Cluster analysis of high-dimensional data: A case study

Normal mixture models are often used to cluster continuous data. However, conventional approaches for fitting these models will have problems in producing nonsingular estimates of the component-covariance matrices when the dimension of the observations is large relative to the number of observations. In this case, methods such as principal components analysis (PCA) and the mixture of factor analyzers model can be adopted to avoid these estimation problems. We examine these approaches applied to the Cabernet wine data set of Ashenfelter (1999), considering the clustering of both the wines and the judges, and comparing our results with another analysis. The mixture of factor analyzers model proves particularly effective in clustering the wines, accurately classifying many of the wines by location.

A new indexing method for high dimensional dataset

Indexing high dimensional datasets has attracted extensive attention from many researchers in the last decade. Since R-tree type of index structures are known as suffering curse of dimensionality problems, Pyramid-tree type of index structures, which are based on the B-tree, have been proposed to break the curse of dimensionality. However, for high dimensional data, the number of pyramids is often insufficient to discriminate data points when the number of dimensions is high. Its effectiveness degrades dramatically with the increase of dimensionality. In this paper, we focus on one particular issue of curse of dimensionality; that is, the surface of a hypercube in a high dimensional space approaches 100% of the total hypercube volume when the number of dimensions approaches infinite. We propose a new indexing method based on the surface of dimensionality. We prove that the Pyramid tree technology is a special case of our method. The results of our experiments demonstrate clear priority of our novel method.

An adaptive and dynamic dimensionality reduction method for high-dimensional indexing

The notorious "dimensionality curse" is a well-known phenomenon for any multi-dimensional indexes attempting to scale up to high dimensions. One well-known approach to overcome degradation in performance with respect to increasing dimensions is to reduce the dimensionality of the original dataset before constructing the index. However, identifying the correlation among the dimensions and effectively reducing them are challenging tasks. In this paper, we present an adaptive Multi-level Mahalanobis-based Dimensionality Reduction (MMDR) technique for high-dimensional indexing. Our MMDR technique has four notable features compared to existing methods. First, it discovers elliptical clusters for more effective dimensionality reduction by using only the low-dimensional subspaces. Second, data points in the different axis systems are indexed using a single B+-tree. Third, our technique is highly scalable in terms of data size and dimension. Finally, it is also dynamic and adaptive to insertions. An extensive performance study was conducted using both real and synthetic datasets, and the results show that our technique not only achieves higher precision, but also enables queries to be processed efficiently. Copyright Springer-Verlag 2005

BM+-tree: A hyperplane-based index method for high-dimensional metric spaces

In this paper, we propose a novel high-dimensional index method, the BM+-tree, to support efficient processing of similarity search queries in high-dimensional spaces. The main idea of the proposed index is to improve data partitioning efficiency in a high-dimensional space by using a rotary binary hyperplane, which further partitions a subspace and can also take advantage of the twin node concept used in the M+-tree. Compared with the key dimension concept in the M+-tree, the binary hyperplane is more effective in data filtering. High space utilization is achieved by dynamically performing data reallocation between twin nodes. In addition, a post processing step is used after index building to ensure effective filtration. Experimental results using two types of real data sets illustrate a significantly improved filtering efficiency.

Approximate processing of massive continuous quantile queries over high-speed data streams

Quantile computation has many applications including data mining and financial data analysis. It has been shown that an is an element of-approximate summary can be maintained so that, given a quantile query d (phi, is an element of), the data item at rank [phi N] may be approximately obtained within the rank error precision is an element of N over all N data items in a data stream or in a sliding window. However, scalable online processing of massive continuous quantile queries with different phi and is an element of poses a new challenge because the summary is continuously updated with new arrivals of data items. In this paper, first we aim to dramatically reduce the number of distinct query results by grouping a set of different queries into a cluster so that they can be processed virtually as a single query while the precision requirements from users can be retained. Second, we aim to minimize the total query processing costs. Efficient algorithms are developed to minimize the total number of times for reprocessing clusters and to produce the minimum number of clusters, respectively. The techniques are extended to maintain near-optimal clustering when queries are registered and removed in an arbitrary fashion against whole data streams or sliding windows. In addition to theoretical analysis, our performance study indicates that the proposed techniques are indeed scalable with respect to the number of input queries as well as the number of items and the item arrival rate in a data stream.

Issues of robustness and high dimensionality in cluster analysis

Finite mixture models are being increasingly used to model the distributions of a wide variety of random phenomena. While normal mixture models are often used to cluster data sets of continuous multivariate data, a more robust clustering can be obtained by considering the t mixture model-based approach. Mixtures of factor analyzers enable model-based density estimation to be undertaken for high-dimensional data where the number of observations n is very large relative to their dimension p. As the approach using the multivariate normal family of distributions is sensitive to outliers, it is more robust to adopt the multivariate t family for the component error and factor distributions. The computational aspects associated with robustness and high dimensionality in these approaches to cluster analysis are discussed and illustrated.

