Landslides, movement of soil and rock under the influence of gravity, are common phenomena that cause significant human and economic losses every year. Experts use heterogeneous features such as slope, elevation, land cover, lithology, rock age, and rock family to predict landslides. To work with such features, we adapted convolutional neural networks to consider relative spatial information for the prediction task. Traditional filters in these networks either have a fixed orientation or are rotationally invariant. Intuitively, the filters should orient uphill, but there is not enough data to learn the concept of uphill; instead, it can be provided as prior knowledge. We propose a model called Locally Aligned Convolutional Neural Network, LACNN, that follows the ground surface at multiple scales to predict possible landslide occurrence for a single point. To validate our method, we created a standardized dataset of georeferenced images consisting of the heterogeneous features as inputs, and compared our method to several baselines, including linear regression, a neural network, and a convolutional network, using log-likelihood error and Receiver Operating Characteristic curves on the test set. Our model achieves 2-7% improvement in terms of accuracy and 2-15% boost in terms of log likelihood compared to the other proposed baselines.