Approximate Computation of Distance-Based Queries

In modern database applications the similarity or dissimilarity of complex objects is examined by performing distance-based queries (DBQs)on data of high dimensionality. The R-tree and its variations are commonly cited multidimensional access methods that can be used for answering such queries. Although, the related algorithms work well for low-dimensional data spaces, their performance degrades as the number of dimensions increases (dimensionality curse). In order to obtain accept- able response time in high-dimensional data spaces, algorithms that ob- tain approximate solutions can be used. Three approximation techniques (α-allowance, N-consider and M-consider) and the respective recursive branch-and-bound algorithms for DBQs are presented and studied in this paper. We investigate the performance of these algorithms for the most representative DBQs (the K-nearest neighbors query and the K-closest pairs query) in high-dimensional data spaces, where the point data sets are indexed by tree-like structures belonging to the R-tree family:R*- trees and X-trees. The searching strategy is tuned according to several parameters, in order to examine the trade-off between cost (I/O activ- ity and response time) and accuracy of the result. The outcome of the experimental evaluation is the derivation of the outperforming DBQ ap- proximate algorithm for large high-dimensional point data sets.

In order to solve the problem that traditional grid-based clustering techniques lack of the capability of dealing with data of high dimensionality, we propose an intersecting grid partition method and a density estimation method. The partition method can greatly reduce the number of grid cells generated in high dimensional data space and make the neighbor-searching easily. On basis of the two methods, we propose grid-based clustering algorithm (GCOD), which merges two intersecting grids according to density estimation. The algorithm requires only one parameter and the time complexity is linear to the size of the input data set or data dimension. The experimental results show that GCOD can discover arbitrary shapes of clusters and scale well.

A scientific visualization tool, based on a virtual reality system, has been created to explore remotely sensed data. The main aim is to find possible relationships between results of different spectral unmixing techniques in order to improve image classifications. In particular, data from fuzzy classifiers and linear spectral unmixing techniques, has been considered. The tool offers the possibility to use different representations for high dimensional data due to the fact that none of the existing representations is always effective to visualise multi-dimensional data. Furthermore, the possibility to visually link different representations of the same data, by using a technique called data brushing, will help the analyst in to get more insight into the structures present in the high dimensional data space and, to find relationships between the data spaces. The exploratory tool has been based on a virtual reality system in order to create new human-computer interaction paradigms. Furthermore, it has been used to assess the usability of immersive computer interfaces, called virtual environments, in data exploration. The main advantages in using this kind of interface has been an increased interface space and a more natural human-computer interaction which means more information content requiring less time to become familiar with the tool.

During the last decade, the deluge of multimedia data has impacted a wide range of research areas, including multimedia retrieval, 3D tracking, database management, data mining, machine learning, social media analysis, medical imaging, and so on. Machine learning is largely involved in multimedia applications of building models for classification and regression tasks, etc., and the learning principle consists in designing the models based on the information contained in the multimedia dataset. While many paradigms exist and are widely used in the context of machine learning, most of them suffer from the `curse of dimensionality', which means that some strange phenomena appears when data are represented in a high-dimensional space. Given the high dimensionality and the high complexity of multimedia data, it is important to investigate new machine learning algorithms to facilitate multimedia data analysis. To deal with the impact of high dimensionality, an intuitive way is to reduce the dimensionality. On the other hand, some researchers devoted themselves to designing some effective learning schemes for high-dimensional data. In this survey, we cover feature transformation, feature selection and feature encoding, three approaches fighting the consequences of the curse of dimensionality. Next, we briefly introduce some recent progress of effective learning algorithms. Finally, promising future trends on multimedia learning are envisaged.

Massive amount of Earth science data open an unprecedented opportunity to discover potentially valuable information. Earth science data are complex, nonlinear, high-dimensional data, and the sparsity of data in high-dimensional space poses major challenge in clustering of the data. Shared nearest neighbor clustering (SNN) algorithm is one of the well-known and efficient methods to handle high-dimensional spatiotemporal data. The SNN clustering method does not cluster all the data forming rigid boundary selection. This paper reports fuzzy shared nearest neighbor (FSNN) algorithm which is an enhancement of the SNN clustering method that has the capability of handling the data lying in the boundary regions by means of a fuzzy concept. The clusters obtained can be characterized by the cluster centroid, which summarizes the behavior of the ocean points in the cluster. The statistical measure is used to find the significant relation between the cluster centroids and the existing climate indices. In this study, correlation measure is used to find the significant pattern, such as teleconnection or dipole. The experimentation is performed on Indian continent latitude range $$7.5^{\circ }{-}37.5^{\circ }\hbox {N}$$ and longitude range $$67.5^{\circ }{-}97.5^{\circ }\hbox {E}$$ . Extensive experiments are carried out to compare the proposed approach with existing clustering methods such as K-means, fuzzy C-means and SNN. The proposed method, FSNN algorithm, not only handles the data lying in the overlapping region, but it also finds more compact and well-separated clusters. FSNN shows better results in terms of finding a significant correlation between cluster centroids and existing climate indices and validated by ground truth dataset.

