Przemysław Spurek

Cross-entropy clustering

We build a general and easily applicable clustering theory, which we call crossentropy clustering (shortly CEC), which joins the advantages of classical kmeans (easy implementation and speed) with those of EM (ane invariance and ability to adapt to clusters of desired shapes). Moreover, contrary to k-means and EM, CEC nds the optimal number of clusters by automatically removing groups which have negative information cost.

General split gaussian Cross-Entropy clustering

We have applied highly applicable clustering method to non-normal data.We use a generalization of Split Normal distribution.We use Cross-Entropy clustering method instead of EM approach.Our algorithm gives better results than classical methods. Robust mixture models approaches, which use non-normal distributions have recently been upgraded to accommodate asymmetric data. In this article we propose a new method based on the General Split Gaussian distribution (GSG) and Cross-Entropy Clustering (CEC). The GSG is a flexible density with reasonably small number of parameters which are easy to estimate. We combine the model with a clustering method which allows to treat groups separately and estimate parameters individually in each cluster. Consequently, we introduce an effective clustering algorithm which deals with non-normal data.

Active function Cross-Entropy Clustering

Gaussian Mixture Models (GMM) have found many applications in density estimation and data clustering. However, the model does not adapt well to curved and strongly nonlinear data. Recently there appeared an improvement called AcaGMM (Active curve axis Gaussian Mixture Model), which fits Gaussians along curves using an EM-like (Expectation Maximization) approach. Using the ideas standing behind AcaGMM, we build an alternative active function model of clustering, which has some advantages over AcaGMM. In particular it is naturally defined in arbitrary dimensions and enables an easy adaptation to clustering of complicated datasets along the predefined family of functions. Moreover, it does not need external methods to determine the number of clusters as it automatically reduces the number of groups on-line.

Detection of Disk-Like Particles in Electron Microscopy Images

Quantitative and qualitative description of particles is one of the most important tasks in the Electron Microscopy (EM) analysis. In this paper, we present an algorithm for identifying ball-like nanostructures of gahnite in the Transmission Electron Microscopy (TEM) images. Our solution is based on the cross-entropy clustering which allows to count and measure disk-like objects which are not necessary disjoint or with not smooth borders.

R Package CEC

Abstract Cross-Entropy Clustering (CEC) is a model-based clustering method which divides data into Gaussian-like clusters. The main advantage of CEC is that it combines the speed and simplicity of k-means with the ability of using various Gaussian models similarly to EM. Moreover, the method is capable of the automatic reduction of unnecessary clusters. In this paper we present the R Package CEC implementing CEC method.

ICA based on asymmetry

We build a new approach to ICA which is based on the data asymmetry.Instead of densities with heavy tails, we use asymmetric ones - Split Gaussians.We verified our approach on images, sound and EEG data.In the case of source signal reconstructing our approach gives better results. Independent Component Analysis (ICA) - one of the basic tools in data analysis - aims to find a coordinate system in which the components of the data are independent. Most of existing methods are based on the minimization of the function of fourth-order moment (kurtosis). Skewness (third-order moment) has received much less attention.In this paper we present a competitive approach to ICA based on the Split Gaussian distribution, which is well adapted to asymmetric data. Consequently, we obtain a method which works better than the classical approaches, especially in the case when the underlying density is not symmetric, which is a typical situation in the color distribution in images.

Deep learning approach to bacterial colony classification

In microbiology it is diagnostically useful to recognize various genera and species of bacteria. It can be achieved using computer-aided methods, which make the recognition processes more automatic and thus significantly reduce the time necessary for the classification. Moreover, in case of diagnostic uncertainty (the misleading similarity in shape or structure of bacterial cells), such methods can minimize the risk of incorrect recognition. In this article, we apply the state of the art method for texture analysis to classify genera and species of bacteria. This method uses deep Convolutional Neural Networks to obtain image descriptors, which are then encoded and classified with Support Vector Machine or Random Forest. To evaluate this approach and to make it comparable with other approaches, we provide a new dataset of images. DIBaS dataset (Digital Image of Bacterial Species) contains 660 images with 33 different genera and species of bacteria.

Cross-Entropy Clustering Approach to One-Class Classification

Cross-entropy clustering (CEC) is a density model based clustering algorithm. In this paper we apply CEC to the one-class classification, which has several advantages over classical approaches based on Expectation Maximization (EM) and Support Vector Machines (SVM). More precisely, our model allows the use of various types of gaussian models with low computational complexity. We test the designed method on real data coming from the monitoring systems of wind turbines.

A Local Gaussian Filter and Adaptive Morphology as Tools for Completing Partially Discontinuous Curves

This paper presents a method for extraction and analysis of curve–type structures, which consist of disconnected components. Such structures are found in electron–microscopy (EM) images of metal nano- grains, which are widely used in the field of nanosensor technology. The topography of metal nanograins in compound nanomaterials is crucial to nanosensor characteristics. The method of completing such templates consists of three steps. In the first step, a local Gaussian filter is used with different weights for each neighborhood. In the second step, an adaptive morphology operation is applied to detect the endpoints of curve segments and connect them. In the last step, pruning is employed to extract a curve which optimally fits the template.

Weighted Approach to Projective Clustering

k-means is the basic method applied in many data clustering problems. As is known, its natural modification can be applied to projection clustering by changing the cost function from the squared-distance from the point to the squared distance from the affine subspace. However, to apply thus approach we need the beforehand knowledge of the dimension.