Matrix Decomposition Methods for Data Mining : Computational Complexity and Algorithms

Matrix decompositions, where a given matrix is represented as a product of two other matrices, are regularly used in data mining. Most matrix decompositions have their roots in linear algebra, but the needs of data mining are not always those of linear algebra. In data mining one needs to have results that are interpretable -- and what is considered interpretable in data mining can be very different to what is considered interpretable in linear algebra. --- The purpose of this thesis is to study matrix decompositions that directly address the issue of interpretability. An example is a decomposition of binary matrices where the factor matrices are assumed to be binary and the matrix multiplication is Boolean. The restriction to binary factor matrices increases interpretability -- factor matrices are of the same type as the original matrix -- and allows the use of Boolean matrix multiplication, which is often more intuitive than normal matrix multiplication with binary matrices. Also several other decomposition methods are described, and the computational complexity of computing them is studied together with the hardness of approximating the related optimization problems. Based on these studies, algorithms for constructing the decompositions are proposed. Constructing the decompositions turns out to be computationally hard, and the proposed algorithms are mostly based on various heuristics. Nevertheless, the algorithms are shown to be capable of finding good results in empirical experiments conducted with both synthetic and real-world data.

Renormalization methods in KAM theory

It is well known that an integrable (in the sense of Arnold-Jost) Hamiltonian system gives rise to quasi-periodic motion with trajectories running on invariant tori. These tori foliate the whole phase space. If we perturb an integrable system, the Kolmogorow-Arnold-Moser (KAM) theorem states that, provided some non-degeneracy condition and that the perturbation is sufficiently small, most of the invariant tori carrying quasi-periodic motion persist, getting only slightly deformed. The measure of the persisting invariant tori is large together with the inverse of the size of the perturbation. In the first part of the thesis we shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non analytic perturbation (the latter will only be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which theperturbations are analytic approximations of the original one. We will finally show that the approximate solutions will converge to a differentiable solution of our original problem. In the second part we will use an RG scheme using continuous scales, so that instead of solving an iterative equation as in the classical RG KAM, we will end up solving a partial differential equation. This will allow us to reduce the complications of treating a sequence of iterative equations to the use of the Banach fixed point theorem in a suitable Banach space.

Evaluation of methods and applications for behavioural profiling of transgenic mice

During the last 10-15 years interest in mouse behavioural analysis has evolved considerably. The driving force is development in molecular biological techniques that allow manipulation of the mouse genome by changing the expression of genes. Therefore, with some limitations it is possible to study how genes participate in regulation of physiological functions and to create models explaining genetic contribution to various pathological conditions. The first aim of our study was to establish a framework for behavioural phenotyping of genetically modified mice. We established comprehensive battery of tests for the initial screening of mutant mice. These included tests for exploratory and locomotor activity, emotional behaviour, sensory functions, and cognitive performance. Our interest was in the behavioural patterns of common background strains used for genetic manipulations in mice. Additionally we studied the behavioural effect of sex differences, test history, and individual housing. Our findings highlight the importance of careful consideration of genetic background for analysis of mutant mice. It was evident that some backgrounds may mask or modify the behavioural phenotype of mutants and thereby lead to false positive or negative findings. Moreover, there is no universal strain that is equally suitable for all tests, and using different backgrounds allows one to address possible phenotype modifying factors. We discovered that previous experience affected performance in several tasks. The most sensitive traits were the exploratory and emotional behaviour, as well as motor and nociceptive functions. Therefore, it may be essential to repeat some of the tests in naïve animals for assuring the phenotype. Social isolation for a long time period had strong effects on exploratory behaviour, but also on learning and memory. All experiments revealed significant interactions between strain and environmental factors (test history or housing condition) indicating genotype-dependent effects of environmental manipulations. Several mutant line analyses utilize this information. For example, we studied mice overexpressing as well as those lacking extracellular matrix protein heparin-binding growth-associated molecule (HB-GAM), and mice lacking N-syndecan (a receptor for HB-GAM). All mutant mice appeared to be fertile and healthy, without any apparent neurological or sensory defects. The lack of HB-GAM and N-syndecan, however, significantly reduced the learning capacity of the mice. On the other hand, overexpression of HB-GAM resulted in facilitated learning. Moreover, HB-GAM knockout mice displayed higher anxiety-like behaviour, whereas anxiety was reduced in HB-GAM overexpressing mice. Changes in hippocampal plasticity accompanied the behavioural phenotypes. We conclude that HB-GAM and N-syndecan are involved in the modulation of synaptic plasticity in hippocampus and play a role in regulation of anxiety- and learning-related behaviour.

