Number Of Distance Computations Research Articles

Improving the Retrieval of Arabic Web Search Results Using Enhanced k-Means Clustering Algorithm.

Traditional information retrieval systems return a ranked list of results to a user’s query. This list is often long, and the user cannot explore all the results retrieved. It is also ineffective for a highly ambiguous language such as Arabic. The modern writing style of Arabic excludes the diacritical marking, without which Arabic words become ambiguous. For a search query, the user has to skim over the document to infer if the word has the same meaning they are after, which is a time-consuming task. It is hoped that clustering the retrieved documents will collate documents into clear and meaningful groups. In this paper, we use an enhanced k-means clustering algorithm, which yields a faster clustering time than the regular k-means. The algorithm uses the distance calculated from previous iterations to minimize the number of distance calculations. We propose a system to cluster Arabic search results using the enhanced k-means algorithm, labeling each cluster with the most frequent word in the cluster. This system will help Arabic web users identify each cluster’s topic and go directly to the required cluster. Experimentally, the enhanced k-means algorithm reduced the execution time by 60% for the stemmed dataset and 47% for the non-stemmed dataset when compared to the regular k-means, while slightly improving the purity.

An efficient K-means clustering algorithm for tall data

The analysis of continously larger datasets is a task of major importance in a wide variety of scientific fields. Therefore, the development of efficient and parallel algorithms to perform such an analysis is a a crucial topic in unsupervised learning. Cluster analysis algorithms are a key element of exploratory data analysis and, among them, the K-means algorithm stands out as the most popular approach due to its easiness in the implementation, straightforward parallelizability and relatively low computational cost. Unfortunately, the K-means algorithm also has some drawbacks that have been extensively studied, such as its high dependency on the initial conditions, as well as to the fact that it might not scale well on massive datasets. In this article, we propose a recursive and parallel approximation to the K-means algorithm that scales well on the number of instances of the problem, without affecting the quality of the approximation. In order to achieve this, instead of analyzing the entire dataset, we work on small weighted sets of representative points that are distributed in such a way that more importance is given to those regions where it is harder to determine the correct cluster assignment of the original instances. In addition to different theoretical properties, which explain the reasoning behind the algorithm, experimental results indicate that our method outperforms the state-of-the-art in terms of the trade-off between number of distance computations and the quality of the solution obtained.

A comprehensive analysis of delayed insertions in metric access methods

Similarity queries are fundamental operations for applications that deal with complex data. This paper presents MIA (Metric Indexing Assisted by auxiliary memory with limited capacity), a new delayed insertion approach that can be employed to create enhanced dynamic metric access methods through short-term memories. We present a comprehensive evaluation of delayed insertion methods for metric access methods while comparing MIA to dynamic forced reinsertions. Our experimental results show that metric access methods can benefit from these strategies, decreasing the node overlap, the number of distance calculations, the number of disk accesses, and the execution time to run k-nearest neighbor queries.

Hierarchical Clustering-Based Graphs for Large Scale Approximate Nearest Neighbor Search

This paper presents a novel approach to perform fast approximate nearest neighbors search in high dimensional data, using a nearest neighbor graph created over large collections. This graph is created based on the fusion of multiple hierarchical clustering results, where a minimum-spanning-tree structure is used to connect all elements in a cluster. We propose a novel search technique to guide the navigation on the graph without computing exhaustively the distances to all neighbors in each step of the search, just to those in the direction of the query. The objective is to determine the nearest point to the query with a few number of distance calculations. We experimented in three datasets of 1 million SIFT, GIST, and GloVe features. Results show better speedups than another graph-based technique, and competitive speedups at high recall values when compared to classic and recent state-of-the-art techniques.

