Distance In High-dimensional Space Research Articles

Low-dimensional representation of monthly electricity demand profiles

This paper addresses the problem of reducing the number of values required to characterize an electricity demand profile, which is usually known as its dimensionality. This reduction may have a significant impact on the computational efforts and storage capacities required to analyze and process high volumes of electricity load curves. Also, the reduction to 2 or even 1 component enables its graphic representation. Specifically, this work is mainly focused on profiles defined by their monthly demand values, and where the clients are aggregated by locations and/or economic activities. This approach is of great interest for marketing analysis and decision-making of electricity retailers. In this sense, the use of dimensionality reduction techniques based on knowledge (calendar and temperature) along with the application of data-driven procedures (Principal Component Analysis and autoencoders), are explored in the paper. The results of this research show that autoencoders clearly outperform the other techniques, yielding errors in the reduction process between 15% to 40% lower and preserving distances between profiles in the low-dimensional spaces, with a correlation of 0.93 with the distances in high dimensional space. Additionally, the bidimensional graphical representation of a profile can easily be interpreted in a polar way, where the angle denotes the shape of the profile, and the radius reveals its scale. To reach these results, a very large dataset has been employed, with about half a million aggregated profiles corresponding to the electricity consumption during 3 years of more than 27 million clients in Spain.

A novel density-based outlier detection method using key attributes

Outlier detection has attracted extensive attention in medical, financial, telecommunications and other fields. Although many related technologies have been proposed, most of them are faced with the problems of the neighborhood size of an object is difficult to determine and the distance in high-dimensional space is unreliable. To overcome these weaknesses, we propose a novel density-based outlier detection method that introduces the concept of Minimum the Sum of Edge Set and other related definitions in key attributes space. Based on the stability of Reverse Minimum the Sum of Edge Set, the proposed method can adaptively select the parameter representing the neighborhood size. In addition, some properties of the proposed local outlier factor are derived. Experiments on synthetic and real-world datasets demonstrate that our method is more effective than the existing outlier detection approaches.

Similarity measure method based on spectra subspace and locally linear embedding algorithm

Due to the high dimensionality, redundancy, noise and nonlinearity of the near infrared (NIR) spectra data result the difficulty of the similarity measure. This paper presented a similarity measure method SSLLE based on the spectra subspace and locally linear embedding (LLE) algorithm. Firstly, we divided the high dimensional spectra data into several subspaces according to the absorption band of the major chemical compositions, which effectively avoids the influence of irrelevant features and noise and reduces the dimension and computation complexity of the LLE. Then, we modified the LLE algorithm by introducing the geodesic distance instead of Euclidean distance, which solves the measure problem of the Euclidean distance in high dimensional space. In order to make the sample more evenly distributed, the method of distance calculation in LLE was also modified. For each spectra subspace, the distance matrix was calculated according to the embedding that was mapped from the high dimensional space by using the modified LLE. Subsequently, the spectral similarity matrix of the sample set was integrated by adding all of the individual distance matrices of each subspace so that the sample with the highest similarity can be found.In order to investigate the effectiveness of the algorithm, the spectral projection of the samples was analyzed first, the results showed that the SSLLE distinguished the tobacco samples from different areas significantly better than the methods of principal component analysis (PCA) and LLE. Secondly, we compared the results of searching the most spectrally similar sample with the target tobacco, it showed that the SSLLE had the minimum differences in the chemical composition, and the highest consistency with the recommendation of the experts than that of PCA and LLE algorithm. It also had good robustness and precision.

Employing GPU architectures for permutation-based indexing

Permutation-based indexing is one of the most popular techniques for the approximate nearest-neighbor search problem in high-dimensional spaces. Due to the exponential increase of multimedia data, the time required to index this data has become a serious constraint. One of the possible steps towards faster index construction is utilization of massively parallel platforms such as the GPGPU architectures. In this paper, we have analyzed the computational costs of individual steps of the permutation-based index construction in a high-dimensional feature space and summarized our hybrid CPU-GPU solution. Our experience gained from this research may be utilized in other individual problems that require computing Lp distances in high-dimensional spaces, parallel top-k selection, or partial sorting of multiple smaller sets. We also provide guidelines how to balance workload in hybrid CPU-GPU systems.

Choosing ℓp norms in high-dimensional spaces based on hub analysis

The hubness phenomenon is a recently discovered aspect of the curse of dimensionality. Hub objects have a small distance to an exceptionally large number of data points while anti-hubs lie far from all other data points. A closely related problem is the concentration of distances in high-dimensional spaces. Previous work has already advocated the use of fractional ℓp norms instead of the ubiquitous Euclidean norm to avoid the negative effects of distance concentration. However, which exact fractional norm to use is a largely unsolved problem. The contribution of this work is an empirical analysis of the relation of different ℓp norms and hubness. We propose an unsupervised approach for choosing an ℓp norm which minimizes hubs while simultaneously maximizing nearest neighbor classification. Our approach is evaluated on seven high-dimensional data sets and compared to three approaches that re-scale distances to avoid hubness.

Resveratrol Delays Age-Related Deterioration and Mimics Transcriptional Aspects of Dietary Restriction without Extending Life Span

A small molecule that safely mimics the ability of dietary restriction (DR) to delay age-related diseases in laboratory animals is greatly sought after. We and others have shown that resveratrol mimics effects of DR in lower organisms. In mice, we find that resveratrol induces gene expression patterns in multiple tissues that parallel those induced by DR and every-other-day feeding. Moreover, resveratrol-fed elderly mice show a marked reduction in signs of aging, including reduced albuminuria, decreased inflammation, and apoptosis in the vascular endothelium, increased aortic elasticity, greater motor coordination, reduced cataract formation, and preserved bone mineral density. However, mice fed a standard diet did not live longer when treated with resveratrol beginning at 12 months of age. Our findings indicate that resveratrol treatment has a range of beneficial effects in mice but does not increase the longevity of ad libitum-fed animals when started midlife.