Dimensionality reduction for tensor data based on projection distance minimization and hilbert-schmidt independence criterion maximization1

Tensor data are becoming more and more common in machine learning. Compared with vector data, the curse of dimensionality of tensor data is more serious. The motivation of this paper is to combine Hilbert-Schmidt Independence Criterion (HSIC) and tensor algebra to create a new dimensionality reduction algorithm for tensor data. There are three contributions in this paper. (1) An HSIC-based algorithm is proposed in which the dimension-reduced tensor is determined by maximizing HSIC between the dimension-reduced and high-dimensional tensors. (2) A tensor algebra-based algorithm is proposed, in which the high-dimensional tensor are projected onto a subspace and the projection coordinate is set to be the dimension-reduced tensor. The subspace is determined by minimizing the distance between the high-dimensional tensor data and their projection in the subspace. (3) By combining the above two algorithms, a new dimensionality reduction algorithm, called PDMHSIC, is proposed, in which the dimensionality reduction must satisfy two criteria at the same time: HSIC maximization and subspace projection distance minimization. The proposed algorithm is a new attempt to combine HSIC with other algorithms to create new algorithms and has achieved better experimental results on 8 commonly-used datasets than the other 7 well-known algorithms.

Projector-Based Augmented Reality System for Computer Assisted Orthopaedic Surgery

This paper presents a projector-based augmented reality (AR) system for Computer- Assisted Orthopaedic Surgery (CAOS). After calibration, our AR system allows for projection of not only the virtual model directly on the surface of the target organ to create an augmented reality but also important clinical information such as distance and angular deviations from a surgical plan, which are important for various computer-assisted surgical procedures such as trajectory drilling and fracture reduction. The feasibility and accuracy of the system is experimentally validated on a 3D printed phantom model with pyramid shape, a dry goat bone and an in vitro pig leg. An average projection distance error of 1.03±0.58mm and an average drill alignment error of 1.17±0.43°were found. The results demonstrate the efficacy of the proposed AR system.

How far actually is the Galactic Center IRS 13E3 from Sagittarius A*?

The Galactic Center IRS 13E cluster is a very intriguing infrared object located at ${\sim } 0.13$ pc from Sagittarius A$^\ast$ (Sgr A$^\ast$) in projection distance. There are arguments both for and against the hypothesis that a dark mass like an intermediate mass black hole (IMBH) exists in the cluster. We recently detected the rotating ionized gas ring around IRS 13E3, which belongs to the cluster, in the H30$\alpha$ recombination line using ALMA. The enclosed mass is derived to be $M_{\mathrm{encl.}}\simeq 2\times 10^{4}\, M_\odot$, which agrees with an IMBH and is barely less than the astrometric upper limit mass of an IMBH around Sgr A$^\ast$. Because the limit mass depends on the true three-dimensional (3D) distance from Sgr A$^\ast$, it is very important to determine it observationally. However, the 3D distance is indefinite because it is hard to determine the line-of-sight (LOS) distance by usual methods. We attempt here to estimate the LOS distance from spectroscopic information. The CH$_3$OH molecule is easily destroyed by the cosmic rays around Sgr A$^{\ast }$. However, we detected a highly excited CH$_3$OH emission line in the ionized gas stream associated with IRS 13E3. This indicates that IRS 13E3 is located at $r\gtrsim 0.4$ pc from Sgr A$^{\ast }$.

An Online Method to Detect Urban Computing Outliers via Higher-Order Singular Value Decomposition

Here we propose an online method to explore the multiway nature of urban spaces data for outlier detection based on higher-order singular value tensor decomposition. Our proposal has two sequential steps: (i) the offline modeling step, where we model the outliers detection problem as a system; and (ii) the online modeling step, where the projection distance of each data vector is decomposed by a multidimensional method as new data arrives and an outlier statistical index is calculated. We used real data gathered and streamed by urban sensors from three cities in Finland, chosen during a continuous time interval: Helsinki, Tuusula, and Lohja. The results showed greater efficiency for the online method of detection of outliers when compared to the offline approach, in terms of accuracy between a range of 8.5% to 10% gain. We observed that online detection of outliers from real-time monitoring through the sliding window becomes a more adequate approach once it achieves better accuracy.

Design of an LED Spot Light System with a Projection Distance of 10 km

We designed a spot light system with an illumination range of 10 km. In the designed system, an appropriate white light-emitting diode (LED) was selected according to the exitance and injection power required. Subsequently, through a first-order optical design, the geometry of the lens and reflector was determined using geometrical calculation. Because the central illuminance of the projection spot of the reflector was 2.5 times that of the cover lens, we first considered the fabrication error of the reflector. According to the adjustment of the optimized distance between the white LED and reflector, we modified the design of the cover lens to fit the new location of the white LED. An LED spot light module containing 16 spot light units was used. The module’s power injection was only 68.2 W. Because of the excellent performance of the designed system in terms of the divergence angle of the projection beam and maximum luminous intensity, which were 1.6° and 2,840,000 cd, respectively, the projection distance of the LED spot light module was 3.37 Km, according to the ANSI regulation. Finally, a spot light system with nine modules and capable of achieving a projection distance of 10 km was successfully fabricated.