Sequential Principal Curves Analysis

by   Valero Laparra, et al.

This work includes all the technical details of the Sequential Principal Curves Analysis (SPCA) in a single document. SPCA is an unsupervised nonlinear and invertible feature extraction technique. The identified curvilinear features can be interpreted as a set of nonlinear sensors: the response of each sensor is the projection onto the corresponding feature. Moreover, it can be easily tuned for different optimization criteria; e.g. infomax, error minimization, decorrelation; by choosing the right way to measure distances along each curvilinear feature. Even though proposed in [Laparra et al. Neural Comp. 12] and shown to work in multiple modalities in [Laparra and Malo Frontiers Hum. Neuro. 15], the SPCA framework has its original roots in the nonlinear ICA algorithm in [Malo and Gutierrez Network 06]. Later on, the SPCA philosophy for nonlinear generalization of PCA originated substantially faster alternatives at the cost of introducing different constraints in the model. Namely, the Principal Polynomial Analysis (PPA) [Laparra et al. IJNS 14], and the Dimensionality Reduction via Regression (DRR) [Laparra et al. IEEE TGRS 15]. This report illustrates the reasons why we developed such family and is the appropriate technical companion for the missing details in [Laparra et al., NeCo 12, Laparra and Malo, Front.Hum.Neuro. 15]. See also the data, code and examples in the dedicated sites and effects.html


page 10

page 11

page 12

page 15


Supervised Dimensionality Reduction via Distance Correlation Maximization

In our work, we propose a novel formulation for supervised dimensionalit...

n-metrics for multiple graph alignment

The work of Ioannidis et al. 2018 introduces a family of distances betwe...

Theoretical Guarantees for Sparse Principal Component Analysis based on the Elastic Net

Sparse principal component analysis (SPCA) is widely used for dimensiona...

Nonlinearities and Adaptation of Color Vision from Sequential Principal Curves Analysis

Mechanisms of human color vision are characterized by two phenomenologic...

A General Framework for Sequential Decision-Making under Adaptivity Constraints

We take the first step in studying general sequential decision-making un...

Making Document-Level Information Extraction Right for the Right Reasons

Document-level information extraction is a flexible framework compatible...

Sequential Learning of Principal Curves: Summarizing Data Streams on the Fly

When confronted with massive data streams, summarizing data with dimensi...

Please sign up or login with your details

Forgot password? Click here to reset