Vasileios Megalooikonomou

A multiresolution symbolic representation of time series

Efficiently and accurately searching for similarities among time series and discovering interesting patterns is an important and non-trivial problem. In this paper, we introduce a new representation of time series, the multiresolution vector quantized (MVQ) approximation, along with a new distance function. The novelty of MVQ is that it keeps both local and global information about the original time series in a hierarchical mechanism, processing the original time series at multiple resolutions. Moreover, the proposed representation is symbolic employing key subsequences and potentially allows the application of text-based retrieval techniques into the similarity analysis of time series. The proposed method is fast and scales linearly with the size of database and the dimensionality. Contrary to the vast majority in the literature that uses the Euclidean distance, MVQ uses a multi-resolution/hierarchical distance function. We performed experiments with real and synthetic data. The proposed distance function consistently outperforms all the major competitors (Euclidean, dynamic time warping, piecewise aggregate approximation) achieving up to 20% better precision/recall and clustering accuracy on the tested datasets.

Data mining in brain imaging.

Data mining in brain imaging is proving to be an effective methodology for disease prognosis and prevention. This, together with the rapid accumulation of massive heterogeneous data sets, motivates the need for efficient methods that filter, clarify, assess, correlate and cluster brain-related information. Here, we present data mining methods that have been or could be employed in the analysis of brain images. These methods address two types of brain imaging data: structural and functional. We introduce statistical methods that aid the discovery of interesting associations and patterns between brain images and other clinical data. We consider several applications of these methods, such as the analysis of task-activation, lesion-deficit, and structure morphological variability; the development of probabilistic atlases; and tumour analysis. We include examples of applications to real brain data. Several data mining issues, such as that of method validation or verification, are also discussed.

Quantizer design for distributed estimation with communication constraints and unknown observation statistics

We consider the problem of quantizer design in a distributed estimation system with communication constraints in the case where only a training sequence is available. Our approach is based on a generalization of regression trees. The look-ahead method that we also propose improves significantly the performance. The final system performs similarly to the one that assumes known statistics.

Patient classification of fMRI activation maps

The analysis of brain activations using functional magnetic resonance imaging (fMRI) is an active area of neuropsychological research. Standard techniques for analysis have traditionally focused on finding the most significant areas of brain activation, and have only recently begun to explore the importance of their spatial characteristics. We compare fMRI contrast images and significance maps to training sets of similar maps using the spatial distribution of activation values. We demonstrate that a Fisher linear discriminant (FLD) classifier for either type of map can differentiate patients from controls accurately for Alzheimer’s disease, schizophrenia, and mild traumatic brain injury (MTBI).

On data mining, compression, and Kolmogorov complexity

Will we ever have a theory of data mining analogous to the relational algebra in databases? Why do we have so many clearly different clustering algorithms? Could data mining be automated? We show that the answer to all these questions is negative, because data mining is closely related to compression and Kolmogorov complexity; and the latter is undecidable. Therefore, data mining will always be an art, where our goal will be to find better models (patterns) that fit our datasets as best as possible.

A dimensionality reduction technique for efficient time series similarity analysis

We propose a dimensionality reduction technique for time series analysis that significantly improves the efficiency and accuracy of similarity searches. In contrast to piecewise constant approximation (PCA) techniques that approximate each time series with constant value segments, the proposed method--Piecewise Vector Quantized Approximation--uses the closest (based on a distance measure) codeword from a codebook of key-sequences to represent each segment. The new representation is symbolic and it allows for the application of text-based retrieval techniques into time series similarity analysis. Experiments on real and simulated datasets show that the proposed technique generally outperforms PCA techniques in clustering and similarity searches.

An elastic partial shape matching technique

We consider the problem of partial shape matching. We propose to transform shapes into sequences and utilize an algorithm that determines a subsequence of a target sequence that best matches a query. In the proposed algorithm we map the problem of the best matching subsequence to the problem of a cheapest path in a directed acyclic graph (DAG). The approach allows us to compute the optimal scale and translation of sequence values, which is a nontrivial problem in the case of subsequence matching. Our experimental results demonstrate that the proposed algorithm outperforms the commonly used techniques in retrieval accuracy.

Mining lesion-deficit associations in a brain image database

We present a data mining process for discovering associations between structures and functions of the human brain. Our approach is through the study of lesioned (abnormal) structures and associated functional deficits (disorders). For this purpose we have developed a BRAinImage Database (BRAID) that integrates image processing and visualization capabilities with statistical analysis of spatial and clinical data, providing access via extended SQL through a web interface. We present visualization and statistical methods for mining lesion-deficit associations. We consider issues of scalability and morphological variability. We demonstrate the use of the proposed mining methods by applying them to epidemiological data finding clinically meaningful associ-

Optimal Subsequence Bijection

We consider the problem of elastic matching of sequences of real numbers. Since both a query and a target sequence may be noisy, i.e., contain some outlier elements, it is desirable to exclude the outlier elements from matching in order to obtain a robust matching performance. Moreover, in many applications like shape alignment or stereo correspondence it is also desirable to have a one-to-one and onto correspondence (bijection) between the remaining elements. We propose an algorithm that determines the optimal subsequence bijection (OSB) of a query and target sequence. The OSB is efficiently computed since we map the problems solution to a cheapest path in a DAG (directed acyclic graph). We obtained excellent results on standard benchmark time series datasets. We compared OSB to Dynamic Time Warping (DTW) with and without warping window. We do not claim that OSB is always superior to DTW. However, our results demonstrate that skipping outlier elements as done by OSB can significantly improve matching results for many real datasets. Moreover, OSB is particularly suitable for partial matching. We applied it to the object recognition problem when only parts of contours are given. We obtained sequences representing shapes by representing object contours as sequences of curvatures.

Partial elastic matching of time series

We consider the problem of elastic matching of time series. We propose an algorithm that determines a subsequence of a target time series that best matches a query series. In the proposed algorithm, we map the problem of the best matching subsequence to the problem of a cheapest path in a DAG (directed acyclic graph). The proposed approach allows us to also compute the optimal scale and translation of time series values, which is a nontrivial problem in the case of subsequence matching.