SPCNNet: spiking point cloud neural network for morphological neuron classification

Abstract

Morphological neuron classification helps to reveal the functional characteristics and information transmission mechanisms of the nervous system. However, existing methods that use geometric feature extraction or image-based transformation do not consider the 3D properties of neurons, often resulting in a significant loss of valuable morphological information. To address this, we propose a spiking point cloud neural network (SPCNNet) model to improve classification performance, which is capable of directly processing 3D point clouds and applying spike signals to represent morphological features and classify neurons. A neuronal representation strategy is designed to convert original SWC data into 3D point clouds, and encode real-valued point cloud data into spike trains for further processing by the spiking neural networks. Furthermore, the SPCNNet model with spike-based deep learning algorithm learns the spatial features of neurons for classification tasks. In experiment, we analyzed the impact of different SPCNNet parameters on neuron classification performance, including the number of sampled points, simulation duration and batch size. We also conducted ablation experiments to verify the effectiveness of the proposed method. Experimental results demonstrate that our SPCNNet method precisely represents neuronal morphologies and achieves superior performance on the two NeuroMorpho datasets, with classification accuracies of 84.76% and 85.42% respectively. Compared with other mainstream machine learning methods, our spike-driven method is more plausible for solving complex morphological neuron classification problems on NeuMorph dataset.

Introduction

With the continuous advancement of research in the field of neuroscience, humans have gained a comprehensive understanding of the structure and functional mechanisms of the biological nervous system¹. Neurons, as fundamental units for processing complex information, construct intricate neural networks through their interconnections, thereby achieving the diverse structures and functions of the nervous system. Neurons have complex temporal firing patterns and transmit neural signals in the form of brief electrical spikes, which are transmitted through axonss to other neurons, resulting in a highly interconnected dynamic nervous system². In addition, the 3D morphological structure of neurons can be obtained by reconstruction techniques³, the morphology of neuronal cells exhibits significant heterogeneity, and their geometric morphological structures are not entirely consistent. These morphological differences have a significant impact on the functions and information processing capabilities of neurons^4,5. Therefore, in-depth analysis of neuronal morphology is crucial to reveal brain function and operational mechanisms of the nervous system. Classifying neurons based on their geometric morphology is currently an important research direction in neuroscience⁶.

Currently, some researchers have applied machine learning approaches to solve the morphological neuron classification problem, which have achieved many important results^7,8. Based on differences in feature representation, neuronal morphology classification methods can be mainly divided into three categories. (1) Geometric feature extraction methods. The geometric features are extracted from the 3D neuronal data, and the traditional machine learning classifier is applied to classify neuronal types^9–11. The morphological features include the soma surface area, the stem number, the compartment and branch characteristics, the bifurcation point properties, etc. However, the geometric morphological structure of 3D neurons is very complex¹², and the extracted morphological features cannot accurately represent the geometric morphology of neurons. These methods have the following limitations: the accuracy of neuronal classification depends on the obtained features, while the extraction and selection of geometric morphological features lack a unified standard, and the classification results of different neuronal datasets have great differences. (2) Image-based transformation methods. These methods project 3D neuronal data onto multiple 2D images, and deep learning models can be used to extract image features for classification of neuronal morphology^13,14. However, there are still disadvantages in projecting 3D neurons onto multiple 2D images for neuron classification, the neuronal morphology is 3D structure, and the images can only capture their 2D projections, which will lead to the loss of a large amount of 3D structural information. (3) 3D neuron direct training method. In fact, 3D neural data can be directly used for neuronal morphology classification^15,16. The 3D neural network model can be selected to train 3D neural data, but the experimental results were not ideal. Although research in this area is still scarce, there have been some advances and methods in exploring this field in recent years^17,18.

Based on the analysis above, the existing methods that use geometric feature extraction or image-based transformation do not fully consider the 3D structural information of neurons, often resulting in a significant loss of valuable morphological information. In order to reduce the loss of 3D structural information of neurons, we use a spiking neural network model to classify 3D neuronal data directly. The 3D neuronal data can be represented as point cloud data, and the SNN model exhibits unique advantages in processing point cloud data^19,20. As a new generation of neural network model inspired by the biological brain, SNN boasts prominent biological properties that closely mimic the structural and functional mechanisms of biological nervous systems²¹. Unlike traditional artificial neural networks, SNN can more accurately simulate the working principles of biological neurons−such as the integration of postsynaptic potentials, repolarization, and hyperpolarization processes during neural signal transmission, as well as the information coding mode relying on precise spike timing. Moreover, SNN inherently incorporates temporal information into the encoding process, offering stronger spatiotemporal information processing capabilities that align with the dynamic information processing characteristics of the brain²². Inspired by the brain, SNN encodes and processes information through sparse binary spikes, which is an efficient spatiotemporal pattern computation model that significantly improves energy efficiency, reduces computational cost, and memory consumption^23,24. The SNN computation model stems from the imitation of the working mechanism of biological neurons, including spike firing process and synaptic weight changes, which not only enhances the biological plausibility, but also makes it of great value in the fields of neuroscience and engineering application.

