Patrik O. Hoyer

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Non-negative matrix factorization (NMF) is a recently developed technique for finding parts-based, linear representations of non-negative data. Although it has successfully been applied in several applications, it does not always result in parts-based representations. In this paper, we show how explicitly incorporating the notion of ‘sparseness’ improves(More)
Non-negative sparse coding is a method for decomposing multivariate data into non-negative sparse components. In this paper we briefly describe the motivation behind this type of data representation and its relation to standard sparse coding and non-negative matrix factorization. We then give a simple yet efficient multiplicative algorithm for finding the(More)
Olshausen and Field (1996) applied the principle of independence maximization by sparse coding to extract features from natural images. This leads to the emergence of oriented linear filters that have simultaneous localization in space and in frequency, thus resembling Gabor functions and simple cell receptive fields. In this article, we show that the same(More)
In recent years, several methods have been proposed for the discovery of causal structure from non-experimental data. Such methods make various assumptions on the data generating process to facilitate its identification from purely observational data. Continuing this line of research, we show how to discover the complete causal structure of(More)
Spend your few moment to read a book even only few pages. Reading book is not obligation and force for everybody. When you don't want to read, you can get punishment from the publisher. Read a book becomes a choice of your different characteristics. Many people with reading habit will always be enjoyable to read, or on the contrary. For some reasons, this(More)
The discovery of causal relationships between a set of observed variables is a fundamental problem in science. For continuous-valued data linear acyclic causal models with additive noise are often used because these models are well understood and there are well-known methods to fit them to data. In reality, of course, many causal relationships are more or(More)
The classical receptive fields of simple cells in the visual cortex have been shown to emerge from the statistical properties of natural images by forcing the cell responses to be maximally sparse, i.e. significantly activated only rarely. Here, we show that this single principle of sparseness can also lead to emergence of topography (columnar organization)(More)
Previous work has shown that independent component analysis (ICA) applied to feature extraction from natural image data yields features resembling Gabor functions and simple-cell receptive fields. This article considers the effects of including chromatic and stereo information. The inclusion of colour leads to features divided into separate red/green,(More)
An important approach in visual neuroscience considers how the function of the early visual system relates to the statistics of its natural input. Previous studies have shown how many basic properties of the primary visual cortex, such as the receptive fields of simple and complex cells and the spatial organization (topography) of the cells, can be(More)
An important approach in visual neuroscience considers how the processing of the early visual system is dependent on the statistics of the natural environment. A particularly influential model in this respect has been sparse coding. In this paper we argue for a non-negative variant of the model. This is based partly on neurophysiological grounds and partly(More)