📝 Original Info
- Title: Semantic distillation: a method for clustering objects by their contextual specificity
- ArXiv ID: 0710.1203
- Date: 2007-10-05
- Authors: Researchers from original ArXiv paper
📝 Abstract
Techniques for data-mining, latent semantic analysis, contextual search of databases, etc. have long ago been developed by computer scientists working on information retrieval (IR). Experimental scientists, from all disciplines, having to analyse large collections of raw experimental data (astronomical, physical, biological, etc.) have developed powerful methods for their statistical analysis and for clustering, categorising, and classifying objects. Finally, physicists have developed a theory of quantum measurement, unifying the logical, algebraic, and probabilistic aspects of queries into a single formalism. The purpose of this paper is twofold: first to show that when formulated at an abstract level, problems from IR, from statistical data analysis, and from physical measurement theories are very similar and hence can profitably be cross-fertilised, and, secondly, to propose a novel method of fuzzy hierarchical clustering, termed \textit{semantic distillation} -- strongly inspired from the theory of quantum measurement --, we developed to analyse raw data coming from various types of experiments on DNA arrays. We illustrate the method by analysing DNA arrays experiments and clustering the genes of the array according to their specificity.
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Deep Dive into Semantic distillation: a method for clustering objects by their contextual specificity.
Techniques for data-mining, latent semantic analysis, contextual search of databases, etc. have long ago been developed by computer scientists working on information retrieval (IR). Experimental scientists, from all disciplines, having to analyse large collections of raw experimental data (astronomical, physical, biological, etc.) have developed powerful methods for their statistical analysis and for clustering, categorising, and classifying objects. Finally, physicists have developed a theory of quantum measurement, unifying the logical, algebraic, and probabilistic aspects of queries into a single formalism. The purpose of this paper is twofold: first to show that when formulated at an abstract level, problems from IR, from statistical data analysis, and from physical measurement theories are very similar and hence can profitably be cross-fertilised, and, secondly, to propose a novel method of fuzzy hierarchical clustering, termed \textit{semantic distillation} – strongly inspired f
📄 Full Content
Sequencing the genome constituted a culminating point in the analytic approach of Biology. Now starts the era of the synthetic approach in Systems Biology where interactions among genes induce their differential expression that leads to the functional specificity of cells, the coherent organisation of cells into tissues, organs, and finally organisms.
However, we are yet far from a complete explanatory theory of living matter. It is therefore important to establish precise and quantitative phenomenology before being able to formulate a theory. The contribution of this paper is to provide the reader with a novel algorithmic method, termed semantic distillation, to analyse DNA arrays experiments (where genes are hybridised with various cell lines corresponding to various tissues or specific individuals) by determining the degree of specificity of every gene to the particular context. The method provides experimental biologists with lists of candidate genes (ordered by their degree of specificity) for every biological context, clinicians with improved tools for diagnosis, pharmacologists with patient-tailored therapies, etc.
In the sequel we present the method split into several algorithmic tasks thought as subroutines of the general algorithm. It is worth noting that the method, although can profitably exploit, does not rely on any previous information stored in the existing databases; its rationale is to help analysing raw experimental data even in the absence of any previous knowledge.
The main idea of the method is summarised as follows. Experimental information hold on the objects of the system undergoes a sequence of processing steps; each step is performed on a different representation of the information. Those different representation spaces and the corresponding information processing act as successive filters revealing at the end the most pertinent and significant part of the information, hence the name “semantic distillation”.
At the first stage, raw experimental data, containing all available information, are represented in an abstract Hilbert space, the space of concepts -reminiscent of the space of pure states in Quantum Mechanics -, endowing the set of objects with a metric space structure that is exploited to quantify the interactions among objects and encode them into a weighed graph on the vertex set of objects and with object interactions as edge weights. Now objects (genes) are parts of an organised system (cell, tissue, organism). Therefore their mutual interactions are not just independent random variables; they are interconnected through precise, although certainly very complicated and mostly unknown relationships. We seek to reveal (hidden and unknown) interactions among genes. This is achieved by trading the weighed graph representation for a lowdimensional representation and using spectral properties of the weighed Laplacian on the graph to grasp the essential interactions.
The following step consists in a fuzzy divisive clustering of objects among two subsets by exploiting the previous low-dimensional representation. This procedure assigns a fuzzy membership to each object relative to characters of the two subsets. Fuzziness is as a matter of fact a distinctive property of experimental biological data reflecting our incomplete knowledge of fundamental biological processes.
Up to this step, our method is a sequence of known algorithms that have been previously used separately in the literature in various contexts. The novelty of our method relies on the following steps. The previous fuzzy clustering reduced the indeterminacy of the system. This information is fed back to the system to perform a projection to a proper Hilbert subspace. In that way, the information content of the dataset is modified by the information gained by the previous observations. After this feeding back, the three previous steps are repeated but now referring to a Hilbert spaces of lower dimension. Therefore our method is not a mere fuzzy clustering algorithm but a genuine non-classical interaction information retrieval procedure where previous observations alter the informational content of the system, reminiscent of the measurement procedure in Quantum Mechanics.
Let B be a finite set of documents (or objects, or books) and A a finite set of attributes (or contexts, or keywords). The dataset is a |B| × |A| matrix X = (x ba ) b∈B,a∈A of real or complex elements, where | • | represents cardinality. Equivalent ways of representing the dataset are
Example 1. In the experiments we analysed B is a set of 12000 human genes and A a set of 12 tissular contexts. The matrix elements x ba are real numbers encoding luminescence intensities (or their logarithms) of DNA array ultimately representing the level of expression of gene b in context a.
Example 2. Let B be a set of books in a library and A a set of bibliographic keywords. The matrix elements x ba can be {0, 1}-valued: if the term a is present in the book b
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