Sampling and Estimation of Pairwise Similarity in Spatio-Temporal Data Based on Neural Networks

Increasingly fast computing systems for simulations and high-accuracy measurement techniques drive the generation of time-dependent volumetric data sets with high resolution in both time and space. To gain insights from this spatio-temporal data, the computation and direct visualization of pairwise distances between time steps not only supports interactive user exploration, but also drives automatic analysis techniques like the generation of a meaningful static overview visualization, the identification of rare events, or the visual analysis of recurrent processes. However, the computation of pairwise differences between all time steps is prohibitively expensive for large-scale data not only due to the significant cost of computing expressive distance between high-resolution spatial data, but in particular owing to the large number of distance computations ( O ( | T | 2 ) ) , with | T | being the number of time steps). Addressing this issue, we present and evaluate different strategies for the progressive computation of similarity information in a time series, as well as an approach for estimating distance information that has not been determined so far. In particular, we investigate and analyze the utility of using neural networks for estimating pairwise distances. On this basis, our approach automatically determines the sampling strategy yielding the best result in combination with trained networks for estimation. We evaluate our approach with a variety of time-dependent 2D and 3D data from simulations and measurements as well as artificially generated data, and compare it against an alternative technique. Finally, we discuss prospects and limitations, and discuss different directions for improvement in future work.

Reducing the Distance Calculations when Searching an M‑Tree

Recent years have brought rising interest in efficiently searching for similar entities in a broad range of domains. Such search can be used to facilitate working with unstructured data such as genome sequences, text corpora, complex production information, or multimedia content, where queries always contain an amount of noise. In such domains the only common structure is a distance function obeying the axioms of a metric. As mostly no other structure information is available, a lot of distances have to be computed during the course of a search. Contrary to classical database indexes, where the optimization focus is on reducing the number of disk accesses (or in case of in-memory databases the number of tree traversal operations), a major cost driver in such multimedia domains is this number of distance calculations which can be very computation intense. There exists a range of index structures for supporting similarity search in metric spaces. A very promising one is the M‑Tree, along with a number of compatible extensions (e. g. Slim-Tree, Bulk Loaded M‑Tree, multi way insertion M‑Tree, $$M^{2}$$ -Tree, etc.). The M‑Tree family uses common algorithms for the $$k$$ -nearest-neighbor and range search. These algorithms leave room for optimization in terms of necessary distance calculations. In this paper we present new algorithms for these tasks to considerably improve retrieval performance of all M‑Tree-compatible data structures.

Using the k-d Tree Data Structure to Accelerate Monte Carlo Simulations.

The k-d tree data structure is implemented in a Monte Carlo (MC) molecular simulation program to accelerate the range search for particles or interaction sites within the cutoff distance when Lennard-Jones and Coulomb interactions are computed. MC simulations are performed for different molecules in various ensembles to assess the efficiency enhancements due to the k-d tree data structure. It is found that the use of k-d trees accelerates significantly simulations for Lennard-Jones particles in the NVT and NVT-Gibbs ensembles and for n-butane and 2,4,6,8,10,12,14,16,18,20,22-undecamethylpentacosane represented by the TraPPE-UA force field in the NpT ensemble. Simulations for TraPPE-UA ethanol in the NpT ensemble and for the rigid TIP4P water model in the Gibbs ensemble gain slightly in efficiency with the k-d tree, whereas simulations for TIP4P water in the NpT ensemble do not benefit from the use of the k-d tree. The speed-up can be attributed to the reduction in the number of distance calculations in the range search from scaling as [Formula: see text] to [Formula: see text]. In addition, these tests suggest that the efficiency gain from the use of the k-d tree data structure depends on the flexibility of the molecular model (requiring configurational-bias MC moves to sample changes in conformation), on the ensemble (with open ensembles requiring special MC moves to aid particle transfers), and on the number of interaction sites per molecule (with compact multisite models not seeing an efficiency gain). Overall, the use of the k-d tree data structure can substantially enhance MC simulation efficiency for a variety of systems, and it will enable simulations for larger system sizes in the future.

