Optimal N-ary ECOC Matrices for Ensemble Classification

• URL: http://arxiv.org/abs/2110.02161v1
• Date: Tue, 5 Oct 2021 16:50:15 GMT
• Title: Optimal N-ary ECOC Matrices for Ensemble Classification
• Authors: Hieu D. Nguyen and Lucas J. Lavalva and Shen-Shyang Ho and Mohammed Sarosh Khan and Nicholas Kaegi
• Abstract summary: A new construction of $N$-ary error-correcting output code (ECOC) matrices for ensemble classification methods is presented. Given any prime integer $N$, this deterministic construction generates base-$N$ symmetric square matrices $M$ of prime-power dimension having optimal minimum Hamming distance between any two of its rows and columns.
• Score: 1.3561997774592662
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: A new recursive construction of $N$-ary error-correcting output code (ECOC) matrices for ensemble classification methods is presented, generalizing the classic doubling construction for binary Hadamard matrices. Given any prime integer $N$, this deterministic construction generates base-$N$ symmetric square matrices $M$ of prime-power dimension having optimal minimum Hamming distance between any two of its rows and columns. Experimental results for six datasets demonstrate that using these deterministic coding matrices for $N$-ary ECOC classification yields comparable and in many cases higher accuracy compared to using randomly generated coding matrices. This is particular true when $N$ is adaptively chosen so that the dimension of $M$ matches closely with the number of classes in a dataset, which reduces the loss in minimum Hamming distance when $M$ is truncated to fit the dataset. This is verified through a distance formula for $M$ which shows that these adaptive matrices have significantly higher minimum Hamming distance in comparison to randomly generated ones.

Related papers

• Optimal Sketching for Residual Error Estimation for Matrix and Vector Norms [50.15964512954274]
  We study the problem of residual error estimation for matrix and vector norms using a linear sketch. We demonstrate that this gives a substantial advantage empirically, for roughly the same sketch size and accuracy as in previous work. We also show an $Omega(k2/pn1-2/p)$ lower bound for the sparse recovery problem, which is tight up to a $mathrmpoly(log n)$ factor.
  arXiv  Detail & Related papers  (2024-08-16T02:33:07Z)
• Private Matrix Approximation and Geometry of Unitary Orbits [29.072423395363668]
  This problem seeks to approximate $A$ by a matrix whose spectrum is the same as $Lambda$. We give efficient and private algorithms that come with upper and lower bounds on the approximation error.
  arXiv  Detail & Related papers  (2022-07-06T16:31:44Z)
• Leverage Score Sampling for Tensor Product Matrices in Input Sparsity Time [54.65688986250061]
  We give an input sparsity time sampling algorithm for approximating the Gram matrix corresponding to the $q$-fold column-wise tensor product of $q$ matrices. Our sampling technique relies on a collection of $q$ partially correlated random projections which can be simultaneously applied to a dataset $X$ in total time.
  arXiv  Detail & Related papers  (2022-02-09T15:26:03Z)
• Classification of high-dimensional data with spiked covariance matrix structure [0.2741266294612775]
  We study the classification problem for high-dimensional data with $n$ observations on $p$ features. We propose an adaptive classifier that first performs dimension reduction on the feature vectors prior to classification in the dimensionally reduced space. We show that the resulting classifier is Bayes optimal whenever $n rightarrow infty$ and $s sqrtn-1 ln p rightarrow 0$.
  arXiv  Detail & Related papers  (2021-10-05T11:26:53Z)
• Unfolding Projection-free SDP Relaxation of Binary Graph Classifier via GDPA Linearization [59.87663954467815]
  Algorithm unfolding creates an interpretable and parsimonious neural network architecture by implementing each iteration of a model-based algorithm as a neural layer. In this paper, leveraging a recent linear algebraic theorem called Gershgorin disc perfect alignment (GDPA), we unroll a projection-free algorithm for semi-definite programming relaxation (SDR) of a binary graph. Experimental results show that our unrolled network outperformed pure model-based graph classifiers, and achieved comparable performance to pure data-driven networks but using far fewer parameters.
  arXiv  Detail & Related papers  (2021-09-10T07:01:15Z)
• Hashing embeddings of optimal dimension, with applications to linear least squares [1.2891210250935143]
  We present subspace embedding properties for $s$-hashing sketching matrices, with $sgeq 1$, that are optimal in the projection dimension $m$ of the sketch. We apply these results to the special case of Linear Least Squares (LLS), and develop Ski-LLS, a generic software package for these problems.
  arXiv  Detail & Related papers  (2021-05-25T10:35:13Z)
• Householder Dice: A Matrix-Free Algorithm for Simulating Dynamics on Gaussian and Random Orthogonal Ensembles [12.005731086591139]
  Householder Dice (HD) is an algorithm for simulating dynamics on dense random matrix ensembles with translation-invariant properties. The memory and costs of the HD algorithm are $mathcalO(nT)$ and $mathcalO(nT2)$, respectively. Numerical results demonstrate the promise of the HD algorithm as a new computational tool in the study of high-dimensional random systems.
  arXiv  Detail & Related papers  (2021-01-19T04:50:53Z)
• Sparse PCA via $l_{2,p}$-Norm Regularization for Unsupervised Feature Selection [138.97647716793333]
  We propose a simple and efficient unsupervised feature selection method, by combining reconstruction error with $l_2,p$-norm regularization. We present an efficient optimization algorithm to solve the proposed unsupervised model, and analyse the convergence and computational complexity of the algorithm theoretically.
  arXiv  Detail & Related papers  (2020-12-29T04:08:38Z)
• Linear-Sample Learning of Low-Rank Distributions [56.59844655107251]
  We show that learning $ktimes k$, rank-$r$, matrices to normalized $L_1$ distance requires $Omega(frackrepsilon2)$ samples. We propose an algorithm that uses $cal O(frackrepsilon2log2fracepsilon)$ samples, a number linear in the high dimension, and nearly linear in the matrices, typically low, rank proofs.
  arXiv  Detail & Related papers  (2020-09-30T19:10:32Z)
• Compressed sensing of low-rank plus sparse matrices [3.8073142980733]
  This manuscript develops similar guarantees showing that $mtimes n$ that can be expressed as the sum of a rank-rparse matrix and a $s-sparse matrix can be recovered by computationally tractable methods. Results are shown for synthetic problems, dynamic-foreground/static separation, multispectral imaging, and Robust PCA.
  arXiv  Detail & Related papers  (2020-07-18T15:36:11Z)
• Supervised Quantile Normalization for Low-rank Matrix Approximation [50.445371939523305]
  We learn the parameters of quantile normalization operators that can operate row-wise on the values of $X$ and/or of its factorization $UV$ to improve the quality of the low-rank representation of $X$ itself. We demonstrate the applicability of these techniques on synthetic and genomics datasets.
  arXiv  Detail & Related papers  (2020-02-08T21:06:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.