.5 . In this comparison as well GraSP significantly outperformed them, F (4, 20) = 2120, p = 0 Tukey HSD p = 0 against each published predictor set and their combination. GraSP is significantly faster than traditional methods, selecting genes and training the final model in about 8 minutes, similar to DT, but much faster than the 2 hours for RF, and 6 hours for SVM. The Gradient Boosting Machine was also explored as a traditional method, but with the full list of available genes it ran for 36 hours before it was abandoned due to inefficiency - The completed iteration classified only 39 subclasses. These efficiency differences are because NNs train on GPUs, whereas these traditional methods are sequential and as implemented in R train on the CPU. GPU clusters or simply devices with more vRAM would train GraSP even faster. Finally, we clustered the GraSP genes using both UMAP and t-SNE projections to ensure we were not being misled by our target statistic. Encouragingly, we reproduced published clusters with both techniques - validating that the separation of clusters is preserved regardless of embedding algorithm as shown in Fig. 2 and Sup. Fig. A.6 . This observation indicates the robustness of our novel method for preserving the practical outcome of our dimensionality reduction, ultimately validating that we could reduce the number of genes needed for clustering by 60 fold. Download figure Open in new tab Figure 2. UMAP projection of GraSP minimized retinal cell gene vectors for the indicated classes with spatial location of these classes indicated by the diagram of a retinal cross section. Download figure Open in new tab Figure 3. A) CuttleNet diagram, with Carl the Cuttlefish grasping at cell clusters. Box colors indicate: Blue = Input Layer, Orange = ReLU, Salmon = Hidden Layer, Light Green = Inner Output Layer, Green = Final Output Layer. Number of nodes indicated in each layer with 6 + g in the subclass’ input tentacle indicates the concatenation of the class output with the g genes available to that layer. Dashed arrows indicate conditionally engaged connections. B) Benchmarking CuttleNet vs. CellTICS. 3.2 CuttleNet A worrisome compromise we introduced in creating a pan-retinal cell expression matrix from independent studies of cell classes was the imputation of genes not measured between studies. That is, if a gene was found to be sufficiently variable to pass our initial culling of one expression matrix, it is not guaranteed to have been measured in the other scRNAseq studies. Instead of discarding such candidate genes, we imputed values of zero for studies which did not include them. We suspected that some of the performance of our NNs might stem from this decision. To test this, we performed an ablation study by removing all genes with imputed 0s from our GraSP subset expression matrix and trained a version of our NN. This caused a slight but significant performance drop using a paired T-test of our subclass classification F1 score, t (153299) = 19.3, p = 2 × 10 −16 . The practical significance in this case is small, but it gave additional credence to our concern about the impact of imputed values, Table 1 . Thus, we devised a hierarchical modification to our NN, leveraging biologic design principles in which separate NNs acted as sub-networks responsible for either classes, or a specific set of subclasses. Such an architecture, like that found in a cuttlefish’s nervous system, allows for quasi-independence of networks, where subregions of the network receive from upstream regions only the information necessary for their task, but all of the sub-networks ultimately act together to perform complex behaviors. The specific information entering a given sub-network was the set of available genes free of imputed 0s, and samples predicted to be the respective class. The ultimate output was an aggregation of the activated subclass-specialized sub-network’s predictions ( Fig. 3A ). View this table: View inline View popup Download powerpoint Table 1: Ablation Study: Median ± standard deviations F1 scores. 0s shows if model uses imputations. We finally benchmarked our networks against CellTICS, the most cutting-edge hierarchical NN model for simultaneous cell class and subclass classification [ 7 ]. Appreciating the extensive benchmarking of CellTICS against previously leading methods, and its superior performance to them, we deemed it the best reference for evaluating CuttleNet. To fully compare it, we trained it with versions of our retina expression matrix both with and without imputed values. Furthermore, we trained both the 1 Layer architecture, which is most similar to our own, and the developer’s recommended 5 Layer network ( Sup. Fig. A.7 ). To ensure robust comparisons, we re-trained and evaluated CellTICS five times. Before benchmarking, we performed a comprehensive grid search of CuttleNet’s training hyperparameters to optimize it as CellTICS had been ( Sup. Fig. A.8 ). 4 CuttleNet demonstrated significant superiority over CellTICS for our specific application. We performed ANOVAs and post-hoc Tukey tests on the class and subclass F1 scores for CuttleNet and the CellTICS models with 1 layer and the developer optimized 5 layers. In both the class and subclass-focused ANOVA, we rejected the null hypothesis as expected from Fig. 3B , with f (2, 372) = 939.3, p = 0 and f (2, 357) = 54.13, p = 0, respectively. It should come as no surprise based on Fig. 3B that post-hoc testing also rejected the null hypothesis for each of our models against CellTICS with classes and subclasses with p = 0 and p = .009 for the 5 Layer for subclasses. In comparing CuttleNet with the simpler NN, in a separate ANOVA, it is worth highlighting that for class classification performance CuttleNet is significantly better ( p = .006), as with subclass performance ( p = .012). That said, the practical difference in performance between the models is small, with a Cohen’s d = 0.228. This demonstrates that CuttleNet does not sacrifice power as a result of its added complexity. By contrast, CuttleNet is a superior model for inference because it selectively ignores imputed values, and thus solves a real-world problem facing researchers who have had to merge datasets in this very common manner. Our ablation studies highlight ( Table 1 ) how models might use the 0s as “obvious” class markers to cheat. In our case, the practical difference of this cheating is small, but on other datasets, it could have a meaningful impact. 