Membership-Mappings for Data Representation Learning: Measure Theoretic Conceptualization

Simultaneously learning affinity matrix and data representations for machine fault diagnosis

Dimension reduction plays an important role in handling the massive quantity of high dimensional data such as biomedical text data, gene expression data, and mass spectrometry data, and so forth. In this paper, we introduce distance preserving dimension reduction (DPDR) based on the QR factorization (DPDR/QR) or the Cholesky factorization (DPDR/C). DPDR generates lower dimensional representations of the high-dimensional data, which can exactly preserve Euclidean distances and cosine similarities between any pair of data points in the original dimensional space. After projecting data points to the lower dimensional space obtained from DPDR, one can execute other data analysis algorithms. DPDR can substantially reduce the computing time and/or memory requirement of a given data analysis algorithm, especially when we need to run the data analysis algorithm many times for estimating parameters or searching for a better solution.

A clustering method based on multidimensional texture analysis

Discoveries of gaps in data have been important in astrophysics. For example, there are kinematic gaps opened by resonances in dynamical systems, or exoplanets of a certain radius that are empirically rare. A gap in a data set is a kind of anomaly, but in an unusual sense: Instead of being a single outlier data point, situated far from other data points, it is a region of the space, or a set of points, that is anomalous compared to its surroundings. Gaps are both interesting and hard to find and characterize, especially when they have non-trivial shapes. We present in this paper a statistic that can be used to estimate the (local) "gappiness" of a point in the data space. It uses the gradient and Hessian of the density estimate (and thus requires a twice-differentiable density estimator). This statistic can be computed at (almost) any point in the space and does not rely on optimization; it allows to highlight under-dense regions of any dimensionality and shape in a general and efficient way. We illustrate our method on the velocity distribution of nearby stars in the Milky Way disk plane, which exhibits gaps that could originate from different processes. Identifying and characterizing those gaps could help determine their origins. We provide in an Appendix implementation notes and additional considerations for finding under-densities in data, using critical points and the properties of the Hessian of the density.

Finding a new drug which is both safe and efficient is an expensive and time-consuming endeavour. In particular, establishing the ‘dose-effect relationship’ – how beneficial a drug is at different dosages – can be challenging. Predicting this curve requires gathering experimental data by exposing and recording how cells respond to various levels of the drug. However, extreme values are often observed at low and high dosages, potentially introducing errors that are hard to correct in the prediction process. Yet, these extreme observations are sometimes genuine so researchers cannot just ignore them. To improve dose-effect estimation, Zhou, Liu, Fang et al. developed a new general-purpose approach. It uses advanced statistical modelling to account for extremes in lab data. This strategy outperformed other methods when dealing with these observations while also providing higher efficiency in data analysis with more uniform data in experiments. To facilitate implementation, Zhou, Liu, Fang et al. set up a user-friendly tool baptized ‘REAP’; this free online resource allows scientists without advanced statistical experience to harness the new approach and to perform dose-effect analysis more easily and accurately. This could boost research across many different disciplines that examine the effects of chemicals on cells.

The existing membrane clustering algorithms may fail to handle the data sets with non-spherical cluster boundaries. To overcome the shortcoming, this paper introduces kernel methods into membrane clustering algorithms and proposes a kernel-based membrane clustering algorithm, KMCA. By using non-linear kernel function, samples in original data space are mapped to data points in a high-dimension feature space, and the data points are clustered by membrane clustering algorithms. Therefore, a data clustering problem is formalized as a kernel clustering problem. In KMCA algorithm, a tissue-like P system is designed to determine the optimal cluster centers for the kernel clustering problem. Due to the use of non-linear kernel function, the proposed KMCA algorithm can well deal with the data sets with non-spherical cluster boundaries. The proposed KMCA algorithm is evaluated on nine benchmark data sets and is compared with four existing clustering algorithms.

For a wrap-around surface, many issues, such as difficulty in parameterisation of data points, incapability of automatic modelling, and high-accuracy surface reconstruction, need to be resolved. Therefore, an automatic accurate non-uniform rational B-spline (NURBS) surface reconstruction method is proposed in the present paper. First, after a method that recognises the central axis from data points is given, the data points in physical space are projected to a plane domain. Consequently, the boundary curve is extracted. Second, by local surface fitting of the data points on sector-distributed cross-sectional plane, the unorganised scatter points become ordered array points. A base surface is created using skinning technology. Finally, using robust arithmetic of the multivariate Bernstein-form polynomials, an algorithm for calculating the closest point is proposed. Using base-surface parameterisation, an accurate surface fitting is finally implemented based on least square iterative procedure. Examples verify the feasibility and validity of the proposed surface reconstruction method.

This article is an addendum to the 2001 paper [1] which investigated an approach to hierarchical clustering based on the level sets of a density function induced on data points in a d-dimensional feature space. We refer to this as the “level-sets approach” to hierarchical clustering. The density functions considered in [1] were those formed as the sum of identical radial basis functions centered at the data points, each radial basis function assumed to be continuous, monotone decreasing, convex on every ray, and rising to positive infinity at its center point. Such a framework can be investigated with respect to both the Euclidean (L2) and Manhattan (L1) metrics. The addendum here puts forth some observations and questions about the level-sets approach that go beyond those in [1]. In particular, we detail and ask the following questions. How does the level-sets approach compare with other related approaches? How is the resulting hierarchical clustering affected by the choice of radial basis function? What are the structural properties of a function formed as the sum of radial basis functions? Can the levels-sets approach be theoretically validated? Is there an efficient algorithm to implement the level-sets approach?