In this paper, we propose a novel SNN-based method for neuronal morphology classification, which is distinguished by its direct utilization of raw 3D neuronal data without the need for manual extraction of geometric features.Firstly, two distinct datasets for 3D neuronal classification are constructed, where each set of 3D neuronal data is formatted in the standard SWC structure. The farthest point sampling (FPS) algorithm is then employed to convert the raw data into 3D point cloud representations for each dataset, which effectively reduces the data volume while preserving the key topological points²⁵.Secondly, we design a spiking point cloud neural network tailored specifically for neuronal morphology classification, termed SPCNNet. The proposed SPCNNet model is applied to the generated point cloud data to automatically learn discriminative features and perform neuronal classification in an end-to-end manner.Finally, comprehensive experiments are conducted on the two self-constructed datasets to validate the effectiveness and robustness of the SPCNNet model.Compared with the existing literature, the main contributions of this paper are summarized as follows:

• We constructed two 3D neuron morphology datasets based on neuronal types from different animals, including the C. elegans dataset and the zebrafish dataset. To address the issue of 3D structural information loss of neurons in existing methods, we propose a neuronal point cloud representation method that enables direct classification in the 3D space.

• We propose a spike driven SPCNNet model for neuronal morphology classification, which can directly process the 3D point cloud data and learn the corresponding spatial features of all points. The corresponding learning algorithm is also introduced to update the synaptic weights in the SPCNNet model.

• We conducted extensive experiments to verify the effectiveness of the proposed neuronal morphology classification method. The C. elegans and zebrafish datasets were selected to test the performance of the SPCNNet model and compare it with other state-of-the-art methods; additionally, ablation experiments were carried out to further validate its effectiveness. Furthermore, our model demonstrated excellent generalization ability on the larger-scale NeuMorph dataset.

The remaining sections of this paper are organized as follows. In “Related work”, we introduce the background and related work of the proposed morphological classification method. In “Proposed method”, we present two neuron datasets and a neuronal 3D point cloud representation method. In addition, the SPCNNet model is proposed for morphological neuron classification. In “Experimental results”, we demonstrate the flexibility and performance of the proposed SPCNNet method through two 3D neuron datasets. Finally, “Conclusions” concludes this work.

Related work

Morphological neuron classification

Neuron classification is an important field in neuroscience that works to describe and classify different types of neurons^6,7. The morphology of neurons is closely related to their function, and different types of neurons may have significant differences in morphology, and these differences reflect their different roles and functions in neural circuits. Therefore, morphological classification systems are an important aspect in the study of neuroscience. Currently, there are three main methods for classifying neuronal morphologies.

The first type is geometric feature extraction methods, and researchers have applied the method to achieve many results in morphology classification. It includes both traditional machine learning methods, such as logistic regression(LR)²⁶, naive Bayesian(NB)²⁷, decision tree(DT)²⁸ and k-nearest neighbor(KNN)²⁹. Hearst et al.³⁰ proposed the support vector machine (SVM), a classifier widely used in subsequent neuronal morphology classification studies. Alavi et al.³¹ extracted the geometric morphological features of neurons, which were then used to classify dopamine neurons in rodents. The study also evaluated the performance of three classifiers: SVM³⁰, backpropagation neural network, and LR. Lavalley et al.²⁶ proposed the LR classifier, which was later adopted in neuronal morphology classification research. Scorcioni et al.³² developed L-Measure, a tool for calculating neuronal geometrical features, laying a foundation for subsequent feature-based classification studies. Han and Zeng³³ used fractal geometry to describe the spatial structure of neurons, calculated the fractal dimension of neurons as morphological features, and combined them with 16 other morphological features to form a set of categorical features. Experimental results based on SVM show that the fractal dimension plays an important role in neuronal classification. Mihaljevic et al.^27,34 constructed a Bayesian network classifier, and successfully classified the geometric morphology of GABAergic interneurons by analyzing and selecting five types of axonal branch features. Besides, there are several deep learning methods, such as long short-term memory(LSTM)³⁵, deep belief network(DBN)³⁶. He et al.³⁷ proposed the deep residual neural network (DRNN), which provided a powerful deep learning framework for neuronal morphology classification. Hernández-Pérez et al.¹¹ proposed a methodology to classify neurons based on DRNN³⁷; the method initially normalizes the geometric morphology features, and subsequently performs classification on the neuron dataset. In reference³⁸, the DRNN model was used to classify 18 types of human neurons, and 43 geometrical features were calculated by L-Measure³². Lin et al.³⁹ further extended DRNN with different residual cumulative modes for neuronal morphology classification, which contains two computational models: a locally cumulative connected deep neural network (LCCDNN) and a fully cumulative connected deep neural network (FCCDNN).

