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Subspace Learning Machine (SLM): Methodology and Performance
Machine Learning · Submitted 11 May 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Furthermore, ensembles of SLM/SLR trees can yield a stronger predictor.
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The abstract, sentence by sentence
Inspired by the feedforward multilayer perceptron (FF-MLP), decision tree (DT) and extreme learning machine (ELM), a new classification model, called the subspace learning machine (SLM), is proposed in this work. SLM first identifies a discriminant subspace, $S^0$, by examining the discriminant power of each input feature. Then, it uses probabilistic projections of features in $S^0$ to yield 1D subspaces and finds the optimal partition for each of them. This is equivalent to partitioning $S^0$ with hyperplanes. A criterion is developed to choose the best $q$ partitions that yield $2q$ partitioned subspaces among them. We assign $S^0$ to the root node of a decision tree and the intersections of $2q$ subspaces to its child nodes of depth one. The partitioning process is recursively applied at each child node to build an SLM tree. When the samples at a child node are sufficiently pure, the partitioning process stops and each leaf node makes a prediction. The idea can be generalized to regression, leading to the subspace learning regressor (SLR). Furthermore, ensembles of SLM/SLR trees can yield a stronger predictor. Extensive experiments are conducted for performance benchmarking among SLM/SLR trees, ensembles and classical classifiers/regressors.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Inspired by the feedforward multilayer perceptron (FF-MLP), decision tree (DT) and extreme learning machine (ELM), a new classification model, called the subspace learning machine (SLM), is proposed in this work. | contribution 1.00 | 0.86 | 0.07 | asserted 1.00 |
| s1 | SLM first identifies a discriminant subspace, $S^0$, by examining the discriminant power of each input feature. | method 0.99 | 0.75 | 0.04 | asserted 1.00 |
| s2 | Then, it uses probabilistic projections of features in $S^0$ to yield 1D subspaces and finds the optimal partition for each of them. | method 1.00 | 0.82 | 0.03 | asserted 1.00 |
| s3 | This is equivalent to partitioning $S^0$ with hyperplanes. | method 0.74 | 0.58 | 0.02 | asserted 1.00 |
| s4 | A criterion is developed to choose the best $q$ partitions that yield $2q$ partitioned subspaces among them. | method 0.98 | 0.91 | 0.03 | asserted 1.00 |
| s5 | We assign $S^0$ to the root node of a decision tree and the intersections of $2q$ subspaces to its child nodes of depth one. | method 1.00 | 0.81 | 0.03 | asserted 1.00 |
| s6 | The partitioning process is recursively applied at each child node to build an SLM tree. | method 1.00 | 0.74 | 0.04 | asserted 1.00 |
| s7 | When the samples at a child node are sufficiently pure, the partitioning process stops and each leaf node makes a prediction. | method 1.00 | 0.60 | 0.04 | asserted 1.00 |
| s8 | The idea can be generalized to regression, leading to the subspace learning regressor (SLR). | contribution 0.59 | 0.64 | 0.06 | asserted 0.50 |
| s9 | Furthermore, ensembles of SLM/SLR trees can yield a stronger predictor. | contribution 0.57 | 0.38 | 0.14 | hedged possibility 0.82 |
| s10 | Extensive experiments are conducted for performance benchmarking among SLM/SLR trees, ensembles and classical classifiers/regressors. | method 0.60 | 0.95 | 0.08 | asserted 0.89 |
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The paper
Original abstract
Inspired by the feedforward multilayer perceptron (FF-MLP), decision tree (DT) and extreme learning machine (ELM), a new classification model, called the subspace learning machine (SLM), is proposed in this work. SLM first identifies a discriminant subspace, $S^0$, by examining the discriminant power of each input feature. Then, it uses probabilistic projections of features in $S^0$ to yield 1D subspaces and finds the optimal partition for each of them. This is equivalent to partitioning $S^0$ with hyperplanes. A criterion is developed to choose the best $q$ partitions that yield $2q$ partitioned subspaces among them. We assign $S^0$ to the root node of a decision tree and the intersections of $2q$ subspaces to its child nodes of depth one. The partitioning process is recursively applied at each child node to build an SLM tree. When the samples at a child node are sufficiently pure, the partitioning process stops and each leaf node makes a prediction. The idea can be generalized to regression, leading to the subspace learning regressor (SLR). Furthermore, ensembles of SLM/SLR trees can yield a stronger predictor. Extensive experiments are conducted for performance benchmarking among SLM/SLR trees, ensembles and classical classifiers/regressors.
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How the literature uses it
3 arXiv papers cite this in 15 sentences
Papers citing it · 11 sentences without a confident label
Uses its method or tool 1 paper
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New and powerful tools have been developed to address each of them in the last several years, e.g., the Saak [ref] and Saab transforms [ref] for Problem 1, the PixelHop [ref] , PixelHop++ [ref] and IPHop [ref] learning systems for Problem 2, the discriminant and relevant feature tests [ref] for Problem 3, the subspace learning machine [ref] for Problem 4.
Green Learning: Introduction, Examples and Outlook · Introduction · 0.82
Cites it as background 2 papers
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Built upon the classical decision tree (DT) [ref] idea, SLM has been recently proposed in [ref] .
Acceleration of Subspace Learning Machine via Particle Swarm Optimization and Parallel Processing · Introduction · 0.89
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[ref] develop and evaluate the Subspace Learning Machine (SLM), incorporating decision trees and nonhomogeneous media analysis for optimized classification.
Discriminative Subspace Emersion from learning feature relevances across different populations · Introduction · 0.92
What it cites · 3 sentences without a confident label
Uses the method or tool of 2 papers
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We use the discriminant feature test (DFT) [ref] to evaluate the discriminant quality of the projected 1D subspace as given in Eq. ([ref]).
On Supervised Feature Selection from High Dimensional Feature Spaces · Selection Criterion · 1.00
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For consistency with [ref] , we remove the feature dimension that has the zero variance from the data. * Banknote Dataset.
From Two-Class Linear Discriminant Analysis to Interpretable Multilayer Perceptron Design · Performance Evalution of SLM · 0.81
Uses data or values from 1 paper
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For the two MLP models, the network architectures of FF-MLP and BP-MLP and their performance results are taken from [ref] .
From Two-Class Linear Discriminant Analysis to Interpretable Multilayer Perceptron Design · Performance Evalution of SLM · 0.94
Cites as background 2 papers
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MLP also serves as the building blocks in transformer models [ref] .
An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale · Multilayer Perceptron (MLP) · 0.83
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Examples of classical classifiers/regressors include support vector machine (SVM) [ref] , decision tree (DT) [ref] , multilayer perceptron (MLP) [ref] , feedforward multilayer perceptron (FF-MLP) [ref] and extreme learning machine (ELM) [ref] .
From Two-Class Linear Discriminant Analysis to Interpretable Multilayer Perceptron Design · Introduction · 1.00
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