0000000001220359
AUTHOR
Joni Virta
showing 8 related works from this author
Dimension Estimation in Two-Dimensional PCA
2021
We propose an automated way of determining the optimal number of low-rank components in dimension reduction of image data. The method is based on the combination of two-dimensional principal component analysis and an augmentation estimator proposed recently in the literature. Intuitively, the main idea is to combine a scree plot with information extracted from the eigenvectors of a variation matrix. Simulation studies show that the method provides accurate estimates and a demonstration with a finger data set showcases its performance in practice. peerReviewed
Applying fully tensorial ICA to fMRI data
2016
There are two aspects in functional magnetic resonance imaging (fMRI) data that make them awkward to analyse with traditional multivariate methods - high order and high dimension. The first of these refers to the tensorial nature of observations as array-valued elements instead of vectors. Although this can be circumvented by vectorizing the array, doing so simultaneously loses all the structural information in the original observations. The second aspect refers to the high dimensionality along each dimension making the concept of dimension reduction a valuable tool in the processing of fMRI data. Different methods of tensor dimension reduction are currently gaining popUlarity in literature…
Large-sample properties of unsupervised estimation of the linear discriminant using projection pursuit
2021
We study the estimation of the linear discriminant with projection pursuit, a method that is unsupervised in the sense that it does not use the class labels in the estimation. Our viewpoint is asymptotic and, as our main contribution, we derive central limit theorems for estimators based on three different projection indices, skewness, kurtosis, and their convex combination. The results show that in each case the limiting covariance matrix is proportional to that of linear discriminant analysis (LDA), a supervised estimator of the discriminant. An extensive comparative study between the asymptotic variances reveals that projection pursuit gets arbitrarily close in efficiency to LDA when the…
Dimension reduction for time series in a blind source separation context using r
2021
Funding Information: The work of KN was supported by the CRoNoS COST Action IC1408 and the Austrian Science Fund P31881-N32. The work of ST was supported by the CRoNoS COST Action IC1408. The work of JV was supported by Academy of Finland (grant 321883). We would like to thank the anonymous reviewers for their comments which improved the paper and package considerably. Publisher Copyright: © 2021, American Statistical Association. All rights reserved. Multivariate time series observations are increasingly common in multiple fields of science but the complex dependencies of such data often translate into intractable models with large number of parameters. An alternative is given by first red…
Signal dimension estimation in BSS models with serial dependence
2022
Many modern multivariate time series datasets contain a large amount of noise, and the first step of the data analysis is to separate the noise channels from the signals of interest. A crucial part of this dimension reduction is determining the number of signals. In this paper we approach this problem by considering a noisy latent variable time series model which comprises many popular blind source separation models. We propose a general framework for the estimation of the signal dimension that is based on testing for sub-sphericity and give examples of different tests suitable for time series settings. In the inference we rely on bootstrap null distributions. Several simulation studies are…
The “Seili-index” For The Prediction of Chlorophyll-α Levels In The Archipelago Sea of The Northern Baltic Sea, Southwest Finland
2021
AbstractTo build a forecasting tool for the state of eutrophication in the Archipelago Sea, we fitted a Generalized Additive Mixed Model (GAMM) to marine environmental monitoring data, which were collected over the years 2011–2019 by an automated profiling buoy at the Seili ODAS-station. The resulting “Seili-index” can be used to predict the chlorophyll-α (chl-a) concentration in the seawater a number of days ahead by using the temperature forecast as a covariate. An array of test predictions with two separate models on the 2019 data set showed that the index is adept at predicting the amount of chl-a especially in the upper water layer. The visualization with 10 days of chl-a level predict…
The squared symmetric FastICA estimator
2017
In this paper we study the theoretical properties of the deflation-based FastICA method, the original symmetric FastICA method, and a modified symmetric FastICA method, here called the squared symmetric FastICA. This modification is obtained by replacing the absolute values in the FastICA objective function by their squares. In the deflation-based case this replacement has no effect on the estimate since the maximization problem stays the same. However, in the symmetric case we obtain a different estimate which has been mentioned in the literature, but its theoretical properties have not been studied at all. In the paper we review the classic deflation-based and symmetric FastICA approaches…
Large-Sample Properties of Blind Estimation of the Linear Discriminant Using Projection Pursuit
2021
We study the estimation of the linear discriminant with projection pursuit, a method that is blind in the sense that it does not use the class labels in the estimation. Our viewpoint is asymptotic and, as our main contribution, we derive central limit theorems for estimators based on three different projection indices, skewness, kurtosis and their convex combination. The results show that in each case the limiting covariance matrix is proportional to that of linear discriminant analysis (LDA), an unblind estimator of the discriminant. An extensive comparative study between the asymptotic variances reveals that projection pursuit is able to achieve efficiency equal to LDA when the groups are…