Envelope-based boundary image matching for smart devices under arbitrary rotations

Recently, a variety of smart devices have been introduced for entertainment or industrial purposes, and there have been a lot of needs for image matching applications exploiting a large number of images stored in those smart devices. Boundary image matching identifies similar boundary images using their corresponding time-series, and supporting the rotation invariance is crucial to provide more intuitive matching results not only in conventional computing devices but also in smart devices such as smartphones, smart pads, and smart cameras. Computing the rotation-invariant distance between image time-series, however, is a very time-consuming process since it requires a lot of Euclidean distance computations for all possible rotations. We here note that, for smart devices, a very efficient mechanism of computing rotation-invariant distances is required. For this purpose, in this paper we use a novel notion of envelope-based lower bound proposed by Keogh et al. (VLDB J 18:611---630, 2009) to reduce the number of distance computations dramatically. With the help of Keogh et al.'s prior work (Keogh in Proceedings of the 28th International Conference on Very Large Data Bases, 406---417, 2002; Keogh et al. in VLDB J 18:611---630, 2009), we first explain how to construct a single envelope from a query sequence and how to obtain a lower bound of the rotation-invariant distance using the envelope. We then explain that the single envelope lower bound can reduce a number of distance computations. This single envelope approach, however, may cause bad performance since it may incur a larger lower bound due to considering all possible rotated sequences in a single envelope. To solve this problem, we present a concept of rotation interval, and using the concept of multiple envelopes proposed by Keogh et al. (VLDB J 18:611---630, 2009) with these rotation intervals, we then generalize the envelope-based lower bound by exploiting multiple envelopes rather than a single envelope. We also propose equi-width and envelope-minimization divisions as the method of determining rotation intervals in the multi-envelope approach. We further present an advanced multi-step matching algorithm that progressively prunes search spaces by dividing the rotation interval in half. Experimental results show that our envelope-based solutions outperform naive solutions by one to three orders of magnitude. We believe that this performance improvement makes our algorithms very suitable for smart devices.

Triangular inequality-based rotation-invariant boundary image matching for smart devices

Nowadays there are many efforts to develop image matching applications exploiting a large number of images stored in smart devices such as smartphones, smart pads, and smart cameras. Boundary image matching converts boundary images to time-series and identifies similar boundary images using time-series matching on those time-series. In boundary image matching, computing the rotation-invariant distance between image time-series is a very time-consuming process since it requires a lot of Euclidean distance computations for all possible rotations. To support the boundary image matching in smart devices, we need to devise a simple but fast computation mechanism for rotation-invariant distances. For this purpose, in this paper we propose a novel rotation-invariant matching solution that significantly reduces the number of distance computations using the triangular inequality. To this end, we first present the notion of self-rotation distance and formally show that the self-rotation distance with the triangular inequality produces a tight lower bound and prunes many unnecessary distance computations. Using the self-rotation distance, we then propose a triangular inequality-based solution to rotation-invariant image matching. We next present the concept of k-self rotation distance as a generalized version of the self-rotation distance and formally show that this $$k$$ k -self rotation distance produces a tighter lower bound and prunes more unnecessary distance computations. Using the $$k$$ k -self rotation distance we also propose an advanced triangular inequality-based solution to rotation-invariant image matching. Experimental results show that our self-rotation distance-based algorithms significantly outperform the existing algorithms by up to one or two orders of magnitude, and we believe that this performance improvement makes our algorithms very suitable for smart devices.

Efficient Dimension Reduction Technique for Basic K-Means Clustering Algorithm

K-means clustering is being widely studied problem in a variety of application domains. The computational complexity of the basic k-means is very high, the number of distance calculations also increases with the increase of the dimensionality of the data. Several algorithms have been proposed to improve the performance of the basic k-means. Here we investigate the behavior of the basic k-means clustering algorithm and two alternatives to it, we have analyzed the performances of three different standardization methods. Equivalently, we prove that z-score and principal components are the best preprocessing methods that will simplify the analysis and visualize the multidimensional dataset. The analyzed result revealed that the z-score outperform min-max and decimal scaling also principal component analysis picks up the dimensions with the largest variances. Our results also provide effective ways to solve the k-means clustering problems. Keywords: Decimal Scaling; K-Means Clustering; Min-Max; Principal Component Analysis; Standardization; z-score. 2010 Mathematics Subject Classification: 62H30; 68T10

Bregman Hyperplane Trees for Fast Approximate Nearest Neighbor Search

This article presents a new approximate index structure, the Bregman hyperplane tree, for indexing the Bregman divergence, aiming to decrease the number of distance computations required at query processing time, by sacrificing some accuracy in the result. The experimental results on various high-dimensional data sets demonstrate that the proposed index structure performs comparably to the state-of-the-art Bregman ball tree in terms of search performance and result quality. Moreover, this method results in a speedup of well over an order of magnitude for index construction. The authors also apply their space partitioning principle to the Bregman ball tree and obtain a new index structure for exact nearest neighbor search that is faster to build and a slightly slower at query processing than the original.