The sparsity and the problem of the curse of dimensionality of high-dimensional data, which make the most of the traditional clustering algorithm, lose action in high-dimensional space. Therefore, clustering of data in high-dimensional space is becoming the hot research areas. By utilizing the subtractive clustering as initialized method, and combine with the revised clustering validation indices, this paper offers a subspace clustering algorithm for automatically determining the optimal number of clusters on high dimensional data. The experiment results show that the proposed clustering algorithm can get better cluster validation performance than that of conventional indices.

High dimension and complexity of network high-dimensional data lead to poor feature selection effect network high-dimensional data. To effectively solve this problem, feature selection algorithms for high-dimensional network data based on supervised discriminant projection (SDP) have been designed. The sparse representation problem of high-dimensional network data is transformed into an Lp norm optimization problem, and the sparse subspace clustering method is used to cluster high-dimensional network data. Dimensionless processing is carried out for the clustering processing results. Based on the linear projection matrix and the best transformation matrix, the dimensionless processing results are reduced by combining the SDP. The sparse constraint method is used to achieve feature selection of high-dimensional data in the network, and the relevant feature selection results are obtained. The experimental findings demonstrate that the suggested algorithm can effectively cluster seven different types of data and converges when the number of iterations approaches 24. The F1 value, recall, and precision are all kept at high levels. High-dimensional network data feature selection accuracy on average is 96.9%, and feature selection time on average is 65.1 milliseconds. The selection effect for network high-dimensional data features is good.

There are a large number of high-dimensional data in the Internet of Brain Things, and the data is reduced from the high-dimensional to low-dimensional to maintain the similarity between the data, thereby effectively ensuring the operating speed of the Internet of Brain Things. In the traditional method, the distributed dimensionality reduction reconstruction algorithm of the High dimensional data has poor dimensionality reduction effect and serious data distortion after reconstruction. A method for dimensionality reconstruction of high-dimensional data in the Internet of Brain Things is proposed. By using the algorithm of linear discriminant analysis, the projection matrix of high dimensional data is constructed to solve it. According to the solution results, using improved implicit variable model to establish a high dimensional large data dimensionality reduction model for the Internet of Brain Things. The fitness value of data after dimensionality reduction is calculated by quantum immune clonal algorithm, and the optimal individual and optimal solution are determined. The data reconfiguration is realized through the optimal solution marshalling. Experimental results show that the proposed algorithm can effectively improve the dimensionality reduction of High dimensional data in the Internet of Brain Things. After reconstruction, the reconstructed data retain accurate data information, the reliability of reconstructed data is high, and the computational complexity is not high, the need for small storage space, and the advantages of strong promotion ability.

Various machine learning, cloud computing and big data models are most utilized control parameters in software applications. Therefore these systems are most demand at current trending decades. But these models are needs very low data access time, speed for process. Day to day life data storage servers and devices are costly and hardware complex, so dimensionality is increases with rapid manner. Any type of optimization techniques access takes more time consumption for high dimensional data. So, more applications related problems are occurs only at high dimensional data space does not at low space dimensional data. In this research proposes a dimensional reduction technique with Logistic regression (LR) model. This LR model is most helpful for dimensional reduction and clustering problems. LRML method has reduced the dimensional data size and achieved thee efficiency by 95.3% and ratio of reduction by 35.76%.

Multi-level adaptive neuro-fuzzy inference system-based reconstruction of 1D ISOMAP representations

The technique of machinery condition monitoring has been greatly enhanced over recent years with the application of many effective classifiers. However, these classification methods suffer from the 'curse of dimensionality' when applied to high-dimensional condition monitoring data. Actually, many classification algorithms are simply intractable when the number of features in the data is sufficiently large. In order to solve the problem, engineers have to resort to complicated feature extraction methods and other statistical theories to reduce the data dimensionality. However, features extracted using these methods lose their original engineering meaning and become obscure for engineers. In this study, a novel feature selection algorithm is presented to help to identify machinery condition quickly, based only on frequency spectrum data and without considering any complicated feature extraction methods. This brings many significant benefits: it can not only help engineers out of difficulties with complicated feature extraction methods, but it also gives a clear insight into the real condition of machinery without any loss of engineering meaning from the features used. The algorithm forms a functional extension of a relevance vector machine to feature selection, with a fast step-variable sequential backward search algorithm to search relevant scale parameters within a kernel function. Two case studies on different levels of condition monitoring are conducted to demonstrate the potential of applying the algorithm to high-dimensional engineering data.

