Combining forecasts from multiple temporal aggregation levels exploits information differences and mitigates model uncertainty, while reconciliation ensures a unified prediction that supports aligned decisions at different horizons. It can be challenging to estimate the full cross-covariance matrix for hierarchy, which easily of very large dimension, yet it is difficult know priori part error s...

Inspired by random walks on graphs, the diffusion map (DM) is a class of unsupervised machine learning that offers automatic identification low-dimensional data structure hidden in high-dimensional set. In recent years, among its many applications, DM has been successfully applied to discover relevant order parameters many-body systems, enabling classification quantum phases matter. However, cl...

In this paper we describe a novel approach towards dimensionality reduction of patterns to be classi ed. It consists of local processing of the patterns as an alternative to the well-known global principal component analysis (PCA) algorithm. We use a feed-forward neural network architecture with spatial or spatio-temporal receptive eld connections between the rst two layers that yields a transf...

Visual attributes are high-level semantic description of visual data that are close to the language of human. They have been intensively used in various applications such as image classification [1,2], active learning [3,4], and interactive search [5]. However, the usage of attributes in dimensionality reduction has not been considered yet. In this work, we propose to utilize relative attribute...

Dimensionality reduction is a generic name for any procedure that takes a complicated object living in a high-dimensional (or possibly even infinite-dimensional) space and approximates it in some sense by a finite-dimensional vector. We are interested in a particular class of dimensionality reduction methods. Consider a data source that generates vectors in some Hilbert space H , which is eithe...

Dimensionality reduction methods are of interest in applications such as content based image and video retrieval. In large multimedia databases, it may not be practical to search through the entire database in order to retrieve the nearest neighbors of a query. Good data structures for similarity search and indexing are needed, and the existing data structures do not scale well for the high dim...

A common objective in image analysis is dimensionality reduction. The most common often used data-exploratory technique with this objective is principal component analysis. We propose a new method based on the projection of the images as matrices after a Procrustes rotation and show that it leads to a better reconstruction of images.