Probabilistic enhancement of approximate indexing in metric spaces

Some approximate indexing schemes have been recently proposed in metric spaces which sort the objects in the database according to pseudo-scores. It is known that (1) some of them provide a very good trade-off between response time and accuracy, and (2) probability-based pseudo-scores can provide an optimal trade-off in range queries if the probabilities are correctly estimated. Based on these facts, we propose a probabilistic enhancement scheme which can be applied to any pseudo-score based scheme. Our scheme computes probability-based pseudo-scores using pseudo-scores obtained from a pseudo-score based scheme. In order to estimate the probability-based pseudo-scores, we use the object-specific parameters in logistic regression and learn the parameters using MAP (Maximum a Posteriori) estimation and the empirical Bayes method. We also propose a technique which speeds up learning the parameters using pseudo-scores. We applied our scheme to the two state-of-the-art schemes: the standard pivot-based scheme and the permutation-based scheme, and evaluated them using various kinds of datasets from the Metric Space Library. The results showed that our scheme outperformed the conventional schemes, with regard to both the number of distance computations and the CPU time, in all the datasets.

D-Cache: Universal Distance Cache for Metric Access Methods

The caching of accessed disk pages has been successfully used for decades in database technology, resulting in effective amortization of I/O operations needed within a stream of query or update requests. However, in modern complex databases, like multimedia databases, the I/O cost becomes a minor performance factor. In particular, metric access methods (MAMs), used for similarity search in complex unstructured data, have been designed to minimize rather the number of distance computations than I/O cost (when indexing or querying). Inspired by I/O caching in traditional databases, in this paper we introduce the idea of distance caching for usage with MAMs—a novel approach to streamline similarity search. As a result, we present the D-cache, a main-memory data structure which can be easily implemented into any MAM, in order to spare the distance computations spent by queries/updates. In particular, we have modified two state-of-the-art MAMs to make use of D-cache—the M-tree and Pivot tables. Moreover, we present the D-file, an index-free MAM based on simple sequential search augmented by D-cache. The experimental evaluation shows that performance gain achieved due to D-cache is significant for all the MAMs, especially for the D-file.

Fuzzy vector quantization for image compression based on competitive agglomeration and a novel codeword migration strategy

The implementation of fuzzy clustering in the design process of vector quantizers faces three challenges. The first is the high computational cost. The second challenge arises because a vector quantizer is required to assign each training sample to only one cluster. However, such an aggressive interpretation of fuzzy clustering results to a crisp partition of inferior quality. The third one is the dependence on initialization. In this paper we develop a fuzzy clustering-based vector quantization algorithm that deals with the aforementioned problems. The algorithm utilizes a specialized objective function, which involves the c-means and the fuzzy c-means along with a competitive agglomeration term. The joint effect is a learning process where the number of codewords (i.e. cluster centers) affected by a specific training sample is gradually reducing and therefore, the number of distance calculations is also reducing. Thus, the computational cost becomes smaller. In addition, the partition is smoothly transferred from fuzzy to crisp conditions and there is no need to employ any aggressive interpretation of fuzzy clustering. The competitive agglomeration term refines large clusters from small and spurious ones. Then, contrary to the classical competitive agglomeration method, we do not discard the small clusters but instead migrate them close to large clusters, rendering more competitive. Thus, the codeword migration process uses the net effect of the competitive agglomeration and acts to further reduce the dependence on initialization in order to obtain a better local minimum. The algorithm is applied to grayscale image compression. The main simulation findings can be summarized as follows: (a) a comparison between the proposed method and other related approaches shows its statistically significant superiority, (b) the algorithm is a fast process, (c) the algorithm is insensitive with respect to its design parameters, and (d) the reconstructed images maintain high quality, which is quantified in terms of the distortion measure.