Hierarchical indexing structure for efficient similarity search in video retrieval

With the rapid increase in both centralized video archives and distributed WWW video resources, content-based video retrieval is gaining its importance. To support such applications efficiently, content-based video indexing must be addressed. Typically, each video is represented by a sequence of frames. Due to the high dimensionality of frame representation and the large number of frames, video indexing introduces an additional degree of complexity. In this paper, we address the problem of content-based video indexing and propose an efficient solution, called the Ordered VA-File (OVA-File) based on the VA-file. OVA-File is a hierarchical structure and has two novel features: 1) partitioning the whole file into slices such that only a small number of slices are accessed and checked during k Nearest Neighbor (kNN) search and 2) efficient handling of insertions of new vectors into the OVA-File, such that the average distance between the new vectors and those approximations near that position is minimized. To facilitate a search, we present an efficient approximate kNN algorithm named Ordered VA-LOW (OVA-LOW) based on the proposed OVA-File. OVA-LOW first chooses possible OVA-Slices by ranking the distances between their corresponding centers and the query vector, and then visits all approximations in the selected OVA-Slices to work out approximate kNN. The number of possible OVA-Slices is controlled by a user-defined parameter delta. By adjusting delta, OVA-LOW provides a trade-off between the query cost and the result quality. Query by video clip consisting of multiple frames is also discussed. Extensive experimental studies using real video data sets were conducted and the results showed that our methods can yield a significant speed-up over an existing VA-file-based method and iDistance with high query result quality. Furthermore, by incorporating temporal correlation of video content, our methods achieved much more efficient performance.

Toward efficient multifeature query processing

In many advanced applications, data are described by multiple high-dimensional features. Moreover, different queries may weight these features differently; some may not even specify all the features. In this paper, we propose our solution to support efficient query processing in these applications. We devise a novel representation that compactly captures f features into two components: The first component is a 2D vector that reflects a distance range ( minimum and maximum values) of the f features with respect to a reference point ( the center of the space) in a metric space and the second component is a bit signature, with two bits per dimension, obtained by analyzing each feature's descending energy histogram. This representation enables two levels of filtering: The first component prunes away points that do not share similar distance ranges, while the bit signature filters away points based on the dimensions of the relevant features. Moreover, the representation facilitates the use of a single index structure to further speed up processing. We employ the classical B+-tree for this purpose. We also propose a KNN search algorithm that exploits the access orders of critical dimensions of highly selective features and partial distances to prune the search space more effectively. Our extensive experiments on both real-life and synthetic data sets show that the proposed solution offers significant performance advantages over sequential scan and retrieval methods using single and multiple VA-files.

Space efficient quantile summary for constrained sliding windows on a data stream

In many online applications, we need to maintain quantile statistics for a sliding window on a data stream. The sliding windows in natural form are defined as the most recent N data items. In this paper, we study the problem of estimating quantiles over other types of sliding windows. We present a uniform framework to process quantile queries for time constrained and filter based sliding windows. Our algorithm makes one pass on the data stream and maintains an E-approximate summary. It uses O((1)/(epsilon2) log(2) epsilonN) space where N is the number of data items in the window. We extend this framework to further process generalized constrained sliding window queries and proved that our technique is applicable for flexible window settings. Our performance study indicates that the space required in practice is much less than the given theoretical bound and the algorithm supports high speed data streams.

Data quality initiatives - striving for continuous improvements

Although managers consider accurate, timely, and relevant information as critical to the quality of their decisions, evidence of large variations in data quality abounds. Over a period of twelve months, the action research project reported herein attempted to investigate and track data quality initiatives undertaken by the participating organisation. The investigation focused on two types of errors: transaction input errors and processing errors. Whenever the action research initiative identified non-trivial errors, the participating organisation introduced actions to correct the errors and prevent similar errors in the future. Data quality metrics were taken quarterly to measure improvements resulting from the activities undertaken during the action research project. The action research project results indicated that for a mission-critical database to ensure and maintain data quality, commitment to continuous data quality improvement is necessary. Also, communication among all stakeholders is required to ensure common understanding of data quality improvement goals. The action research project found that to further substantially improve data quality, structural changes within the organisation and to the information systems are sometimes necessary. The major goal of the action research study is to increase the level of data quality awareness within all organisations and to motivate them to examine the importance of achieving and maintaining high-quality data.

On aggregation issues in spatial data management

Large amounts of information can be overwhelming and costly to process, especially when transmitting data over a network. A typical modern Geographical Information System (GIS) brings all types of data together based on the geographic component of the data and provides simple point-and-click query capabilities as well as complex analysis tools. Querying a Geographical Information System, however, can be prohibitively expensive due to the large amounts of data which may need to be processed. Since the use of GIS technology has grown dramatically in the past few years, there is now a need more than ever, to provide users with the fastest and least expensive query capabilities, especially since an approximated 80 % of data stored in corporate databases has a geographical component. However, not every application requires the same, high quality data for its processing. In this paper we address the issues of reducing the cost and response time of GIS queries by preaggregating data by compromising the data accuracy and precision. We present computational issues in generation of multi-level resolutions of spatial data and show that the problem of finding the best approximation for the given region and a real value function on this region, under a predictable error, in general is "NP-complete.

Rapid manufacturing of aluminum components

A manufacturing technique for the production of aluminum components is described. A resin-bonded part is formed by a rapid prototyping technique and then debound and infiltrated by a second aluminum alloy under a nitrogen atmosphere. During thermal processing, the aluminum reacts with the nitrogen and is partially transformed into a rigid aluminum nitride skeleton, which provides the structural rigidity during infiltration. The simplicity and rapidity of this process in comparison to conventional production routes, combined with the ability to fabricate complicated parts of almost any geometry and with high dimensional precision, provide an additional means to manufacture aluminum components.