Nassir Mohammad

Nassir Mohammad

A computational theory for clustering and a semi-supervised clustering algorithm is presented. Clustering is defined to be the obtainment of groupings of data such that each group contains no anomalies with respect to a chosen grouping principle and measure; all other examples are considered to be fringe points, isolated anomalies, anomalous clusters or unknown clusters. More precisely, after appropriate modelling under the assumption of uniform random distribution, any example whose expectation of occurrence is <1 with respect to a group is considered an anomaly; otherwise it is assigned a membership of that group. Thus, clustering is conceived as the dual of anomaly detection. The representation of data is taken to be the Euclidean distance of a point to a cluster median. This is due to the robustness properties of the median to outliers, its approximate location of centrality and so that decision boundaries are general purpose. The kernel of the clustering method is the perception anomaly detection algorithm, resulting in a parameter-free, fast, and efficient clustering algorithm. Acknowledging that clustering is an interactive and iterative process, the algorithm relies on a small fraction of known relationships between examples. These relationships serve as seeds to define the user's objectives and guide the clustering process. The method then expands the clusters accordingly, leaving the remaining examples for exploration and subsequent iterations. Results are presented on synthetic and realworld data sets, demonstrating the advantages over the most popular unsupervised and semi-supervised clustering methods.

Nassir Mohammad

A fundamental problem in the field of unsupervised machine learning is the detection of anomalies corresponding to rare and unusual observations of interest; reasons include for their rejection, accommodation or further investigation. Anomalies are intuitively understood to be something unusual or inconsistent, whose occurrence sparks immediate attention. More formally anomalies are those observations-under appropriate random variable modelling-whose expectation of occurrence with respect to a grouping of prior interest is less than one; such a definition and understanding has been used to develop the parameter-free perception anomaly detection algorithm. The present work seeks to establish important and practical connections between the approach used by the perception algorithm and prior decades of research in neurophysiology and computational neuroscience; particularly that of information processing in the retina and visual cortex. The algorithm is conceptualised as a neuron model which forms the kernel of an unsupervised neural network that learns to signal unexpected observations as anomalies. Both the network and neuron display properties observed in biological processes including: immediate intelligence; parallel processing; redundancy; global degradation; contrast invariance; parameter-free computation, dynamic thresholds and non-linear processing. A robust and accurate model for anomaly detection in univariate and multivariate data is built using this network as a concrete application.

Nassir Mohammad

In the fields of statistics and unsupervised machine learning a fundamental and well-studied problem is anomaly detection. Anomalies are difficult to define, yet many algorithms have been proposed. Underlying the approaches is the nebulous understanding that anomalies are rare, unusual or inconsistent with the majority of data. The present work provides a philosophical treatise to clearly define anomalies and develops an algorithm for their efficient detection with minimal user intervention. Inspired by the Gestalt School of Psychology and the Helmholtz principle of human perception, anomalies are assumed to be observations that are unexpected to occur with respect to certain groupings made by the majority of the data. Under appropriate random variable modelling anomalies are directly found in a set of data by a uniform and independent random assumption of the distribution of constituent elements of the observations, with anomalies corresponding to those observations where the expectation of the number of occurrences of the elements in a given view is $<1$. Starting from fundamental principles of human perception an unsupervised anomaly detection algorithm is developed that is simple, real-time and parameter-free. Experiments suggest it as a competing choice for univariate data with promising results on the detection of global anomalies in multivariate data.