Related papers: Approximate Principal Direction Trees

In this paper we offer a new perspective on the well established agglomerative clustering algorithm, focusing on recovery of hierarchical structure. We recommend a simple variant of the standard algorithm, in which clusters are merged by…

In ad hoc networks scalability is a critical requirement if these technologies have to reach their full potential. Most of the proposed routing protocols do not operate efficiently with networks of more than a few hundred nodes. In this…

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

Studies of the degrees of freedom or "synergies" in musculoskeletal systems rely critically on algorithms to estimate the "dimension" of kinematic or neural data. Linear algorithms such as principal component analysis (PCA) are used almost…

Decision trees are interpretable models that are well-suited to non-linear learning problems. Much work has been done on extending decision tree learning algorithms with differential privacy, a system that guarantees the privacy of samples…

Optimization tasks over relational data, such as clustering, often suffer from the prohibitive cost of join operations, which are necessary to access the full dataset. While geometric data structures like BBD trees yield fast approximation…

Loss functions are fundamental to learning accurate 3D point cloud models, yet common choices trade geometric fidelity for computational cost. Chamfer Distance is efficient but permits many-to-one correspondences, while Earth Mover Distance…

Recent advances in neural-network architecture allow for seamless integration of convex optimization problems as differentiable layers in an end-to-end trainable neural network. Integrating medium and large scale quadratic programs into a…

LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to…

This paper compares two neural network input selection schemes, the Principal Component Analysis (PCA) and the Automatic Relevance Determination (ARD) based on Mac-Kay's evidence framework. The PCA takes all the input data and projects it…

Neural network training is inherently sequential where the layers finish the forward propagation in succession, followed by the calculation and back-propagation of gradients (based on a loss function) starting from the last layer. The…

In this paper, we propose new learning algorithms for approximating high-dimensional functions using tree tensor networks in a least-squares setting. Given a dimension tree or architecture of the tensor network, we provide an algorithm that…

Decision trees are a widely used method for classification, both by themselves and as the building blocks of multiple different ensemble learning methods. The Max-Cut decision tree involves novel modifications to a standard, baseline model…

Although deep learning has demonstrated remarkable capability in learning from unstructured data, modern tree-based ensemble models remain superior in extracting relevant information and learning from structured datasets. While several…

We present a new universal source code for distributions of unlabeled binary and ordinal trees that achieves optimal compression to within lower order terms for all tree sources covered by existing universal codes. At the same time, it…

Corporations today collect data at an unprecedented and accelerating scale, making the need to run queries on large datasets increasingly important. Technologies such as columnar block-based data organization and compression have become…

In order to process efficiently ever-higher dimensional data such as images, sentences, or audio recordings, one needs to find a proper way to reduce the dimensionality of such data. In this regard, SVD-based methods including PCA and…

Robots often need to solve path planning problems where essential and discrete aspects of the environment are partially observable. This introduces a multi-modality, where the robot must be able to observe and infer the state of its…

We give the first non-trivial fully dynamic probabilistic tree embedding algorithm for weighted graphs undergoing edge insertions and deletions. We obtain a trade-off between amortized update time and expected stretch against an oblivious…

Topology optimization is a structural design methodology widely utilized to address engineering challenges. However, sensitivity-based topology optimization methods struggle to solve optimization problems characterized by strong…