Clustering Time Series from Mixture Polynomial Models with Discretised Data

Clustering time series is an active research area with applications in many fields. One common feature of time series is the likely presence of outliers. These uncharacteristic data can significantly effect the quality of clusters formed. This paper evaluates a method of over-coming the detrimental effects of outliers. We describe some of the alternative approaches to clustering time series, then specify a particular class of model for experimentation with k-means clustering and a correlation based distance metric. For data derived from this class of model we demonstrate that discretising the data into a binary series of above and below the median improves the clustering when the data has outliers. More specifically, we show that firstly discretisation does not significantly effect the accuracy of the clusters when there are no outliers and secondly it significantly increases the accuracy in the presence of outliers, even when the probability of outlier is very low

Adaptive probability scheme for behaviour monitoring of the elderly using a specialised ambient device

A Hidden Markov Model (HMM) modified to work in combination with a Fuzzy System is utilised to determine the current behavioural state of the user from information obtained with specialised hardware. Due to the high dimensionality and not-linearly-separable nature of the Fuzzy System and the sensor data obtained with the hardware which informs the state decision, a new method is devised to update the HMM and replace the initial Fuzzy System such that subsequent state decisions are based on the most recent information. The resultant system first reduces the dimensionality of the original information by using a manifold representation in the high dimension which is unfolded in the lower dimension. The data is then linearly separable in the lower dimension where a simple linear classifier, such as the perceptron used here, is applied to determine the probability of the observations belonging to a state. Experiments using the new system verify its applicability in a real scenario

Modelling human control behaviour with a Markov-chain switched bank of control laws

A probabilistic model of human control behaviour is described. It assumes that human behaviour can be represented by switching among a number of relatively simple behaviours. The model structure is closely related to the Hidden Markov Models (HMMs) commonly used for speech recognition. An HMM with context-dependent transition functions switching between linear control laws is identified from experimental data. The applicability of the approach is demonstrated in a pitch control task for a simplified helicopter model

Hidden Markov Models with Generalised Emission Distribution for the Analysis of High-Dimensional, Non-Euclidean Data

iAbstract Hidden Markov models (HMM) are tremendously popular for the analysis of sequential data, such as biological sequences, speech recognition as well as ges-ture recognition. However, since the method has got some limitations, that is mainly the restrictive emission distribution assumption in each hidden state, a generalised extension of the ordinary HMM is introduced. The method proposed in this work aims to overcome this limitation through adapting the multivari-ate Gaussian density so it can handle data obtained from non-Euclidean metric space. The generalised emission distribution is only dependent on the pairwise distances of all observations and no longer on a center of mass nor a variance term. We show that our method performs as good as the original HMM in many scenarios and even outperforms it in a certain non-Euclidean data situation. In addition we apply the method to ChIP-chip data in order to find out whether or not we can determine distinct gene classes that can be distinguished by different transcription state sequences