A Survey of Outlier Detection Methodologies <s> Unsupervised neural methods <s> The detection of novel or abnormal input vectors is of importance in many monitoring tasks, such as fault detection in complex systems and detection of abnormal patterns in medical diagnostics. We have developed a robust method for novelty detection, which aims to minimize the number of heuristically chosen thresholds in the novelty decision process. We achieve this by growing a gaussian mixture model to form a representation of a training set of "normal" system states. When previously unseen data are to be screened for novelty we use the same threshold as was used during training to define a novelty decision boundary. We show on a sample problem of medical signal processing that this method is capable of providing robust novelty decision boundaries and apply the technique to the detection of epileptic seizures within a data record. <s> BIB001 </s> A Survey of Outlier Detection Methodologies <s> Unsupervised neural methods <s> This paper presents a "curious design agent", i.e. an agent that uses the search for novel designs to guide its design actions. A computational model of curiosity based on a process called novelty detection is presented. The behaviour of the computational model is illustrated with a curious design agent searching the space of two- dimensional patterns generated by a simulated Spirograph is reported. 1. A Computational Model of Curiosity Curiosity is the motivation to discover new knowledge when faced with an unfamiliar situation (Berlyne, 1971). It promotes self-directed learning by rewarding behaviour that results in the assimilation of new knowledge. Curiosity can be used to guide the search and exploration of unfamiliar design spaces to find new knowledge with the goal of gaining a better understanding of a non-routine design task. Curious search can be used to guide problem solving to find interesting design solutions. Curious exploration can be used to guide problem finding to discover interesting design problems. In this paper we concentrate on the role of curiosity in the search for interesting design solutions. The curious design agent presented here uses a computational process called novelty detection to determine its level of interest in designs. The curious design agent uses the detection of novelty to guide its search during the course of a design session. Determining interestingness based on novelty depends upon the knowledge of the agent and its computational abilities; things are boring if either too much or too little is known about them (Schmidhuber, 1997). A neural network called a self-organising map or SOM (Kohonen, 1995) is used in the following experiment to implement a simple novelty detector. SOMs project vectors in the high dimensional space onto a hyperplane, typically two-dimensional. The projection provides an ordered map of the high dimensional space with similar vectors clustered together into neighbourhoods. <s> BIB002 </s> A Survey of Outlier Detection Methodologies <s> Unsupervised neural methods <s> This paper is concerned with the motivation of design agents to promote the exploration of design spaces. A general form of motivation common to designers is a curiosity to discover interesting designs. This paper presents computational models of interest and curiosity based on the detection of novelty. We illustrate the behaviour of our model of interest in emergent properties of a design and develop a curious design agent that is motivated to discover interesting situations whilst designing. <s> BIB003
Supervised networks require a pre-classified data set to permit learning. If this pre-classification is unavailable then an unsupervised neural network is desirable. Unsupervised neural networks contain nodes which compete to represent portions of the data set. As with perceptronbased neural networks, decision trees or k-means, they require a training data set to allow the network to learn. They autonomously cluster the input vectors through node placement to allow the underlying data distribution to be modelled and the normal/abnormal classes differentiated. They assume that related vectors have common feature values and rely on identifying these features and their values to topologically model the data distribution. Self organising maps,  are competitive, unsupervised neural networks. SOMs perform vector quantisation and non-linear mapping to project the data distribution onto a lower dimensional grid network whose topology needs to be pre-specified by the user. Each node in the grid has an associated weight vector analogous to the mean vector representing each cluster in a k-means system. The network learns by iteratively reading each input from the training data set, finding the best matching unit, updating the winner's weight vector to reflect the new match like k-means. However, the SOM also updates the neighbouring nodes around the winner unlike k-means. This clusters the network into regions of similarity. The radius of the local neighbourhood shrinks during training in the standard SOM and training terminates when the radius of the neighbourhood reaches its minimum permissible value. Conversely,  enlarges the final neighbourhood to increase the SOMs 'stiffness' by providing broader nodes to prevent over fitting. After training, the network has evolved to represent the normal class. In Figure 5 , the SOM nodes would model the normal class, distributed according to the probability density of the data distribution. During novelty recognition, the unseen exemplar forms the input to the network and the SOM algorithm determines the best matching