Robust Data Clustering with Outliers via Transformed Tensor Low-Rank Representation

Conceptos Básicos

The author presents a novel method, OR-TLRR, for robust data clustering with outliers using tensor low-rank representation.

Resumen

The content discusses the development of an outlier-robust tensor low-rank representation method for data clustering in the presence of outliers. It introduces theoretical guarantees and extends the method to handle missing data entries. Experimental results on synthetic and real data demonstrate the effectiveness of the proposed algorithms.
The paper focuses on addressing the challenge of clustering tensor data in the presence of outliers by introducing an innovative approach called OR-TLRR. This method provides outlier detection and tensor data clustering simultaneously based on a t-SVD framework. Theoretical performance guarantees are provided for exact recovery of clean data row space and outlier detection under mild conditions. Additionally, an extension is proposed to handle missing data entries.
Existing methods in subspace clustering are effective but lack spatial information within multi-dimensional data. The proposed algorithm aims to maintain the intrinsic structure of multi-dimensional data for efficient processing. Extensive numerical examples have shown its effectiveness in various applications.
Several experiments were conducted to verify the recovery guarantee on randomly generated tensors using different linear transforms such as DFT, DCT, and ROM. The results confirmed that OR-TLRR can successfully recover the row space of clean data and detect outliers with high probability.
In real-world applications, OR-TLRR was evaluated for outlier detection and clustering tasks on datasets like ORL, COIL20, Umist, FRDUE, and USPS. The experiments demonstrated the effectiveness of the proposed algorithms in detecting outliers and performing clustering tasks.

Estadísticas

For any optimal solution (Z⋆, E⋆) to the OR-TLRR problem (4), we have Z⋆ ∈ PLVX.
If Range(L0) and Range(E0) are independent to each other, i.e., Range(L0)∩Range(E0) = {0}, then V0 ∈ PLVX.
The recovered tubal rank of PΘ⊥(X) is exactly equal to 5rℓ.
The relative errors ∥PLV0−PeU∥F/∥PLV0∥F are very small (less than 10^-4).
∥PΘ⊥(L0)−PΘ⊥(eX)∥F/∥PΘ⊥(L0)∥F are very small (less than 10^-4).

Citas

"The proposed algorithms demonstrate high effectiveness in detecting outliers and performing clustering tasks."
"The experimental results confirm that OR-TLRR can successfully recover clean data row space and detect outliers with high probability."

Ideas clave extraídas de

Robust Data Clustering with Outliers via Transformed Tensor Low-Rank Representation

by Tong Wu a las arxiv.org 02-29-2024

https://arxiv.org/pdf/2307.09055.pdf

Consultas más profundas

How does OR-TLRR compare to other existing methods in terms of computational efficiency

OR-TLRR offers a significant improvement in computational efficiency compared to other existing methods. By reformulating the optimization problem and leveraging the skinny t-SVD, OR-TLRR reduces the per-iteration complexity significantly. This reduction in computational cost is crucial for handling large-scale tensor data efficiently. Additionally, by incorporating ADMM and simplifying the problem structure, OR-TLRR achieves faster convergence and lower computational overhead.

What implications could the findings from this study have on real-world applications outside of machine learning

The findings from this study could have profound implications on various real-world applications outside of machine learning. For instance:

Image Processing: In image denoising and inpainting applications, robust data clustering with outliers can enhance the accuracy of reconstructed images by effectively identifying and handling outlier corruptions.
Video Surveillance: In security systems utilizing video analytics, OR-TLRR can improve anomaly detection by accurately clustering normal behavior patterns while flagging potential outliers or irregular activities.
Healthcare: In medical imaging analysis, such as MRI or CT scans interpretation, robust clustering techniques like OR-TLRR can aid in identifying abnormal patterns or anomalies within patient data for accurate diagnosis.

These applications demonstrate how robust data clustering with outliers can enhance decision-making processes across various industries where complex data structures need to be analyzed effectively.

How might incorporating additional constraints or parameters impact the performance of OR-TLRR

Incorporating additional constraints or parameters into OR-TLRR may impact its performance in several ways:

Regularization Strength (λ): Adjusting the regularization parameter λ can influence the balance between low-rank representation recovery and outlier detection sensitivity. Fine-tuning λ based on specific dataset characteristics may lead to improved overall performance.
Missing Data Handling: Introducing constraints related to missing entries handling could enhance OR-TLRR's ability to recover incomplete tensor observations more accurately.
Noise Model Adaptation: Incorporating adaptive noise models based on different types of corruptions (e.g., Gaussian vs sparse) might make OR-TLRR more versatile in handling diverse real-world scenarios.

By carefully selecting and fine-tuning these additional constraints or parameters, it is possible to tailor OR-TLRR for specific use cases and further optimize its performance in practical applications requiring robust data clustering with outliers.