We consider the problem of learning a low dimensional representation for compositional data. Compositional data consists of a collection of nonnegative data that sum to a constant value. Since the parts of the collection are statistically dependent, many standard tools cannot be directly applied. Instead, compositional data must be first transformed before analysis. Focusing on principal component analysis (PCA), we propose an approach that allows low dimensional representation learning directly from the original data.

Instead,compositional datamust be first transformed before analysis.

Bregman divergence properties that have been pervasive in machine learning.

We consider the problem of learning a low dimensional representation for compositional data. Compositional data consists of a collection of nonnegative data that sum to a constant value. Since the parts of the collection are statistically dependent, many standard tools cannot be directly applied. Instead, compositional data must be first transformed before analysis. Focusing on principal component analysis (PCA), we propose an approach that allows low dimensional representation learning directly from the original data.

We consider the problem of learning a low dimensional representation for compositional data.

Bregman divergences play a central role in the design and analysis of a range of machine learning algorithms through a handful of popular theorems. We present a new theorem which shows that "Bregman distortions" (employing a potentially non-convex generator) may be exactly re-written as a scaled Bregman divergence computed over transformed data. This property can be viewed from the standpoints of geometry (a scaled isometry with adaptive metrics) or convex optimization (relating generalized perspective transforms). Admissible distortions include geodesic distances on curved manifolds and projections or gauge-normalisation. Our theorem allows one to leverage to the wealth and convenience of Bregman divergences when analysing algorithms relying on the aforementioned Bregman distortions. We illustrate this with three novel applications of our theorem: a reduction from multi-class density ratio to class-probability estimation, a new adaptive projection free yet norm-enforcing dual norm mirror descent algorithm, and a reduction from clustering on flat manifolds to clustering on curved manifolds. Experiments on each of these domains validate the analyses and suggest that the scaled Bregman theorem might be a worthy addition to the popular handful of Bregman divergence properties that have been pervasive in machine learning.

Tunnel CCTVs are installed to low height and long-distance interval. However, because of the limitation of installation height, severe perspective effect in distance occurs, and it is almost impossible to detect vehicles in far distance from the CCTV in the existing tunnel CCTV-based accident detection system (Pflugfelder 2005). To overcome the limitation, a vehicle object is detected through an object detection algorithm based on an inverse perspective transform by re-setting the region of interest (ROI). It can detect vehicles that are far away from the CCTV. To verify this process, this paper creates each dataset consisting of images and bounding boxes based on the original and warped images of the CCTV at the same time, and then compares performance of the deep learning object detection models trained with the two datasets. As a result, the model that trained the warped image was able to detect vehicle objects more accurately at the position far from the CCTV compared to the model that trained the original image.

In the following paper, we have combined the various basic functionalities provided by the NumPy library and OpenCv library, which is an open source for Computer Vision applications, like conversion of colored images to grayscale, calculating threshold, finding contours and using those contour points to take perspective transform of the image inputted by the user, using Python version 3.7. Additional features include cropping, rotating and saving as well. All these functions and features, when implemented step by step, results in a complete scanning application. The applied procedure involves the following steps: Finding contours, applying Perspective transform and brightening the image, Adaptive Thresholding and applying filters for noise cancellation, and Rotation features and perspective transform for a special cropping algorithm. The described technique is implemented on various samples.

We consider the problem of learning a low dimensional representation for compositional data. Compositional data consists of a collection of nonnegative data that sum to a constant value. Since the parts of the collection are statistically dependent, many standard tools cannot be directly applied. Instead, compositional data must be first transformed before analysis. Focusing on principal component analysis (PCA), we propose an approach that allows low dimensional representation learning directly from the original data.

We consider the problem of learning a low dimensional representation for compositional data. Compositional data consists of a collection of nonnegative data that sum to a constant value. Since the parts of the collection are statistically dependent, many standard tools cannot be directly applied. Instead, compositional data must be first transformed before analysis. Focusing on principal component analysis (PCA), we propose an approach that allows low dimensional representation learning directly from the original data. Our approach combines the benefits of the log-ratio transformation from compositional data analysis and exponential family PCA. A key tool in its derivation is a generalization of the scaled Bregman theorem, that relates the perspective transform of a Bregman divergence to the Bregman divergence of a perspective transform and a remainder conformal divergence. Our proposed approach includes a convenient surrogate (upper bound) loss of the exponential family PCA which has an easy to optimize form. We also derive the corresponding form for nonlinear autoencoders. Experiments on simulated data and microbiome data show the promise of our method.