PIECEWISE ANOMALY DETECTION USING MINIMAL LEARNING MACHINE FOR HYPERSPECTRAL IMAGES

Hyperspectral imaging, with its applications, offers promising tools for remote sensing and Earth observation. Recent development has increased the quality of the sensors. At the same time, the prices of the sensors are lowering. Anomaly detection is one of the popular remote sensing applications, which benefits from real-time solutions. A real-time solution has its limitations, for example, due to a large amount of hyperspectral data, platform’s (drones or a cube satellite) constraints on payload and processing capability. Other examples are the limitations of available energy and the complexity of the machine learning models. When anomalies are detected in real-time from the hyperspectral images, one crucial factor is to utilise a computationally efficient method. The Minimal Learning Machine is a distance-based classification algorithm, which can be modified for anomaly detection. Earlier studies confirms that the Minimal learning Machine (MLM) is capable of detecting efficiently global anomalies from the hyperspectral images with a false alarm rate of zero. In this study, we will show that by using a carefully selected lower threshold besides the higher threshold of the variance, it is possible to detect local and global anomalies with the MLM. The downside is that the improved method is highly sensitive with the respect to the noise. Thus, the second aim of this study is to improve the MLM’s robustness with respect to noise by introducing a novel approach, the piecewise MLM. With the new approach, the piecewise MLM can detect global and local anomalies, and the method is significantly more robust with respect to noise than the MLM. As a result, we have an interesting, easy to implement and computationally light method which is suitable for remote sensing applications.

Do Randomized Algorithms Improve the Efficiency of Minimal Learning Machine?

Minimal Learning Machine (MLM) is a recently popularized supervised learning method, which is composed of distance-regression and multilateration steps. The computational complexity of MLM is dominated by the solution of an ordinary least-squares problem. Several different solvers can be applied to the resulting linear problem. In this paper, a thorough comparison of possible and recently proposed, especially randomized, algorithms is carried out for this problem with a representative set of regression datasets. In addition, we compare MLM with shallow and deep feedforward neural network models and study the effects of the number of observations and the number of features with a special dataset. To our knowledge, this is the first time that both scalability and accuracy of such a distance-regression model are being compared to this extent. We expect our results to be useful on shedding light on the capabilities of MLM and in assessing what solution algorithms can improve the efficiency of MLM. We conclude that (i) randomized solvers are an attractive option when the computing time or resources are limited and (ii) MLM can be used as an out-of-the-box tool especially for high-dimensional problems.

MINIMAL LEARNING MACHINE IN ANOMALY DETECTION FROM HYPERSPECTRAL IMAGES

Anomaly detection from hyperspectral data needs computationally efficient methods to process the data when the data gathering platform is a drone or a cube satellite. In this study, we introduce a minimal learning machine for hyperspectral anomaly detection. Minimal learning machine is a novel distance-based classification algorithm, which is now modified to detect anomalies. Besides being computationally efficient, minimal learning machine is also easy to implement. Based on the results, we show that minimal learning machine is efficient in detecting global anomalies from the hyperspectral data with low false alarm rate.

Parsimonious Minimal Learning Machine via Multiresponse Sparse Regression

The training procedure of the minimal learning machine (MLM) requires the selection of two sets of patterns from the training dataset. These sets are called input reference points (IRP) and output reference points (ORP), which are used to build a mapping between the input geometric configurations and their corresponding outputs. In the original MLM, the number of input reference points is the hyper-parameter and the patterns are chosen at random. Therefore, the conventional proposal does not consider which patterns will belong to each reference point group, since the model does not implement an appropriate way of selecting the most suitable patterns as reference points. Such an approach can impact on the decision function in terms of smoothness, resulting in high complexity models. This paper introduces a new approach to select IRP for MLM applied to classification tasks. The optimally selected minimal learning machine (OS-MLM) relies on the multiresponse sparse regression (MRSR) ranking method and the leave-one-out (LOO) criterion to sort the patterns in terms of relevance and select an appropriate number of input reference points, respectively. The experimental assessment conducted on UCI datasets reports the proposal was able to produce sparser models and achieve competitive performance when compared to the regular strategy of selecting MLM input RPs.