The second type is image-based transformation methods, which project 3D neuronal data onto multiple 2D images, and the deep learning model is used to extract image features for neuronal morphological classification. The deep convolutional neural network (CNN) model has excellent image recognition and classification capability, which can automatically extract useful features from a large number of image samples and map them to the corresponding categories⁴⁰. Therefore, some studies have chosen to project neuronal data as multiple 2D images first^14,41, from which deep features can be extracted to effectively describe the morphology of neurons. Lin et al.⁴² proposed a deep learning network for neuronal morphology classification. In this method, the original neuronal data is reconstructed in 3D voxels, and the 2D neuronal image data is composed through the adaptive projection process. Then, a double convolutional gated recurrent neural network (DCGRNN) is constructed to classify neurons. Sun et al.⁴³ proposed a spiking neural network based on multi-branch spatio-temporal enhancement. By decomposing neuronal trees into multiple subtrees and projecting them onto the temporal dimension, combined with the spatio-temporal enhancement module, the model achieves comprehensive representation and accurate classification of neuronal morphology.

The third type is the 3D neuron direct training method, in which 3D neural data can be directly used in the 3D neural network model for neuron classification. Lin et al.¹⁵ proposed a morphology classification method based on 3D convolutional neural networks (3DCNN). The method first converts SWC format data of neuron into the scaled 3D neuronal images, and obtains the voxel data of neuronal morphology, and then uses 3DCNN for training and classification. Compared with geometric feature extraction and image-based transformation methods, the 3D neuron direct training method can overcome loss of 3D structural information of neurons.

Point cloud and SNN learning

Point cloud data, a prevalent method for representing 3D objects, consists of spatially arranged points without a predefined order, and lacks inherent rotational information^44,45. Due to the ability to handle and interpret 3D data, the point cloud processing method is becoming increasingly prominent in various fields, such as computer vision, autonomous driving, and robotics. Deep learning, a leading technology in artificial intelligence, has been pivotal in tackling numerous challenges related to 3D vision, including object recognition and scene comprehension. However, the unstructured and sparse nature of point cloud data poses unique challenges for the application of deep neural networks, which has kept the field of deep learning for point clouds in its early stages⁴⁶. In recent years, researchers have introduced numerous innovative approaches aimed at improving the efficiency of point cloud data processing. PointNet is a deep learning network architecture that can directly input point clouds for processing^47,48. With the mature application of Transformer in the field of 2D vision, researchers have begun to explore its potential in 3D point cloud data processing. Point Transformer⁴⁹ is a representative work in this direction, which combines spiking neural networks and designs a dedicated self-attention layer for point cloud data, enabling it to capture long-range spatial dependencies between points in the point cloud.

In addition to its biological plausibility, SNN exhibits distinct sparsity, a key advantage derived from its event-driven computational model. Neurons only perform computations when they receive a spike signal, and only trigger a spike when their membrane potential reaches a threshold. In contrast to traditional ANNs, where neurons in each layer perform a full computation during every iteration, most neurons in an SNN remain silent at many moments and do not generate spikes, which not only realizes sparse activation of neurons but also avoids redundant synaptic connections and computations. This sparsity, coupled with its biological properties, endows SNN with significant advantages in terms of computational resource utilization−greatly reducing unnecessary computation while maintaining biological interpretability−making it particularly suitable for low-power and high-efficiency computing scenarios.^24,50,51.

The processing of point clouds is a highly energy-intensive task, typically necessitating a considerable amount of computing resources. Considering the spatiotemporal pattern computation and low energy consumption characteristics of SNNs, Ren et al.⁵² proposed SpikingPointNet, the first spiking neural model for efficient deep learning on point clouds. The proposed method was analyzed on ModelNet10 and ModelNet40 datasets and demonstrated its effectiveness.

Proposed method

Construct 3D neuronal datasets

The 3D morphological structure of neurons can be described using the standard SWC file format, which has been widely used to analyze neuronal morphologies⁵³. A neuron can be discretized into many compartments based on its morphological spatial structure, each row representing one compartment of the neuron, containing seven-dimensional information: compartment number, compartment type (such as soma, axon, dendrite, apical dendrite, etc.), compartment spatial coordinates (x, y, and z), compartment radius, and the parent compartment number connected to the compartment⁵⁴. To enable a more fair comparison, we only utilize the 3D spatial coordinates and connection relationships of neurons for point cloud construction. A screenshot of the neuron data is shown in Fig. 1. All neuron morphological data are obtained from NeuroMorpho.Org, which is a publicly accessible neural source database⁵⁵. It collects a substantial corpus of 3D reconstructed neurons and associated metadata, facilitating researchers’ comprehension of the morphological attributes of various neuronal types. To make a fair comparison with other methods, we first use the same datasets selected in reference³⁹. Two 3D NeuroMorpho datasets are constructed based on different types of neurons in different animals. In addition, we have also constructed a dataset with severe class imbalance.