unit. In BIB002 and  , if the vector distance or quantisation error between the best matching unit (bmu) and new exemplar exceeds some pre-specified threshold (d) then the exemplar is classified as novel. Equation (15) gives the minimum vector distance for the bmu and compares this to the threshold. For example, if the SOM nodes modelled Figure 5 (the normal class from Figure 2) , the points V, W, X, Y and Z from Figure 2 would all be distant from their respective best matching units and would exceed d so V, W, X, Y and Z would be identified as novel. This is analogous to a k-means approach (section 2.1); the SOM equates to a k-means clustering with k equivalent to the number of SOM nodes. However, SOMs use a user-specified global distance threshold whereas k-means autonomously determines the boundary during training allowing local setting of the radius of normality as defined by each cluster. This distance match can be over simplistic and requires the selection of a suitable distance threshold so other approaches examine the response of all nodes in the grid.  look at the quantisation error from the input to all nodes, given by equation (16): where a is the average distance between each training data and its bmu m i . The scaling factor compares the distance between x and its bmu m i against the overall average accuracy of the map nodes during training.  uses a further advancement for mechanical fault detection. They recommend an approach unifying normalised distance measure for 2 and 3 nearest neighbours rather than a single nearest neighbour of Saunders and Gero and Vesanto and normalised meansquare error of mapping. BIB003  systems use an extended SOM, the Habituating SOMs (HSOMs) where every node is connected to an output neuron through habituating synapses which perform inverse Hebbian learning by reducing their connection strength through frequency of activation. The SOM forms a novelty detector where the novelty of the input is proportional to the strength of the output thus simplifying novelty detection compared to a conventional SOM as the output node indicates novelty, there is no requirement for identifying best matching units or complex quantisation error calculations. The HSOM requires minimal computational resources and is capable of operating and performing novelty detection embedded in a robot  . It also trains quickly and accurately. However, HSOMs are susceptible to saturation where any input will produce a low strength output as the HSOM cannot add new nodes and the number of classes (groups of inputs mapping to particular nodes) in the input distribution is equal to or greater than the number of nodes. If the number of classes is known in advance, then a suitable number of nodes can be pre-selected but for many outlier detection problems, particularly on-line learning problems, this information may not be available. Evolutionary neural network growth is analogous to BIB001 approach of adding new Gaussian mixtures when a new datum does not fit any of the existing mixtures.  introduces the grow when required (GWR) evolutionary neural network for type 3 novel feature detection in a mobile inspection robot (robot neotaxis). It is suited to on-line learning and novelty recognition as the network can adapt and accurately model a dynamic data distribution. The growing neural network connects the best matching node and the second best match and adds new nodes when the response of the best matching node for an input vector is below some threshold value. The GWR network grows rapidly during the first phase of training but once all inputs have been processed (assuming a static training set), then the number of nodes stabilises and the network accurately represents the data distribution. As with the SOM, the GWR would learn the normal class in Figure 5 and the points V, W, X, Y and Z from Figure 2 would all then be distant from their respective best matching units which are all within the normal class.  introduce a type 3 recogniser for timeseries monitoring based on the adaptive resonance theory (ART)  incremental unsupervised neural network. The network is plastic while learning, then stable while classifying but can return to plasticity to learn again making them ideal for timeseries monitoring. The ART network trains by taking a new instance vector as input, matching this against the classes currently covered by the network and if the new data does not match an existing class given by equation (17): where n is the input dimensionality and q is a user-specified parameter (vigilance threshold) then it creates a new class by adding a new node within the network to accommodate it. Caudell and Newman monitor the current ART classes and when the network adds a new class this indicates a change in the time series. GWR grows similarly but GWR is topology preserving with neighbourhoods of node representing similar inputs whereas ART simply aims to cover the entire input space uniformly. By only adding a new node if the existing mapping is insufficient and leaving the network unchanged otherwise, the ART network does not suffer from over-fitting which is a problem for MLPs and decision trees. The training phase also requires only a single pass through the input vectors unlike the previously described neural networks which require repeated presentation of the input vectors to train. During empirical evaluation,  noted that the performance of the ART network was extremely disappointing for robot neotaxis. The ART network is not robust and thus susceptible to noise. If the vigilance parameter is set too high the network becomes too sensitive and adds new classes too often.