An Artificial Neural Network (ANN) works by creating connections between different processing elements (artificial neurons). ANNs have been extensively used for Data Mining, which extracts hidden patterns and valuable information from large databases. This paper introduces a new adaptive Higher Order Neural Network (HONN) model and applies it in data mining tasks such as determining breast cancer recurrences and predicting incomes base on census data. An adaptive hyperbolic tangent function is used as the neuron activation function for the new adaptive HONN model. The paper compares the new HONN model against a Multi-Layer Perceptron (MLP) with the sigmoid activation function, an RBF Neural Network with the Gaussian activation function, and a Recurrent Neural Network (RNN) with the sigmoid activation function. Experimental results show that the new adaptive HONN model offers several advantages over conventional ANN models such as better generalisation capabilities as well as abilities in handling missing values in a dataset.