Supervised Isomap with Dissimilarity Measures in Embedding Learning

Ribeiro, Bernardete; Vieira, Armando; Neves, João Carvalho das

doi:10.1007/978-3-540-85920-8_48

Cited by 14 publications

(18 citation statements)

References 12 publications

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“…Regardless of different nonlinear projections (e.g., ISOMAP, local linear embedding (LLE), Laplacian Eigenmaps, and diffusion map), they share the common rationale that the high-dimensional data is cast into low-dimensional manifolds with few degrees of freedom and embedded intrinsic geometry. Ribeiro et al [41,43] incorporate the class information in an Enhanced Supervised ISOMAP (ES-ISOMAP) algorithm to uncover the embedding geometry structure of finance data. With the same goal, non-negative matrix factorization (NMF), a multivariate analysis technique for part-based data representation under the non-negative constraint, is used in [42] to extract the most discriminative features, and subsequently construct a classification model for failure prediction.…”

Section: Background On Bankruptcy Predictionmentioning

confidence: 99%

“…We briefly review in the next subsection the manifold learning methods in particular the ES-ISOMAP algorithm [41,43] for the sake of comparison with both approaches, GNMF and SSSL.…”

Section: Subspace Learning Modelsmentioning

confidence: 99%

“…Table 3 describes in more detail the parameters setup for the research design. We followed the graph weight construction for (B) as indicated in [41]. The Djkstra's Algorithm (see step 2.2, Fig.…”

Section: Clustering and Visualizationmentioning

confidence: 99%

“…With respect to the free parameters in each method, for instance in (A) the PCA method, k indicates the number of principal components. In the case of (B) α is the parameter used to calculate the distance metrics for building the dissimilarity matrix in the ES-ISOMAP approach (see [41]). In the case of NMF (C) and GNMF (D) λ is the parameter for embedding the geometry of the data into the weight matrix.…”

Section: Clustering and Visualizationmentioning

confidence: 99%

“…In this article, we extend our previous work [39,41,43] in the field of financial analysis by embedding explicitly the geometric properties into the submanifold lying in the high-dimensional data, and by using the resulting subspace learning models, which allow compact representations able to enhance visualization, clustering and classification.…”

mentioning

confidence: 97%

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Dimensionality Reduction Using Graph Weighted Subspace Learning for Bankruptcy Prediction

Ribeiro

Chen²

2014

Annals of Information Systems

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Bankruptcy prediction is an extremely actual and important topic in the world. In this complex problem, dimensionality reduction becomes important easing both tasks of visualization and classification. Despite the different motivations, these algorithms can be cast in a graph embedding framework. In this paper we address weighted graph subspace learning methods for dimensionality reduction of bankruptcy data. The rationale behind re-embedding the data in a lower dimensional space that would be better filled is twofold: to get the most compact representation (visualization) and to make subsequent processing of data more easy (classification). To achieve this, two graph weighted subspace learning models are investigated, namely graph regularized non-negative matrix factorization (GNMF) and spatially smooth subspace learning (SSSL). Through an affinity weight graph matrix, the geometric properties are embedded explicitly into the submanifold lying in the high-dimensional data, consequently, the resulting subspace models allow compact representations able to enhance visualization, clustering and classification. The experimental results on a real world database of French companies show that the graph weighted subspace learning models used in a supervised learning manner are very effective for bankruptcy prediction.

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Section: Background On Bankruptcy Predictionmentioning

confidence: 99%

“…We briefly review in the next subsection the manifold learning methods in particular the ES-ISOMAP algorithm [41,43] for the sake of comparison with both approaches, GNMF and SSSL.…”

Section: Subspace Learning Modelsmentioning

confidence: 99%

Section: Clustering and Visualizationmentioning

confidence: 99%

Section: Clustering and Visualizationmentioning

confidence: 99%

mentioning

confidence: 97%

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Dimensionality Reduction Using Graph Weighted Subspace Learning for Bankruptcy Prediction

Ribeiro

Chen²

2014

Annals of Information Systems

Self Cite

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Interpretable linear dimensionality reduction based on bias-variance analysis

Bonetti,

Metelli,

Restelli

2024

Data Min Knowl Disc

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One of the central issues of several machine learning applications on real data is the choice of the input features. Ideally, the designer should select a small number of the relevant, nonredundant features to preserve the complete information contained in the original dataset, with little collinearity among features. This procedure helps mitigate problems like overfitting and the curse of dimensionality, which arise when dealing with high-dimensional problems. On the other hand, it is not desirable to simply discard some features, since they may still contain information that can be exploited to improve results. Instead, dimensionality reduction techniques are designed to limit the number of features in a dataset by projecting them into a lower dimensional space, possibly considering all the original features. However, the projected features resulting from the application of dimensionality reduction techniques are usually difficult to interpret. In this paper, we seek to design a principled dimensionality reduction approach that maintains the interpretability of the resulting features. Specifically, we propose a bias-variance analysis for linear models and we leverage these theoretical results to design an algorithm, Linear Correlated Features Aggregation (LinCFA), which aggregates groups of continuous features with their average if their correlation is “sufficiently large”. In this way, all features are considered, the dimensionality is reduced and the interpretability is preserved. Finally, we provide numerical validations of the proposed algorithm both on synthetic datasets to confirm the theoretical results and on real datasets to show some promising applications.

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Gaining Biological Insights through Supervised Data Visualization

Rhodes,

Aumon,

Morin

et al. 2023

Preprint

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Dimensionality reduction-based data visualization is pivotal in comprehending complex biological data. The most common methods, such as PHATE, t-SNE, and UMAP, are unsupervised and therefore reflect the dominant structure in the data, which may be independent of expert-provided labels. Here we introduce a supervised data visualization method called RF-PHATE, which integrates expert knowledge for further exploration of the data. RF-PHATE leverages random forests to capture intricate featurelabel relationships. Extracting information from the forest, RF-PHATE generates low-dimensional visualizations that highlight relevant data relationships while disregarding extraneous features. This approach scales to large datasets and applies to classification and regression. We illustrate RF-PHATE’s prowess through three case studies. In a multiple sclerosis study using longitudinal clinical and imaging data, RF-PHATE unveils a sub-group of patients with non-benign relapsing-remitting Multiple Sclerosis, demonstrating its aptitude for time-series data. In the context of Raman spectral data, RF-PHATE effectively showcases the impact of antioxidants on diesel exhaust-exposed lung cells, highlighting its proficiency in noisy environments. Furthermore, RF-PHATE aligns established geometric structures with COVID-19 patient outcomes, enriching interpretability in a hierarchical manner. RF-PHATE bridges expert insights and visualizations, promising knowledge generation. Its adaptability, scalability, and noise tolerance underscore its potential for widespread adoption.

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Supervised Isomap with Dissimilarity Measures in Embedding Learning

Cited by 14 publications

References 12 publications

Dimensionality Reduction Using Graph Weighted Subspace Learning for Bankruptcy Prediction

Dimensionality Reduction Using Graph Weighted Subspace Learning for Bankruptcy Prediction

Interpretable linear dimensionality reduction based on bias-variance analysis

Gaining Biological Insights through Supervised Data Visualization

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