Fig. 1.

Presentation of neurons in SWC file format.

C. elegans dataset

This dataset collects different neurons within the somatic nervous system region of C. elegans. The dataset comprises three types of neurons: interneuron, motor neuron, and somatic neuron. In the constructed neuron classification dataset, the number of samples for each category is 64, and the total number of samples is 192. A 3D visualization of the neurons in C.elegans is shown in Fig. 2.

Fig. 2.

3D visualization of three types of neurons from the C. elegans dataset.

Zebrafish dataset

This dataset collects different neurons within the main olfactory bulb region of zebrafish. There are four types of neurons selected, namely large, mitral, output, and small neurons. The number of samples in each category is 53, resulting in a total sample size of 212. A 3D visualization of neurons in zebrafish is shown in Fig. 3.

Fig. 3.

3D visualization of four types of neurons from the zebrafish dataset.

NeuMorph dataset

As shown in Table 1, the NeuMorph dataset contains 7 types of neurons, totaling 1931 digital neurons. It can be seen that there are significant differences in the sample size of different neuronal types, and this obvious class imbalance poses a major challenge to representation learning in neuronal morphology analysis.

Table 1.

Distribution of sample sizes across different neuronal types in NeuMorph dataset.

ID	Category name	Quantity
C1	Bipolar	446
C2	DA	361
C3	Dopaminergic	170
C4	GABAergic	235
C5	Ganglion	256
C6	Glutamatergic	343
C7	Spiny	120

Neuronal point cloud representation

The processing and analysis of 3D data often require the utilization of substantial computing resources, especially when dealing with large datasets or executing complex algorithms. The computational cost and time requirements are considerable. In order to reduce the computational cost and time consumption, a small number of fixed points are selected from the original neuronal spatial data. In the case of point selection, the FPS method is used to generate a 3D point cloud data for each neuronal data. Compared to the random sampling method, the advantage of FPS is to contain as many points as possible in a given space. The FPS downsample process begins with the random selection of an initial point as a sampling point. In each iteration, a point is selected from the unselected point set that is farthest from the selected point set, and it is added to the sampled point set. This process is repeated until the desired number of sampling points is obtained. More detailed information about the neuronal point cloud representation algorithm refers to Algorithm 1.

Algorithm 1.

Neuronal point cloud representation using FPS.

We used this algorithm to process the neuronal morphology datasets, and the different point cloud data of a mitral neuron are shown in Fig. 4. Figure 4a shows a 3D view of the neuron’s raw data. As shown in Fig. 4b–d, the three point cloud data can be obtained with different numbers of sampling points using Algorithm 1. The points selected by the FPS method have good spatial distribution, and the downsampled data can still maintain abundant 3D structural information and availability, to ensure performance and reduce unnecessary waste of computing resources.

Fig. 4.

3D point clouds of a mitral neuron with different numbers of points.

The normalization process has been proven to be an effective method for reducing the impact of high-value data, thereby improving the training speed of machine learning methods. Accordingly, the neuronal point point data obtained through FPS is subjected to a normalization process. The normalization process is as follows: initially, the point number in the point cloud data is determined, and the centroid of the point cloud data is calculated. Subsequently, the point cloud data is shifted along each dimension so that the centroid is situated at the origin. Subsequently, the maximum norm of the point cloud data is calculated, which represents the greatest distance between any given point and the origin. Subsequently, the point cloud data is normalized according to the aforementioned maximum norm, ensuring that the coordinates of the point cloud data fall within the range of to 1.

SPCNNet architecture

The main difference between SNN and traditional ANN is that it uses discrete spike signals instead of continuous analog signals. We use the leaky integrate-and-fire (LIF) neuron model in our neural network architecture^50,56. The LIF neuron is a simplified model that is used to simulate the electrical activity of biological neurons. The change in membrane potential in the LIF neuron model can be described as:

1

where denotes the time constant, and I is the input current. A spike is generated when it reaches the threshold , and V is reset to the resting potential . The forward Euler approach is employed to approximate Eq. 1 for compatibility with sequence-based neural networks:

2

where , the input current can be simplified as , W and X represent the synaptic weights and input spike signals, and denotes the neuron’s output spike.

To further explore the morphological features of neurons in the spatiotemporal domain, we propose a SPCNNet model for point cloud data processing. The SPCNNet architecture includes four main blocks: FPS representation, point cloud calibration, feature extraction, and neuron classification. First, FPS representation and point cloud calibration blocks process the raw neuronal data by selecting key points, applying matrix transformations for alignment, and converting the processed point clouds into spike trains using the LIF neuron model. Next, the feature extraction block analyzes these spike trains to extract the morphological features of the neurons. Finally, the classification block integrates the global features, normalizes them using the Softmax function, and outputs the final classification result. The architecture diagram of the SPCNNet model is illustrated in Fig. 5.

