A Method for Unsupervised Semi-Quantification of Inmunohistochemical Staining with Beta Divergences

In many research laboratories, it is essential to determine the relative expression levels of some proteins of interest in tissue samples. The semi-quantitative scoring of a set of images consists of establishing a scale of scores ranging from zero or one to a maximum number set by the researcher and assigning a score to each image that should represent some predefined characteristic of the IHC staining, such as its intensity. However, manual scoring depends on the judgment of an observer and therefore exposes the assessment to a certain level of bias. In this work, we present a fully automatic and unsupervised method for comparative biomarker quantification in histopathological brightfield images. The method relies on a color separation method that discriminates between two chromogens expressed as brown and blue colors robustly, independent of color variation or biomarker expression level. For this purpose, we have adopted a two-stage stain separation approach in the optical density space. First, a preliminary separation is performed using a deconvolution method in which the color vectors of the stains are determined after an eigendecomposition of the data. Then, we adjust the separation using the non-negative matrix factorization method with beta divergences, initializing the algorithm with the matrices resulting from the previous step. After that, a feature vector of each image based on the intensity of the two chromogens is determined. Finally, the images are annotated using a systematically initialized k-means clustering algorithm with beta divergences. The method clearly defines the initial boundaries of the categories, although some flexibility is added. Experiments for the semi-quantitative scoring of images in five categories have been carried out by comparing the results with the scores of four expert researchers yielding accuracies that range between 76.60% and 94.58%. These results show that the proposed automatic scoring system, which is definable and reproducible, produces consistent results.FEDER / Junta de Andalucía-Consejería de Economía y Conocimiento US-1264994Fondo de Desarrollo (FEDER). Unión Europea PGC2018-096244-B-I00, SAF2016-75442-RMinisterio de Economía, Industria y Competitividad (MINECO). España TEC2017- 82807-

Algorithms for nonnegative matrix factorization with the beta-divergence

This paper describes algorithms for nonnegative matrix factorization (NMF) with the beta-divergence (beta-NMF). The beta-divergence is a family of cost functions parametrized by a single shape parameter beta that takes the Euclidean distance, the Kullback-Leibler divergence and the Itakura-Saito divergence as special cases (beta = 2,1,0, respectively). The proposed algorithms are based on a surrogate auxiliary function (a local majorization of the criterion function). We first describe a majorization-minimization (MM) algorithm that leads to multiplicative updates, which differ from standard heuristic multiplicative updates by a beta-dependent power exponent. The monotonicity of the heuristic algorithm can however be proven for beta in (0,1) using the proposed auxiliary function. Then we introduce the concept of majorization-equalization (ME) algorithm which produces updates that move along constant level sets of the auxiliary function and lead to larger steps than MM. Simulations on synthetic and real data illustrate the faster convergence of the ME approach. The paper also describes how the proposed algorithms can be adapted to two common variants of NMF : penalized NMF (i.e., when a penalty function of the factors is added to the criterion function) and convex-NMF (when the dictionary is assumed to belong to a known subspace).Comment: \`a para\^itre dans Neural Computatio

Electroencephalograph (EEG) signal processing techniques for motor imagery Brain Computer interface systems

Brain-Computer Interface (BCI) system provides a channel for the brain to control external devices using electrical activities of the brain without using the peripheral nervous system. These BCI systems are being used in various medical applications, for example controlling a wheelchair and neuroprosthesis devices for the disabled, thereby assisting them in activities of daily living. People suffering from Amyotrophic Lateral Sclerosis (ALS), Multiple Sclerosis and completely locked in are unable to perform any body movements because of the damage of the peripheral nervous system, but their cognitive function is still intact. BCIs operate external devices by acquiring brain signals and converting them to control commands to operate external devices. Motor-imagery (MI) based BCI systems, in particular, are based on the sensory-motor rhythms which are generated by the imagination of body limbs. These signals can be decoded as control commands in BCI application. Electroencephalogram (EEG) is commonly used for BCI applications because it is non-invasive. The main challenges of decoding the EEG signal are because it is non-stationary and has a low spatial resolution. The common spatial pattern algorithm is considered to be the most effective technique for discrimination of spatial filter but is easily affected by the presence of outliers. Therefore, a robust algorithm is required for extraction of discriminative features from the motor imagery EEG signals. This thesis mainly aims in developing robust spatial filtering criteria which are effective for classification of MI movements. We have proposed two approaches for the robust classification of MI movements. The first approach is for the classification of multiclass MI movements based on the thinICA (Independent Component Analysis) and mCSP (multiclass Common Spatial Pattern Filter) method. The observed results indicate that these approaches can be a step towards the development of robust feature extraction for MI-based BCI system. The main contribution of the thesis is the second criterion, which is based on Alpha- Beta logarithmic-determinant divergence for the classification of two class MI movements. A detailed study has been done by obtaining a link between the AB log det divergence and CSP criterion. We propose a scaling parameter to enable a similar way for selecting the respective filters like the CSP algorithm. Additionally, the optimization of the gradient of AB log-det divergence for this application was also performed. The Sub-ABLD (Subspace Alpha-Beta Log-Det divergence) algorithm is proposed for the discrimination of two class MI movements. The robustness of this algorithm is tested with both the simulated and real data from BCI competition dataset. Finally, the resulting performances of the proposed algorithms have been favorably compared with other existing algorithms