4 Discussion The GraSP method presents a novel approach to feature selection in the context of transcriptomic data analysis. This method addresses a crucial challenge in spSeq studies, where the number of measurable targets is constrained by technical limitations, and thus predictor targets must be minimzed while maintining their ability to discriminate subtly different classes. In our study, the gene set was reduced from approximately 18000 to just 300, without compromising classification performance. This dramatic reduction not only demonstrates the efficiency of our neural network strategy but also lays the foundation for future research where such constraints are commonplace. As spSeq technologies continue to advance, researchers may still opt for minimal classification panels due to cost and time considerations, further underscoring the relevance of our approach. The core of the GraSP method lies in the calculation of the gene importance score , which quantifies the influence of each gene j on the classification performance for a specific target class c . By computing the mean absolute value of the gradients of the loss function with respect to gene expression levels, GraSP captures the sensitivity of the neural network’s predictions to differences in gene expression. This approach effectively ranks the genes according to their discriminative power. Unlike traditional filter, wrapper, or embedded ML methods, GraSP employs a novel approach that does not neatly fit into these categories. GraSP shares some conceptual similarities with embedded methods in using neural networks to evaluate feature importance, or ensemble methods like RF where multiple models are created and contribute to predictions. Unlike these ML tools, GraSP trains an ensemble of specialized neural networks, each focused on a particular target class due to the biased training datasets and then computes gradients of the loss function to provide class-specific feature rankings for each. The novelty thus lies in compiling these rankings into a final list by iterating through each class and adding novel features, prioritizing the most discriminative genes across all classes. This approach, coupled with the use of biased datasets tailored to target classes, distinguishes GraSP from traditional ensemble techniques and embedded methods, making it a unique contribution to feature selection methodologies. A limitation of the current implementation of GraSP is the unoptimized search strategy, thus the algorithm lends itself to further algorithmic improvements. For instance, a simple extension could involve drawing from I c until a specified classification threshold is met for each class c , potentially enhancing the efficiency and interpretability of the gene selection process. Additionally, alternative functions, such as the square of the gradients, could be explored to capture different aspects of gene importance. This is an important future direction necessary to generalize our contribution. A notable contribution of this work is the introduction of CuttleNet to address the challenge of imputed values in merged datasets; a common issue in many real-world scenarios where data is incomplete or derived from multiple sources. By segregating and processing class-specific information through separate sub-networks, CuttleNet demonstrates robustness in the presence of imputed data, enhancing its applicability to practical spSeq studies. The success of CuttleNet underscores the value of biologically-inspired architectures in addressing complex machine learning challenges. It is important to note that CellTICS is a state-of-the-art hierarchical model designed to predict classes and subclasses from full scRNAseq studies, not the minimal constraints imposed by spSeq. Thus, it is not fair to take away from our results that CuttleNet is generally more powerful than CellTICS. On the other hand, CuttleNet is a unique model in that it is specifically designed to account for imputed values, which is a common challenge outside of the context of transcriptomic studies. Thus, future work could extend CuttleNet to other application spaces to evaluate how it can be used to handle this common dataset merging problem. Additionally, CuttleNet allows for each sub-network to have different internal architectures than the simple single hidden layer we here evaluated rigorously. Future work leveraging the general architecture to overcome data-cleaning issues can be easily imagined, as can be implementations with more than two hierarchical levels, which we. 4.1 Conclusion In summary, the GraSP method and CuttleNet architecture represent novel contributions to the field of spatial biology and feature selection. By effectively reducing the gene set required for accurate cell subclass classification and addressing real-world data challenges, our work paves the way for more efficient and practical applications of spatial transcriptomics in biological research. Acknowledgements We would like to thank Drs. Joel Zylberberg, Yaning Liu, Joshua French, and Erin Austin for friendly reviews of an early draft of this manuscript. We would also like to acknowledge that LLMs were used to support the writing of this manuscript and codebase. Specifically, the OpenAI chatGPT models using GPT-3.5, 4, and 4o, as well as Anthropic’s Claude with the Clause 2 and Sonnet architectures. The primary use of these models was to replace Stack Overflow from the author SB’s workflow for function and syntax look-up. Human written drafts of this manuscript were used to prompt these models for clarifying suggestions, as well as to simulate reviewers. Perplexity.ai was used to augment literature review in addition to google scholar, bioRxiv and, similar standard repositories of academic literature. A Appendix A.1 Subclass Proportions in Full Dataset Download figure Open in new tab Figure A.4: Counts and proportions of each cell subclass on a log scale demonstrating the dramatic imbalance in our targets. A.2 AUCPR & MAST Further Comparison Download figure Open in new tab Figure A.5: Percent of cell subclasses classified above 0.9 TPR and Prec out of the total number of subclasses targeted in the original study. BC used the MAST [ 14 ] method to classify 17 subtypes [ 1 ], RGC and AC used the AUCPR method [ 15 ] to classify 45 [ 2 ] and 63 [ 3 ] subtypes, respectively, Retina combined these independent sets to classify all retinal cells. GraSP also targeted all retinal cells. All classifiers were simple NNs with identical architecture and training other than the set of genes in their training data and thus input nodes. A.3 UMAP & t-SNE Clusters Download figure Open in new tab Figure A.6: Projections of cells in test set with GraSP predicted genes only, with colors labeling respective subclasses within an expert defined class A) UMAP projection, B) t-SNE projection. Regardless of choice of projection in this case, we observed classes cluster close together, and at the same time subclass clusters are not mixed. Note that this is not generally going to occur with these methods but the fact that it occurs here is good evidence data separability is preserved. Fig. 2 has the same subclass coloring as shown here, but the legend was removed for legibility in the diagramatic context. Note, that Fig. 2 was a re-implementation of the UMAP clustering shown here, with data limited to cells within a retinal cell class in order to better reveal the homogeneity of clusters and their separation, which is difficult to shown in a static diagram like this. A.4 Grid Search Technical Details This search was a deliberate exploration to pinpoint a balance between training duration, regularization, and early stopping criteria that would yield the best performance for both class and subclass predictions. The optimal parameters emerged at 25 epochs of training, without early stopping, and with a regularization strength of 0.001 Sup. Fig. A.8 ). This configuration not only maximized the subclass performance—with diminishing returns observed beyond—but in general, the grid-search revealed that this architecture rapidly converged on high-quality class predictions, achieving near-perfect accuracy before 10 epochs ( Sup. Fig. A.7 )). This aptitude for class identification may be due to the relatively simple task. The nuanced role of the regularization parameter in our CuttleNet’s performance became evident when examining the longevity of class classification accuracy and subclass differentiation over extended training periods. The optimal regularization strength was found to be 0.001, striking a balance that mitigates overfitting while preserving the network’s ability to generalize. This was an important finding, as it allowed the network to maintain a high level of class classification accuracy, even with prolonged training epochs. Specifically, we observed that without regularization, the F1 scores not only dropped for all cell classes, but the variability between training replicates dramatically increased proportional to training epochs. Conversely, as regularization increased, the network’s capacity to distinguish between the more granular subclass categories diminished. This inverse relationship between regularization strength and subclass accuracy underscores the intricacies of model tuning for our hierarchical architecture ( Sup. Fig. A.7 )). Note that earlier experiments when we were designing GraSP also involved a similar grid-search strategy, including over several other hyperparameters such as hidden layers and custom-loss functions, Sup. Fig. A.9 ). The performance differences between these permutations were all negligible, so for all work in this study the un-optimized, simple NN described in the methods was used. We are including this grid-search for completeness, however, in this case it does not impact our findings one way or another. Download figure Open in new tab Figure A.7: Optimal versions of CuttleNet found after grid search relative to the performance of the CellTICS models trained with 1 or 5 layers and access to the imputed values or not in the GraSP selected genes. Performance is shown for class and subclass classification performance as well as the variance over the 5 validation shuffles. Download figure Open in new tab Figure A.8: Grid search of CuttleNet with various hyperparameters that were explored. Panels are subset by Number of Epochs from top to bottom, Early Stopping parameter left to right. Colors show classes, box plots show F1 score of the subclasses, and X axis shows L1 Regularization parameter. Download figure Open in new tab Figure A.9: Optimal versions of simple NN vs more complicated variants considered but not used for GraSP. Here, each architecture evaluated after performing appropriate grid searches. Each experimental condition in the search included five replicates of training and evaluating the respective model; an 80/20 train/test split was done in all cases with the metrics evaluated here coming only from the testing dataset. A.5 Impact Statement This paper presents an application which will advance the field spatial biology. Neither GraSP nor CuttleNet offer opportunities for abuse or negative societal consequence beyond historic ML methods. 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Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper. We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution. For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review. Footnotes samuel.budoff{at}cuanschutz.edu alon.poleg-polsky{at}cuanschutz.edu ↵ * Use footnote for providing further information about author (webpage, alternative address)— not for acknowledging funding agencies. Following reviewer comments, the description of the GraSP algorithm for feature selection has been heavily updated with an emphasis on formalizing the mathematics and sharing how it was comprehensively evaluated vs existing ML methods. Conforming to space requirements at the venue currently reviewing this manuscript, discussion of the custom-loss function based experiments and biological inspiration for CuttleNet have been removed or signifigantly reduced. ↵ 2 For example, the alphaRGCs mediate high acuity vision and can be easily distinguished from other subclasses based on a small set of genes. Due to the relative simplicity with which they could be classified, spatial maps of these cells were produced [ 5 ] which directly explained hunting behaviors observed in mice [ 6 ]. ↵ 3 The post-hoc testing discussed below revealed no significant differences between the specific thresholds. ↵ 4 See appendix for more specific observations from this grid search. 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