Fig. 5.

The architecture of SPCNNet for neuronal morphology representation learning and classification. It consists of FPS point cloud representation, point cloud calibration, feature extraction and neuron classification.

FPS point cloud representation

FPS point cloud representation is a commonly used point set simplification and sampling algorithm in point cloud processing. Its core idea is to iteratively select the point that is farthest from the selected point set, and finally filter out a representative subset from the original 3D neuronal point data. Compared with traditional random sampling methods, this method can achieve better data coverage with the same number of centroids, thereby more effectively capturing the structural characteristic of 3D neuronal morphology data. Through the FPS representation block, we can obtain the 3D point cloud representation of neurons.

Point cloud calibration

We perform point cloud calibration to convert the real-valued point cloud data into spike trains for further processing by the SNN model. To address the permutation invariance (unordered nature) and rotational invariance of point cloud data, we adapt the T-Net architecture from PointNet and integrate it into the SNN framework. This network generates an affine transformation matrix that aligns the original point cloud through rotation and translation, optimizing its spatial orientation for more effective feature extraction by subsequent network layers. For converting real-valued data into spike trains, we employ the LIF neuron model, where each element generates a spike train over a simulation duration T. This process enables the input of real-valued data into the SNN model in the form of temporal spikes, facilitating efficient encoding and analysis of point cloud data.

Feature extraction

The input data are in the form of , n is the number of the sampled points. It first goes through a series of convolutional operations, and the feature dimensions change to and successively. During the convolution process, sized convolutional kernels are used, and batch normalization is performed after each convolutional layer to accelerate the training process and so on. Then, a MaxPool operation is carried out. Subsequently, through three fully connected layers, the feature dimensions are reduced to 1024, 512, and 256 successively. In this process, each point in the point clouds is mapped to a high dimensional space to reduce feature loss. Finally, after feature extraction by the fully connected layer, the raw score vectors of the k categories are output to predict the category.

Neuron classification

The output block performs the crucial classification task in the entire model. Softmax is used as the final layer of SPCNNet for the output of multiple classification problems. It receives the output from the feature extraction block to obtain the final classification result.

Deep learning for SPCNNet

In the backpropagation algorithm, the training process is to adjust the weights of neural network by calculating gradients, thereby reducing the error between the model prediction and the actual value. In the training of the SPCNNet model, the aim is to minimize the loss function. Given a loss function L, the weight update process can be expressed according to the chain rule as:

3

where the first partial derivative term can be calculated by the category label and the actual network output.

However, the second partial derivative term of Eq. 3 for firing function is non-differentiable, which tends to infinity at the threshold. This means that the gradient almost always goes to zero except for the threshold. This results in a standstill for learning, a condition known as the dead neuron issue. The most common method for solving the ”dead neuron” problem is the surrogate gradient method⁵⁷. We use the Arctan function as a smoothing function instead of the original gradient calculation⁵⁸:

4

The surrogate gradient is calculated based on the distance of the membrane potential from the threshold .

Regarding the third partial derivative term of Eq. 3, the derivative of the membrane potential with respect to the current time weight is:

5

According to , we can obtain . Therefore, the derivative term .

Then, we define the update process of the weights like a traditional backpropagation algorithm:

6

The surrogate gradient technique only utilizes the information derived from SPCNNet during forward propagation, omitting conventional backpropagation data.

Experimental results

Experimental settings

The implementation of the SPCNNet model in this paper is based on the PyTorch framework. With the exception of the network structure parameters, all parameters are recommended by PyTorch. The detailed parameters of the SPCNNet model are shown in Table 2. In the LIF neuron model, the firing threshold , the time constant is set to 2, and the reset and resting membrane potential are set to 0. The simulation duration of SNNs is 100 time steps, and the number of learning epochs is 100. In the results reported here, the ratio of training to testing sets is 8: 2 in each experiment. We conducted 5 repeated experiments and calculated the mean and standard deviation of the results. When evaluating the performance of the classification model, the most intuitive and commonly used performance evaluation indicators are adopted, including accuracy, precision, recall, and F1-score.

Table 2.

Parameter settings of the SPCNNet model.

Parameter description		Value
LIF neuron	Firing threshold	0.5
	Time constant	2
	Reset and resting potential	0
Network train	SNN simulation duration	100
	Batch size	32
	Number of learning epochs	100
	Learning rate	0.001
	Dropout rate	0.4

Learning performance

Under the benchmark experimental parameter settings, Fig. 6 shows the classification accuracy curves for the training process of the two neuron datasets. To ensure the stability of the results, we repeated the experiment five times and presented the results as mean values and standard deviations, so as to more clearly demonstrate the characteristics of the data. For the C. elegans dataset (as shown in Fig. 6a), it can be observed that the accuracy of the training set gradually increases before 75 learning epochs, while the accuracy of the testing set tends to stabilize after 60 learning epochs. The average accuracy is 96.12% in the training set, and the average testing accuracy reaches 84.76%, with the corresponding average precision, recall, and F1-Score of 86.87%, 84.10%, and 83.93%, respectively. Furthermore, the proposed method is evaluated on the zebrafish dataset. Figure 6b shows a training process of the SPCNNet model. After multiple training processes, the average accuracies of the training and testing sets are 97.78% and 85.42%, respectively. In this state, the corresponding average precision, recall, and F1-Score are 85.83%, 85.42%, and 85.41% in the testing set. The results indicate that our SPCNNet model can effectively learn different morphological representations of neurons and accurately identify them.

