A Systematic Evaluation of Interneuron Morphology Representations for Cell Type Discrimination

Abstract

Quantitative analysis of neuronal morphologies usually begins with choosing a particular feature representation in order to make individual morphologies amenable to standard statistics tools and machine learning algorithms. Many different feature representations have been suggested in the literature, ranging from density maps to intersection profiles, but they have never been compared side by side. Here we performed a systematic comparison of various representations, measuring how well they were able to capture the difference between known morphological cell types. For our benchmarking effort, we used several curated data sets consisting of mouse retinal bipolar cells and cortical inhibitory neurons. We found that the best performing feature representations were two-dimensional density maps, two-dimensional persistence images and morphometric statistics, which continued to perform well even when neurons were only partially traced. Combining these feature representations together led to further performance increases suggesting that they captured non-redundant information. The same representations performed well in an unsupervised setting, implying that they can be suitable for dimensionality reduction or clustering.

Keywords: Benchmarking; Cell types; Mouse; Neuroanatomy; Visual cortex.

Fig. 1

Exemplary cells of each cell type for all four data sets. Axons are shown in light green, dendrites in dark green. a Mouse retinal bipolar cells (cone-connecting) from Helmstaedter et al. (2013). The dashed line shows the onset of the inner plexiform layer (IPL). The cell types used for analysis are types 1, 2, 3A, 3B, 4, 5I, 5O, 5T, 5X, 6, and 7. Cell types 8 and 9 were excluded from further analysis due to insufficient sample sizes. b Layer 2/3 inhibitory interneurons in primary visual cortex of adult mice (Jiang et al. 2015). BC: basket cells, BPC: bipolar cells, BTC: bitufted cells, ChC: chandelier cells, DBC: double bouquet cells, MC: Martinotti cells, NGC: neurogliaform cells. c Layer 4 inhibitory interneurons in primary visual cortex of adult mice (Scala et al. 2019). LBC: large basket cells, BPC: bipolar cells, DBC: double bouquet cells, HBC: horizontal basket cells, MC: Martinotti cells, NGC: neurogliaform cells, SBC: small basket cells. d Layer 5 inhibitory interneurons in primary visual cortex of adult mice (Jiang et al. 2015). BC: basket cells, DC: deep-projecting cells, HEC: horizontally elongated cells, MC: Martinotti cells, NGC: neurogliaform cells, SC: shrub cells

Fig. 2

Selected feature representations for retinal bipolar cells of type 1 and type 5O. a Smoothed density map of XZ projection for two exemplary cells. b Smoothed density map of Z projection for all cells of these two types. The cells of type 5O stratify deeper in the inner plexiform layer (IPL) than cells of type 1. Bold lines show class means. c A selection of ten single-valued summary statistics that were included in the morphometric statistics vector. d Sholl intersection profile of the YZ projection for all cells of these two types. Bold lines show class means. e Two-dimensional distribution of path angles and path distances to the soma across all nodes for the same two exemplary cells shown in (a). f The first and the second principal components (PCs) of path-angle/path-distance histograms for all cells of these two types. g Two-dimensional persistence images for the same two exemplary cells shown in (a) and (e). h The first and the second PCs of 2D persistence images for all cells of these two types

Fig. 3

Processing pipeline. Inhibitory interneurons were soma-centered. Retinal bipolar cells were soma-centered in x and y while z = 0 was chosen to correspond to the inner plexiform layer (IPL) onset. The z direction of each cell was aligned with cortical/retinal depth, whereas the x and y direction were left unchanged. Several different feature representations were extracted automatically and used for pairwise and multi-class classifications using logistic regression regularized with elastic net. The performance was assessed using 10 times repeated 5-fold stratified cross-validation

Fig. 4

Cross-validated log-loss for each pair of morphological types in each data set using XZ density maps on full neurons as predictors in logistic regression. Zero log-loss corresponds to perfect prediction, $ln\left(2\right)\approx 0.69$ corresponds to random guessing. For the classification results of other feature representations see Fig. S1 and 10.5281/zenodo.3716519. For abbreviations see Fig. 1

Fig. 5

a–c Pairwise classification performance of the top performing feature representations based on the full-neuron (a), axonal (b), and dendritic (c) features for each data set. Feature representations are grouped into density maps, morphometric statistics, morphometric distributions, persistence images, and combinations of the top three feature representations. Each shown value is cross-validated log-loss, averaged across all pairs. Error bars correspond to 95% confidence intervals. Chance-level log-loss equals $ln\left(2\right)\approx 0.69$ and is indicated in each panel. See Fig. S3a for the results using combined axonal+dendritic feature representations. d Cross-validated log-loss of multinomial classification. Chance level for each data set is indicated on the y-axis. See Fig. S3b for the results using axonal, dendritic, and combined axonal+dendritic feature representations

Fig. 6

Ranked top five feature representations for each classification scheme using different performance measures on full-neuron data. All measures and all classification schemes selected the same top-5 features

Fig. 7

a Cross-validated log-loss of XZ density maps, morphometric statistics and z-projection-based 2D persistence as a function of truncation level. Branches were truncated to mimic what happens when neurons are only partially traced. The classification was performed on all pairs of types in V1 L2/3 data set. Dots and error bars show the means and 95% confidence intervals across all 21 pairs. Dashed grey line shows chance level at $ln\left(2\right)\approx 0.69$. Grey shading shows the chance-level distribution of log-losses obtained by shuffling the labels during the cross-validation (shading intervals go from the minimum to the maximum obtained chance-level values). The arrows mark the levels of truncation shown in panel B. b XZ projections of four exemplary cells at three levels of truncation: 10%, 50%, and 90%. At 50% truncation the global structure of each cell is still preserved, whereas at 90% only the dendritic structures remain. See Fig. 1 for abbreviations

Fig. 8

a T-SNE embeddings of all four data sets using embeddings using the XZ density maps combined with morphometric statistics. b T-SNE embeddings using the XZ density maps combined with morphometric statistics. c T-SNE embeddings using XZ density maps combined with z-projection-based 2D persistence images. The ellipses are 95% coverage ellipses for each type, assuming Gaussian distribution and using robust estimates of location and covariance. They are not influenced by single outliers. For abbreviations see Fig. 1