We study the connectivity properties of random Bluetooth graphs that model certain \ad hoc wireless networks. The graphs are obtained as \irrigation subgraphs of the well-known random geometric graph model. There are two parameters that control the model: the radius r that determines the \visible neighbors of each node and the number of edges c that each node is allowed to send to these. The randomness comes from the underlying distribution of data points in space and from the choices of each vertex. We prove that no connectivity can take place with high probability for a range of parameters r;c and completely characterize the connectivity threshold (in c) for values of r close the critical value for connectivity in the underlying random geometric graph.

Data bases of reversed field pinch (RFP) plasma have been gradually accumulated by recent experiments of several RFP devices. New confinement scalings τX(X=RFPs1)E=0.024Aa2IP/P1/2heat, τX(X=RFPs2)E=0.04s(IN)Aa2I1.25P/P1/2heat which are consistent to the recent data are presented, where units are in [s], [m], [MA] and [MW] respectively and s(IN) is a correction function of IN≡IP/πa2‹ne›20). From the standpoint of new scalings, dependences among parameters of possible RFP reactors are analyzed to find the conditions for RFP reactors. Hs1 Hs2 are defined by the ratios of necessary energy confinement time for RFP reactors for burning against τX(X=RFPs1) and τX(X=RFPs2) respectively. When confinement time follows τX(X=RFPs1)E scaling, confinement enhancement factor of at least Hs1=23 is necessary for RFP reactors to be realistic. When confinement time follows τX(X=RFPs2)E scaling, data points in IP-a space of RFP reactors are within the region of target.

Diffusion representations

In the information era, the distribution pattern of point of interest (POI) data points in urban space is of great reference significance in urban infrastructure planning and urban spatial analysis, providing a basis for studying the identification of urban functional areas. With the downtown area of Changchun as the research object, the POI data was quantified according to the classification of the urban functional areas, identifying the urban functional areas in the downtown area of Changchun. The experimental results were compared with the current urban land use maps in Changchun to demonstrate the feasibility of the experimental method. Compared with traditional methods, this method features fast analysis speed and digital attributes, which is of certain value for urban geospatial planning.

As a promising alternative to traditional search techniques, hashing‐based approximate nearest neighbour search provides an applicable solution for big data. Most existing efforts are devoted to finding better projections to preserve the neighbouring structure of original data points in Hamming space, but ignore the quantisation procedure which may lead to the breakdown of the neighbouring structure maintained in the projection stage. To address this issue, the authors propose a novel multi‐bit quantisation (MBQ) method using a Matthews correlation coefficient (MCC) term and a regularisation term. The authors' method utilises the neighbouring relationship and the distribution information of original data points instead of the projection dimension usually used in the previous MBQ methods to adaptively learn optimal quantisation thresholds, and allocates multiple bits per projection dimension in terms of the learned thresholds. Experiments on two typical image data sets demonstrate that the proposed method effectively preserves the similarity between data points in the original feature space and outperforms state‐of‐the‐art quantisation methods.

Hierarchical clustering analysis is applied to the positioning of two simultaneously-occurring intrusion events in the case of a dual Mach-Zehnder interferometer used for intrusion detection. To simulate the two intrusion events, the sensing fibers of the dual Mach-Zehnder interferometer are heavily knocked at two different positions simultaneously. Then the clockwise (CW) and counter-clockwise (CCW) signals are loaded into a personal computer through a data acquisition module, and analyzed by Fourier transform method for determination of the time delay between the two signals. Hierarchical clustering analysis is then employed twice for dividing the data points in a feature space into several clusters according to the conditions required. To locate the two intrusions, the first clustering analysis is performed on the data points formed by signals detected in a 10 ms time period, with the centroid of the largest cluster being the location of a single intrusion event. Then, 100 pairs of CW and CCW signals detected sequentially are analyzed to give 100 locations. These 100 locations and their CP values (each standing for a ratio of a given spectral amplitude to the summation of the spectral amplitudes over the frequency band of 2500 to 5000 Hz) constitute 100 data points in a feature space for the second hierarchical clustering analysis, which then determines the respective locations of the two intrusion events. In the test of a 1036 m long fiber perimeter, we demonstrated an accuracy to within 21.55 m.

Deep models often suffer from severe performance drop due to the appearance shift in the real clinical setting. Most of the existing learning-based methods rely on images from multiple sites/vendors or even corresponding labels. However, collecting enough unknown data to robustly model segmentation cannot always hold since the complex appearance shift caused by imaging factors in daily application. In this paper, we propose a novel style-invariant method for cardiac image segmentation. Based on the zero-shot style transfer to remove appearance shift and test-time augmentation to explore diverse underlying anatomy, our proposed method is effective in combating the appearance shift. Our contribution is three-fold. First, inspired by the spirit of universal style transfer, we develop a zero-shot stylization for content images to generate stylized images that appearance similarity to the style images. Second, we build up a robust cardiac segmentation model based on the U-Net structure. Our framework mainly consists of two networks during testing: the ST network for removing appearance shift and the segmentation network. Third, we investigate test-time augmentation to explore transformed versions of the stylized image for prediction and the results are merged. Notably, our proposed framework is fully test-time adaptation. Experiment results demonstrate that our methods are promising and generic for generalizing deep segmentation models.