Fig. 6.

Classification accuracies of the training and testing sets on the two datasets using the SPCNNet model.

The confusion matrix heatmap visually presents the correspondence between predicted and true classes, effectively assisting in the analysis of the classification model’s performance. As shown in Fig. 7, the heatmap generated by this method clearly reflects the classification accuracy and error distribution across different classes, providing an intuitive visualization tool for further evaluating the model’s classification performance.

Fig. 7.

Confusion matrix heatmaps on the two datasets using the SPCNNet model.

Parameter analysis

We designed a series of experiments to examine the effects of the SPCNNet model parameters on the neuron classification performance, including the sampled point number, simulation duration, and batch size.

Sampled point number

The number of sampled points in the neuronal point clouds is a key parameter for neuronal morphology classification performance. The C. elegans dataset is composed of small neurons, with each neuron’s SWC file containing a number of compartments within the range of . Therefore, we selected 10, 15, 20, 25, and 30 points for the point cloud representation of neurons, and the results are shown in Fig. 8a. For the C. elegans dataset, when the sampled point numbers are 10, 15, 20, 25, and 30, the classification accuracies are 74.52%, 80.87%, 84.76%, 83.73% and 82.64%, respectively. The zebrafish dataset consists of larger neurons, with the smallest neuron containing 318 compartments and the largest neuron containing 4692 compartments in the SWC files. Consequently, 100, 150, 200, 250 and 300 points were selected for the experiments. As shown in Fig. 8b, the classification accuracies are 77.18%, 78.73%, 82.76%, 85.42%, and 84.38% for the different sampled numbers of point clouds.

Fig. 8.

Evaluation indicators under different numbers of sampled points on the two datasets.

From the experimental results, it can be found that when neurons are represented as point cloud data, a small number of sampled points cannot accurately represent the 3D morphological structure of neurons. A larger number of sampled points can lead to larger neural network scale, making training difficult and resulting in lower classification accuracy. Therefore, the sampled point number is set to 20 for the C. elegans dataset, and 250 for the zebrafish dataset.

SNN simulation duration

Unlike ANN, SNN uses spike trains to transmit information, and each spiking neuron exhibits complex dynamic behavior. Specifically, in addition to information dissemination in the spatial domain, the past history in the temporal domain also has a close impact on the current state. Therefore, SNN runs within a given simulation duration. As shown in Fig. 9, we chose different simulation durations for comparative analysis, with values of 50, 75, 100, 125, and 150, respectively. If the simulation duration is too small, the SPCNNet model cannot effectively extract and learn the morphological features of neurons, resulting in a decrease in classification accuracy. If it is too large, each neuron contains more spikes, making it difficult to calculate the network error gradient, and thus reducing classification performance. Therefore, both datasets achieve the best performance when the simulation duration is 100 time steps.

Fig. 9.

Evaluation indicators under different simulation durations of SNNs on the two datasets.

Batch size

For deep learning networks, a reasonable batch size plays a key role in the well-trained model results. Figure 10 shows the performance comparison of SPCNNet models with different batch sizes. In order to facilitate parallel computing, the batch size in this paper mainly used the power of 2. The selected training batch size are 8, 16, 32, and 64, while the other parameter settings remain the same. As shown in Fig. 10a, the testing accuracies are 78.92%, 81.43%, 84.76% and 82.17% for the different batch sizes on the C. elegans dataset. Fig. 10b shows the accuracy variation on the zebrafish dataset with different batch sizes, the accuracies of testing set are 76.19%, 82.62%, 85.42%, and 84.05%, respectively. Therefore, the batch size of 32 has been selected as the benchmark parameter, the SPCNNet models have highest accuracy of morphological neuron classification.

Fig. 10.

Evaluation indicators under different batch sizes on the two datasets.