High-dimensional data is a key study object for both machine learning (ML) and information visualization. In the field of visualization, dimensionality reduction (DR) methods, also known as projections, are one of the most frequently used classes of techniques for visually exploring large and high-dimensional datasets. In ML, high-dimensional data is generated and processed by classifiers and regressors, which increasingly require visualization for explanation and exploration. This thesis focuses on a recent visualization technique called decision maps. A decision map is a 2D image that visualizes the decision boundaries of a classifier in the data space, and can be used to explain and improve the behavior of ML classifiers. Constructing decision maps essentially involves a DR method and its inverse process (inverse projection). As such, ML techniques can help to create decision maps by providing improved (inverse) projections. We begin with a case study applying decision maps to explain the classification of mineral deposit genesis. Our findings show that decision maps provide extra insights into the mineral classification model, aiding geologists in interpreting the model. However, we also identified gaps in current decision map techniques that present opportunities for improvement. Following this case study, we conducted a comprehensive evaluation of three notable decision map techniques. Our evaluation shows that each technique has unique advantages and disadvantages. Our results can guide users in selecting the most suitable technique for specific tasks. A particularly salient finding of this evaluation was that all tested decision maps exhibit a surface-like behavior when applied to a 3D dataset. We explored the aforementioned surface-like behavior of decision maps across more scenarios. By estimating the intrinsic dimensionality of the maps, we found that existing decision map methods cover only a small portion of the intrinsic dimensionality of high-dimensional data spaces. This finding highlights fundamental limitations in all current approaches to constructing decision maps. To address these limitations, we propose a novel approach for computing inverse projections with the support of ML. Our method allows users to interactively control the location of the inversely projected points, thus also of visualizations like decision maps, within the high-dimensional space. In this way, users can explore larger parts of the data space, bypassing the practical limitations imposed by the aforementioned surface-like behavior of decision maps. We demonstrate the effectiveness of our approach through its application to a style transfer task. Finally, we introduce an accelerated computation method for decision maps. Our method significantly reduces the computation time for both basic decision maps and enhanced variations thereof such as gradient maps. The acceleration facilitates the further deployment of such visualizations in interactive visual analytics workflows for classifier engineering.

A novel feature extraction method that utilizes nonlinear mapping from the original data space to the feature space is presented in this dissertation. Feature extraction methods aim to find compact representations of data that are easy to classify. Measurements with similar values are grouped to same category, while those with differing values are deemed to be of separate categories. For most practical systems, the meaningful features of a pattern class lie in a low dimensional nonlinear constraint region (manifold) within the high dimensional data space. A learning algorithm to model this nonlinear region and to project patterns to this feature space is developed. Least squares estimation approach that utilizes interdependency between points in training patterns is used to form the nonlinear region. The proposed feature extraction strategy is employed to improve face recognition accuracy under varying illumination conditions and facial expressions. Though the face features show variations under these conditions, the features of one individual tend to cluster together and can be considered as a neighborhood. Low dimensional representations of face patterns in the feature space may lie in a nonlinear constraint region, which when modeled leads to efficient pattern classification. A feature space encompassing multiple pattern classes can be trained by modeling a separate constraint region for each pattern class and obtaining a mean constraint region by averaging all the individual regions. Unlike most other nonlinear techniques, the proposed method provides an easy intuitive way to place new points onto a nonlinear region in the feature space. The proposed feature extraction and classification method results in improved accuracy when compared to the classical linear representations. Face recognition accuracy is further improved by introducing the concepts of modularity, discriminant analysis and phase congruency into the proposed method. In the modular approach, feature components are extracted from different sub-modules of the images and concatenated to make a single vector to represent a face region. By doing this we are able to extract features that are more representative of the local features of the face. When projected onto an arbitrary line, samples from well formed clusters could produce a confused mixture of samples from all the classes leading to poor recognition. Discriminant analysis aims to find an optimal line orientation for which the data classes are well separated. Experiments performed on various databases to evaluate the performance of the proposed face recognition technique have shown improvement in recognition accuracy, especially under varying illumination conditions and facial expressions. This shows that the integration of multiple subspaces, each representing a part of a higher order nonlinear function, could represent a pattern with variability. Research work is progressing to investigate the effectiveness of subspace projection methodology for building manifolds with other nonlinear functions and to identify the optimum nonlinear function from an object classification perspective.

Outlier detection aims to find a data sample that is significantly different from other data samples. Various outlier detection methods have been proposed and have been shown to be able to detect anomalies in many practical problems. However, in high dimensional data, conventional outlier detection methods often behave unexpectedly due to a phenomenon called the curse of dimensionality. In this paper, we compare and analyze outlier detection performance in various experimental settings, focusing on text data with dimensions typically in the tens of thousands. Experimental setups were simulated to compare the performance of outlier detection methods in unsupervised versus semi-supervised mode and uni-modal versus multi-modal data distributions. The performance of outlier detection methods based on dimension reduction is compared, and a discussion on using k-NN distance in high dimensional data is also provided. Analysis through experimental comparison in various environments can provide insights into the application of outlier detection methods in high dimensional data.

A topological approach for cancer subtyping from gene expression data.