Magnus Lie Hetland

The Basic Principles of Metric Indexing

This chapter describes several methods of similarity search, based on metric indexing, in terms of their common, underlying principles. Several approaches to creating lower bounds using the metric axioms are discussed, such as pivoting and compact partitioning with metric ball regions and generalized hyperplanes. Finally, pointers are given for further exploration of the subject, including non-metric, approximate, and parallel methods.

Temporal Rule Discovery using Genetic Programming and Specialized Hardware

Discovering association rules is a well-established problem in the field of data mining, with many existing solutions. In later years, several methods have been proposed for mining rules from sequential and temporal data. This paper presents a novel technique based on genetic programming and specialized pattern matching hardware. The advantages of this method are its flexibility and adaptability, and its ability to produce intelligible rules of considerable complexity.

Ptolemaic indexing of the signature quadratic form distance

The signature quadratic form distance has been introduced as an adaptive similarity measure coping with flexible content representations of multimedia data. While this distance has shown high retrieval quality, its high computational complexity underscores the need for efficient search methods. Recent research has shown that a huge improvement in search efficiency is achieved when using metric indexing. In this paper, we analyze the applicability of Ptolemaic indexing to the signature quadratic form distance. We show that it is a Ptolemaic metric and present an application of Ptolemaic pivot tables to image databases, resolving queries nearly four times as fast as the state-of-the-art metric solution, and up to 300 times as fast as sequential scan.

Evolutionary Rule Mining in Time Series Databases

Data mining in the form of rule discovery is a growing field of investigation. A recent addition to this field is the use of evolutionary algorithms in the mining process. While this has been used extensively in the traditional mining of relational databases, it has hardly, if at all, been used in mining sequences and time series. In this paper we describe our method for evolutionary sequence mining, using a specialized piece of hardware for rule evaluation, and show how the method can be applied to several different mining tasks, such as supervised sequence prediction, unsupervised mining of interesting rules, discovering connections between separate time series, and investigating tradeoffs between contradictory objectives by using multiobjective evolution.

Multicategory Incremental Proximal Support Vector Classifiers

Support Vector Machines (SVMs) are an efficient data mining approach for classification, clustering and time series analysis. In recent years, a tremendous growth in the amount of data gathered has changed the focus of SVM classifier algorithms from providing accurate results to enabling incremental (and decremental) learning with new data (or unlearning old data) without the need for computationally costly retraining with the old data. In this paper we propose an efficient algorithm for multicategory classification with the incremental proximal SVM introduced by Fung and Mangasarian.

Incremental and decremental proximal support vector classification using decay coefficients

This paper presents an efficient approach for supporting decremental learning for incremental proximal support vector machines (SVM). The presented decremental algorithm based on decay coefficients is compared with an existing window-based decremental algorithm, and is shown to perform at a similar level in accuracy, but providing significantly better computational performance.

Fast optimal twig joins

In XML search systems twig queries specify predicates on node values and on the structural relationships between nodes, and a key operation is to join individual query node matches into full twig matches. Linear time twig join algorithms exist, but many non-optimal algorithms with better average-case performance have been introduced recently. These use somewhat simpler data structures that are faster in practice, but have exponential worst-case time complexity. In this paper we explore and extend the solution space spanned by previous approaches. We introduce new data structures and improved strategies for filtering out useless data nodes, yielding combinations that are both worst-case optimal and faster in practice. An experimental study shows that our best algorithm outperforms previous approaches by an average factor of three on common benchmarks. On queries with at least one unselective leaf node, our algorithm can be an order of magnitude faster, and it is never more than 20% slower on any tested benchmark query.

Ptolemaic access methods: Challenging the reign of the metric space model

Abstract Metric indexing is the state of the art in general distance-based retrieval. Relying on the triangular inequality, metric indexes achieve significant online speed-up beyond a linear scan. Recently, the idea of Ptolemaic indexing was introduced, which substitutes Ptolemys inequality for the triangular one, potentially yielding higher efficiency for the distances where it applies. In this paper we have adapted several metric indexes to support Ptolemaic indexing, thus establishing a class of Ptolemaic access methods (PtoAM). In particular, we include Ptolemaic Pivot tables, Ptolemaic PM-Trees and the Ptolemaic M-Index. We also show that the most important and promising family of distances suitable for Ptolemaic indexing is the signature quadratic form distance , an adaptive similarity measure which can cope with flexible content representations of multimedia data, among other things. While this distance has shown remarkable qualities regarding the search effectiveness, its high computational complexity underscores the need for efficient search methods. We show that these distances are Ptolemaic metrics and present a study where we apply Ptolemaic indexing methods on real-world image databases, resolving exact queries nearly four times as fast as the state-of-the-art metric solution, and up to three orders of magnitude times as fast as sequential scan.

Indexing inexact proximity search with distance regression in pivot space

We introduce an inexact indexing scheme where, at index building time, training queries drawn from the database are used to fit one linear regression model for each object to be indexed. The response variable is the distance from the object to the query. The predictor variables are the distances from the query to each of a set of pivot objects. At search time, the models can provide distance estimates or probabilities of inclusion in the correct result, either of which can be used to rank the objects for an inexact search where the true distances are calculated in the resulting order, up to a halting point. To reduce storage requirements, the coefficients can be discretized at the cost of some precision in the promise values. We evaluate our scheme on synthetic and real-world data and compare it to a permutation-based scheme that has been reported to outperform other methods in the same experimental setting. We find that, in several of our experiments, the regression-based distance estimates give better query performance than the permutation-based promise values, in some cases even when the pivot set for the regression-based scheme is reduced in order to make its memory size equal to that of the permutation-based index. Limitations of our scheme include high index building cost and vulnerability to deviation from the model assumptions.

The Role of Discretization Parameters in Sequence Rule Evolution

As raw data become available in ever-increasing amounts, there is a need for automated methods that extract comprehensible knowledge from the data. In our previous work we have applied evolutionary algorithms to the problem of mining predictive rules from time series. In this paper we investigate the effect of discretization on the predictive power of the evolved rules. We compare the effects of using simple model selection based on validation performance, majority vote ensembles, and naive Bayesian combination of classifiers.