Comparison of different methods

As shown in Table 3, we compared the proposed SPCNNet model with the different morphological neuron classification methods on the two datasets. In order to make a fair comparison of geometric feature extraction methods, the 43 geometric features are extracted from the two neuronal datasets, and applied to classify types of neurons³⁹. Some traditional machine learning methods are used as classifiers, including LR with generalized linearity²⁶, NB classifier^27,61, DT with information entropy²⁸, k-nearest neighbor (KNN)²⁹, SVM using geometric distance³⁰, and LSTM³⁵ model. Furthermore, we also considered deep learning models, including DBN³⁶, deep feedforward neural network (DFNN)³⁹, densely connected convolutional network (DCCN)⁵⁹, DRNN^11,37 and its extended LCCDNN and FCCDNN models³⁹. For these neuronal classification methods based on geometric feature extraction, the LCCDNN model achieves the highest testing accuracy of 87.44% on the C. elegans dataset, and 81.16% on the zebrafish dataset, while the RCNN model achieves the second best results. In addition, deep learning models have achieved better classification accuracy compared to traditional machine learning methods.

Table 3.

Comparison of our method with other methods on the C. elegans and zebrafish datasets.

Classification method		C. elegans dataset		Zebrafish dataset
		Training accuracy (%)	Testing accuracy (%)	Training accuracy (%)	Testing accuracy (%)
Geometric feature extraction	LR26	87.52±1.00	79.23±8.24	93.14±1.12	74.65±8.52
	NB27	80.85±2.94	57.18±10.54	87.63±1.38	46.28±16.09
	DT28	100	63.85±11.50	100	64.65±11.44
	KNN29	88.04±1.20	78.72±4.53	88.34±1.15	76.51±5.95
	SVM30	94.18±1.55	80.77±10.76	96.27±0.97	71.16±8.29
	LSTM35	99.93±0.21	68.46±9.97	97.81±0.74	70.47±0.74
	DBN36	96.34±1.16	73.08±8.04	94.14±1.10	68.37±6.95
	DRNN37	97.71±4.19	85.90±9.15	93.79±6.32	78.14±8.15
	DFNN39	89.02±9.13	81.35±15.14	75.27±10.21	75.12±9.81
	LCCDNN39	98.03±2.89	87.44±4.09	98.16±1.88	81.16±9.20
	FCCDNN39	97.45±4.14	83.33±9.76	94.02±6.06	72.33±6.05
	DCCN59	97.84±2.58	75.64±13.47	80.36±6.90	66.28±17.82
Image-based transformation	CNN40	100	73.33±7.17	100	70.47±4.25
	DCGRNN42	99.93±0.61	81.54±8.53	96.27±5.20	78.60±3.25
	ACGAN60	52.87±10.44	52.88±7.50	55.09±9.23	61.40±6.60
3D neuron direct training	3DCNN15	79.54±5.56	52.82±6.19	93.55±0.94	53.02±4.22
	3DCNN + LI15	100	64.36±5.47	100	54.19±6.58
	PointNet47	95.47±1.48	66.25±1.28	96.49±2.32	65.37±2.62
	PointNet++48	97.29±1.57	61.98±2.87	97.08±0.95	64.76±1.76
	SpikingPointNet52	95.73±2.41	83.27±0.96	96.88±1.25	81.94±2.35
	SPCNNet (ours)	96.12±0.66	84.76±1.36	97.78±0.58	85.42±1.74

Using the geometric structure information of 3D neurons, image-based transformation and direct training methods were proposed to solve the neuron classification problem. The characteristic of these methods is that they do not require manual extraction of geometric features of neurons, and can directly input neural image information into CNN deep learning models to classify and recognize neuronal morphologies. In reference⁴², the original neuron data is reconstructed into 3D voxels, and the 2D neuron images are generated through the projection process. When using a randomly projected image as input for deep learning models, the single CNN⁴⁰ or the auxiliary classifier generative adversarial network (ACGAN)⁶⁰ cannot effectively classify neurons. After the adaptive projection process, 2D neuronal image data is formed, including two types of data: the projection with the highest pixel number and the projection with the largest image size. A DCGRNN deep learning model is applied to classify neuronal morphologies using the transformed 2D projection images⁴², and the classification accuracies on the two datasets are 81.54% and 78.60%, respectively. In reference¹⁵, a neuronal morphology classification approach based on 3DCNN model is proposed, which uses 3D voxel data as input through linear interpolation (LI). The 3DCNN+LI model achieves testing accuracies of 64.36% and 54.19% on the two datasets, respectively.In reference⁴⁷, a point cloud-based approach was proposed, which can directly process unordered 3D point cloud data and achieved classification accuracies of 66.25% and 65.37% on the two datasets, respectively. In reference⁴⁸, the approach was further optimized, yielding classification results of 61.98% and 64.76% on the corresponding datasets. Notably, in reference⁵², spiking neural networks were applied to 3D point clouds for the first time, achieving impressive classification accuracies of 83.27% and 81.94% on the two datasets.

For the relatively simple C. elegans dataset, our method achieves accuracies of 96.12% and 84.76% in the training and testing sets, respectively. Due to the easier representation of features in small neurons, the LCCDNN and DRNN methods based on geometric feature extraction have achieved better results. For the more complex zebrafish dataset with larger neurons, our method outperforms existing neuron classification methods, with an accuracy of 97.78% in the training set and 85.42% in the testing set. These findings indicate that our SPCNNet model exhibits good classification ability and stability, and can effectively learn the morphological features of 3D neurons and accurately recognize them.