Fast global k-means clustering using cluster membership and inequality

In this paper, we present a fast global k-means clustering algorithm by making use of the cluster membership and geometrical information of a data point. This algorithm is referred to as MFGKM. The algorithm uses a set of inequalities developed in this paper to determine a starting point for the jth cluster center of global k-means clustering. Adopting multiple cluster center selection (MCS) for MFGKM, we also develop another clustering algorithm called MFGKM+MCS. MCS determines more than one starting point for each step of cluster split; while the available fast and modified global k-means clustering algorithms select one starting point for each cluster split. Our proposed method MFGKM can obtain the least distortion; while MFGKM+MCS may give the least computing time. Compared to the modified global k-means clustering algorithm, our method MFGKM can reduce the computing time and number of distance calculations by a factor of 3.78–5.55 and 21.13–31.41, respectively, with the average distortion reduction of 5,487 for the Statlog data set. Compared to the fast global k-means clustering algorithm, our method MFGKM+MCS can reduce the computing time by a factor of 5.78–8.70 with the average reduction of distortion of 30,564 using the same data set. The performances of our proposed methods are more remarkable when a data set with higher dimension is divided into more clusters.

Soft MIMO ML demodulation based on bitwise constellation partitioning

In this letter, we propose a soft-decoding ML MIMO demodulation method that lowers the complexity of the existing ML method. The proposed method finds the nearest point without calculating the Euclidean distance by exploiting the regular structure of bit-to-symbol mapping. It enables significant reduction of the number of distance calculations which is a major complexity burden.

A novel encoding algorithm for vector quantization using transformed codebook

In this paper, a novel encoding algorithm for vector quantization is presented. Our method uses a set of transformed codewords and partial distortion rejection to determine the reproduction vector of an input vector. Experimental results show that our algorithm is superior to other methods in terms of the computing time and number of distance calculations. Compared with available approaches, our method can reduce the computing time and number of distance calculations significantly. Compared with the available best method of reducing the number of distance computations, our approach can reduce the number of distance calculations by 32.3–67.1%. Compared with the best encoding algorithm for vector quantization, our method can also further reduce the computing time by 19.7–23.9%. The performance of our method is better when a larger codebook is used and is weakly correlated to codebook size.

A method to retrieve telops based on the distance of character image features between queries and telops

Video scene retrieval methods based on telop characters can retrieve the corresponding scenes to the query from the huge video data. In this paper, a new video scene retrieval method based on telop characters is proposed. In order to specify the suitable scene, this method recognises the only corresponding telop characters to the query keyword, not all the characters. This method calculates the distance between each image features of telop characters and template image features of query keyword. The number of distance calculations can decrease by indexing the multi-dimensional data for image features of telop characters. Experimental results, using 91 query keywords, show that the average precision of the proposed method using the 1-gram feature becomes 98.61% and using the 2-gram feature becomes 99.59%. Moreover, the retrieval time can be obtained in about 0.5 sec when using the 2-gram feature.

Fast Algorithms for Outlier Detection

Finding fast algorithms to detect outliers (as unusual objects) by their distance to neighboring objects is a big desire. Two algorithms were proposed to detect outliers quickly. The first was based on the Partial Distance (PD) algorithm and the second was an improved version of the PD algorithm. It was found that the proposed algorithms reduced the number of distance calculations compared to the nested-loop method.

Improved search strategies and extensions to k-medoids-based clustering algorithms

In this paper two categories of improvements are suggested that can be applied to most k-medoids-based algorithms - conceptual/algorithmic improvements, and implementational improvements. These include the revisiting of the accepted cases for swap comparison and the application of partial distance searching and previous medoid indexing to clustering. Various hybrids are then applied to a number of k-medoids-based algorithms and the method is shown to be generally applicable. Experimental results on both artificial and real datasets demonstrate that when applied to CLARANS the number of distance calculations can be reduced by up to 98%.