A Breast Cancer Classifier Using a Neuron Model with Dendritic Nonlinearity

Abstract

SUMMARYBreast cancer is a serious disease across the world, and it is one of the largest causes of cancer death for women. The traditional diagnosis is not only time consuming but also easily affected. Hence, artificial intelligence (AI), especially neural networks, has been widely used to assist to detect cancer. However, in recent years, the computational ability of a neuron has attracted more and more attention. The main computational capacity of a neuron is located in the dendrites. In this paper, a novel neuron model with dendritic nonlinearity (NMDN) is proposed to classify breast cancer in the Wisconsin Breast Cancer Database (WBCD). In NMDN, the dendrites possess nonlinearity when realizing the excitatory synapses, inhibitory synapses, constant-1 synapses and constant-0 synapses instead of being simply weighted. Furthermore, the nonlinear interaction among the synapses on a dendrite is defined as a product of the synaptic inputs. The soma adds all of the products of the branches to produce an output. A back-propagation-based learning algorithm is introduced to train the NMDN. The performance of the NMDN is compared with classic back propagation neural networks (BPNNs). Simulation results indicate that NMDN possesses superior capability in terms of the accuracy, convergence rate, stability and area under the ROC curve (AUC). Moreover, regarding ROC, for continuum values, the existing 0-connections branches after evolving can be eliminated from the dendrite morphology to release computational load, but with no influence on the performance of classification. The results disclose that the computational ability of the neuron has been undervalued, and the proposed NMDN can be an interesting choice for medical researchers in further research. key words: neuron model with dendritic nonlinearity, Wisconsin breast cancer database, back propagation neural networks, dendrite mechanisms

Using a Single Dendritic Neuron to Forecast Tourist Arrivals to Japan

“…According to the error back-propagation (BP) learning rule [44], we can perform learning using a function for modifying the connection parameters w i j and θ i j as the connection function during learning. The output vector produced by the input vector is compared to the target vector, which can decrease the error between output vector and teaching signal T p vector by correcting w i j and θ i j .…”

“…• SDNM has been successfully applied on a number of classification problems, such as XOR [64], cancer diagnosis [44], Iris and Glass datasets [45]. On the contrary, some other dendritic neuron models are not able to solve such nonlinearly separated problems [50] (e.g., the Legenstein-Maass model [65]).…”

“…For a specific given task, SDNM is able to identify what type of synapse (excitatory or inhibitory) is needed, where the synapse should be located, which branch of the dendrite is needed, and which one is not needed [42], [43]. This is realized by modeling the synaptic nonlinearity with a sigmoid function, and thus enabling the single neuron to be capable of computing linearly non-separable functions and approximating any complex continuous function [44], [45]. On the other hand, although the tourist arrivals time series apparently is onedimension, it actually contains high-dimensional information and is a result of many factors such as the tourism policy which strongly influences the number of tourists, and thus making the tourism data nonlinear, irregular, and difficult to be predicted.…”

“…By taking the nonlinearity of synapses into consideration, a single dendritic neuron model (SDNM) has been proposed in our previous researches [42], [44], [45]. In [42], an unsupervised learning method was proposed for SDNM to learn two-dimensional eight-directionally selective problems.…”

“…In [42], an unsupervised learning method was proposed for SDNM to learn two-dimensional eight-directionally selective problems. In [44], an error back-propagation (BP) method was used for training SDNM to perform cancer classification tasks. In [45], we demonstrated that SDNM could be approximately realized by using logic NOT, AND and OR operations, corresponding to its dendritic morphology, and thus was suitable for a simple hardware implementation in practice.…”