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

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.

Indexing and integrating multiple features for WWW images

In this paper, we present a novel indexing technique called Multi-scale Similarity Indexing (MSI) to index image's multi-features into a single one-dimensional structure. Both for text and visual feature spaces, the similarity between a point and a local partition's center in individual space is used as the indexing key, where similarity values in different features are distinguished by different scale. Then a single indexing tree can be built on these keys. Based on the property that relevant images have similar similarity values from the center of the same local partition in any feature space, certain number of irrelevant images can be fast pruned based on the triangle inequity on indexing keys. To remove the dimensionality curse existing in high dimensional structure, we propose a new technique called Local Bit Stream (LBS). LBS transforms image's text and visual feature representations into simple, uniform and effective bit stream (BS) representations based on local partition's center. Such BS representations are small in size and fast for comparison since only bit operation are involved. By comparing common bits existing in two BSs, most of irrelevant images can be immediately filtered. To effectively integrate multi-features, we also investigated the following evidence combination techniques-Certainty Factor, Dempster Shafer Theory, Compound Probability, and Linear Combination. Our extensive experiment showed that single one-dimensional index on multi-features improves multi-indices on multi-features greatly. Our LBS method outperforms sequential scan on high dimensional space by an order of magnitude. And Certainty Factor and Dempster Shafer Theory perform best in combining multiple similarities from corresponding multiple features.

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.

Towards effective indexing for very large video sequence database

With rapid advances in video processing technologies and ever fast increments in network bandwidth, the popularity of video content publishing and sharing has made similarity search an indispensable operation to retrieve videos of user interests. The video similarity is usually measured by the percentage of similar frames shared by two video sequences, and each frame is typically represented as a high-dimensional feature vector. Unfortunately, high complexity of video content has posed the following major challenges for fast retrieval: (a) effective and compact video representations, (b) efficient similarity measurements, and (c) efficient indexing on the compact representations. In this paper, we propose a number of methods to achieve fast similarity search for very large video database. First, each video sequence is summarized into a small number of clusters, each of which contains similar frames and is represented by a novel compact model called Video Triplet (ViTri). ViTri models a cluster as a tightly bounded hypersphere described by its position, radius, and density. The ViTri similarity is measured by the volume of intersection between two hyperspheres multiplying the minimal density, i.e., the estimated number of similar frames shared by two clusters. The total number of similar frames is then estimated to derive the overall similarity between two video sequences. Hence the time complexity of video similarity measure can be reduced greatly. To further reduce the number of similarity computations on ViTris, we introduce a new one dimensional transformation technique which rotates and shifts the original axis system using PCA in such a way that the original inter-distance between two high-dimensional vectors can be maximally retained after mapping. An efficient B+-tree is then built on the transformed one dimensional values of ViTris' positions. Such a transformation enables B+-tree to achieve its optimal performance by quickly filtering a large portion of non-similar ViTris. Our extensive experiments on real large video datasets prove the effectiveness of our proposals that outperform existing methods significantly.

Indexing text and visual features for WWW images

In this paper, we present a novel indexing technique called Multi-scale Similarity Indexing (MSI) to index imagersquos multi-features into a single one-dimensional structure. Both for text and visual feature spaces, the similarity between a point and a local partitionrsquos center in individual space is used as the indexing key, where similarity values in different features are distinguished by different scale. Then a single indexing tree can be built on these keys. Based on the property that relevant images haves similar similarity values from the center of the same local partition in any feature space, certain number of irrelevant images can be fast pruned based on the triangle inequity on indexing keys. To remove the ldquodimensionality curserdquo existing in high dimensional structure, we propose a new technique called Local Bit Stream (LBS). LBS transforms imagersquos text and visual feature representations into simple, uniform and effective bit stream (BS) representations based on local partitionrsquos center. Such BS representations are small in size and fast for comparison since only bit operation are involved. By comparing common bits existing in two BSs, most of irrelevant images can be immediately filtered. Our extensive experiment showed that single one-dimensional index on multi-features improves multi-indices on multi-features greatly. Our LBS method outperforms sequential scan on high dimensional space by an order of magnitude.

Spatial indexing for scalability in FCA

The paper provides evidence that spatial indexing structures offer faster resolution of Formal Concept Analysis queries than B-Tree/Hash methods. We show that many Formal Concept Analysis operations, computing the contingent and extent sizes as well as listing the matching objects, enjoy improved performance with the use of spatial indexing structures such as the RD-Tree. Speed improvements can vary up to eighty times faster depending on the data and query. The motivation for our study is the application of Formal Concept Analysis to Semantic File Systems. In such applications millions of formal objects must be dealt with. It has been found that spatial indexing also provides an effective indexing technique for more general purpose applications requiring scalability in Formal Concept Analysis systems. The coverage and benchmarking are presented with general applications in mind.