Ablation experiment

To further illustrate the effectiveness of our proposed method, we conducted ablation experiments: one aimed to verify the superiority of the farthest point sampling adopted in our model over simple random sampling (RS) in point cloud feature extraction, where we replaced the FPS module in the baseline with random sampling while keeping all other parameters and structures unchanged, and by comparing the overall performance metrics of these two sampling strategies, we demonstrated whether FPS could better capture the global spatial distribution of point clouds; the other was designed to evaluate the contribution of LIF neurons to the model’s feature representation capability, for which we constructed an ablation variant by replacing the LIF neuron layer in the baseline model with a ReLU activation function.The results are shown in the Table 4, where Dataset 2 is used for the experiments.

Table 4.

Evaluation of different modules on zebrafish dataset.

Module	Accuracy (%)	Precision (%)	Recall (%)	F1-score (%)
RS+RELU	64.58	65.37	64.58	63.03
RS+LIF	68.75	70.24	68.75	68.89
FPS+RELU	77.08	80.06	77.08	76.55
FPS+LIF	85.42	88.02	85.42	85.82

Evaluation of generalization

To systematically evaluate the generalization performance of the proposed method, we conducted experimental evaluations under the same experimental settings as described in “subsection”.

At the same time, we selected four mainstream models, including 3DCTN⁴⁴, PointNet, PointNet++, and SpikingPointNet, as baseline methods to compare their neuronal morphology classification performance with that of our proposed SPCNNet model on the NeuMorph dataset. Applying the spike-driven SPCNNet model to the NeuMorph dataset demonstrates its excellent classification performance: the model achieves an average classification accuracy of 84.63%, with corresponding average precision, recall, and F1-score of 85.22%, 84.54%, and 84.77%, respectively. As shown in Table 5, although the 3DCTN model also achieved relatively satisfactory classification results, its performance is still slightly lower than that of our proposed SPCNNet model.

Table 5.

Evaluation of different methods on NeuMorph dataset.

Method	Accuracy (%)	Precision (%)	Recall (%)	F1-score (%)
PointNet (ANN)	65.38	75.06	70.65	70.60
PointNet++ (ANN)	70.91	71.96	70.39	68.91
3DCTN (ANN)	83.94	84.41	83.76	84.11
SpikingPointNet (SNN)	78.70	71.40	72.22	71.65
SPCNNet (SNN)	84.63	85.22	84.54	84.77

Conclusions

Biological neurons have complex and diverse spatial morphological structures, and the morphological neuron classification is an important problem in the field of neuroscience research. This paper proposes a spike driven SPCNNet model for morphological neuron classification, which combines the strong spatiotemporal information processing ability of SNNs with the point cloud representation of 3D neurons. The method first converts neuron data in SWC format into 3D point cloud representation using the farthest point sampling, and applies the point cloud calibration to encode the real-valued point cloud data into spike trains for further processing by the SNN model. Then, the proposed SPCNNet model is used to classify neurons. In simulation experiments, the effects of different sampled point numbers, simulation durations, and training batch sizes on the performance of neuron classification are analyzed for the two constructed NeuroMorpho datasets. Compared with other classification methods, the SPCNNet classification method has high accuracy and stability. In addition, our method demonstrates remarkable generalization ability and performs outstandingly on the larger scale NeuMorph dataset.

At present, the main morphological neuron classification methods use geometric feature extraction or image-based transformation, which do not fully consider the 3D properties of neurons and often result in significant loss of valuable morphological information. Compared to existing methods, our SPCNNet method is capable of directly processing 3D point cloud data and applying spike signals to represent morphological features and classify neurons. The proposed SPCNNet method no longer calculates and selects geometric features of 3D neurons, or projects and generates 2D images, providing a new solution for solving the neuron classification problem. However, at this stage, this method only utilizes the coordinate and connection relationship information of 3D neurons, without incorporating the type and radius information of neurons. In addition, the model does not perform any encoding process and directly feeds the raw data into the neural network. Therefore, further in-depth research is urgently needed to explore how to integrate the aforementioned information into the classification model and optimize it through time-based encoding, thereby further improving the accuracy of neuron classification.

Author contributions

X.L. and M.Y. wrote the main manuscript text, developed the core part of the code, and conducted the primary experiments. M.Y. prepared all figures. X.W. analysed the results. All authors reviewed the manuscript.

Funding

This work was supported in part by the National Natural Science Foundation of China under Grants 62266040 and 62502395, and in part by the Natural Science Foundation of Gansu Province under Grant 24JRRA127.

Data availability

All datasets analyzed in this study are publicly accessible at https://neuromorpho.org/.

Declarations

Competing interests

The authors declare no competing interests.