Novel matrix metalloproteinases in intestinal inflammation and in cancer of the gastrointestinal tract

Matrix metalloproteinases (MMPs) comprise a family of 23 zinc-dependent human endopeptidases that can degrade virtually all components of the extracellular matrix (ECM). They are classified into eight subgroups according to their structure and into six subgroups based on their substrate-specificity. MMPs have been implicated in inflammation, tissue destruction, cell migration, arthritis, vascular remodeling, angiogenesis, and tumor growth and invasion. MMPs are inhibited by their natural inhibitors, tissue inhibitors of metalloproteinases (TIMPs). Different MMPs function in the same tasks depending on the tissue or cancer subtype. I investigated the role of recently discovered MMPs, especially MMPs-19 and -26, in intestinal inflammation, in intestinal and cutaneous wound healing, and in intestinal cancer. Several MMPs and TIMPs were studied to determine their exact location at tissue level and to obtain information on possible functions of MMPs in such tissues and diseases as the healthy intestine, inflammatory bowel disease (IBD), neonatal necrotizing enterocolitis (NEC), pyoderma gangrenosum (PG), and colorectal as well as pancreatic cancers. In latent celiac disease (CD), I attempted to identify markers to predict later onset of CD in children and adolescents. The main methods used were immunohistochemistry, in situ hybridization, and Taqman RT-PCR. My results show that MMP-26 is important for re-epithelialization in intestinal and cutaneous wound healing. In colon and pancreatic cancers, MMP-26 seems to be a marker of invasive potential, although it is not itself expressed at the invasive front. MMP-21 is upregulated in pancreatic cancer and may be associated with tumor differentiation. MMPs-19 and -28 are associated with normal tissue turnover in the intestine, but they disappear in tumor progression as if they were protective markers . MMP-12 is an essential protease in intestinal inflammation and tissue destruction, as seen here in NEC and in previous CD studies. In patients with type 1 diabetes (T1D), MMPs-1, -3, and -12 were upregulated in the intestinal mucosa. Furthermore, MMP-7 was strongly elevated in NEC. In a model of aberrant wound repair, PG, MMPs-8, -9, and 10 and TNFα may promote ECM destruction, while absence of MMP-1 and MMP-26 from keratinocytes retards re-epithelialization. Based on my results, I suggest MMP-26 to be considered a putative marker for poor prognosis in pancreatic and colon cancer. However, since it functions differently in various tissues and tumor subtypes, this use cannot be generalized. Furthermore, MMP-26 is a beneficial marker for wound healing if expressed by migrating epithelial cells. MMP-12 expression in latent CD patients warrants research in a larger patient population to confirm its role as a specific marker for CD in pathologically indistinct cases. MMP-7 should be considered one of the most crucial proteases in NEC-associated tissue destruction; hence, specific inhibitors of this MMP are worth investigating. In PG, TNFα inhibitors are potential therapeutic agents, as shown already in clinical trials. In conclusion, studies of several MMPs in specific diseases and in healthy tissues are needed to elucidate their roles at the tissue level. MMPs and TIMPs are not exclusively destructive or reparative in tissues. They seem to function differently in different tissues. To identify selective MMP inhibitors, we must thoroughly understand the MMP profile (degradome) and their functions in various organs not to interfere with normal reparative functions during wound repair or beneficial host-response effects during cancer initiation and growth.

Matrix metalloproteinases as biomarkers in premalignant and malignant tumors of the human skin

The incidence of non-melanoma skin cancer is increasing worldwide. Basal cell carcinoma followed by squamous cell carcinoma and malignant melanoma are the most frequent skin tumors. Immunosuppressed patients have an increased risk of neoplasia, of which non-melanoma skin cancer is the most common. Matrix metalloproteinases (MMPs) are proteolytic enzymes that collectively are capable of degrading virtually all components of the extracellular matrix. MMPs can also process substrates distinct from extracellular matrix proteins and influence cell proliferation, differentiation, angiogenesis, and apoptosis. MMP activity is regulated by their natural inhibitors, tissue inhibitors of metallopro-teinases (TIMPs). In this study, the expression patterns of MMPs, TIMPs, and certain cancer-related molecules were investigated in premalignant and malignant lesions of the human skin. As methods were used immunohistochemisty, in situ hybridization, and reverse transcriptase polymerase chain reaction (RT-PCR) from the cell cultures. Our aim was to evaluate the expression pattern of MMPs in extramammary Paget's disease in order to find markers for more advanced tumors, as well as to shed light on the origin of this rare neoplasm. Novel MMPs -21, -26, and -28 were studied in melanoma cell culture, in primary cutaneous melanomas, and their sentinel nodes. The MMP expression profile in keratoacanthomas and well-differentiated squamous cell carcinomas was analyzed to find markers to differentiate benign keratinocyte hyperproliferation from malignantly transformed cells. Squamous cell carcinomas of immunosuppressed organ transplant recipients were compared to squamous cell carcinomas of matched immunocompetent controls to investigate the factors explaining their more aggressive nature. We found that MMP-7 and -19 proteins are abundant in extramammary Paget's disease and that their presence may predict an underlying adenocarcinoma in these patients. In melanomas, MMP-21 was upregulated in early phases of melanoma progression, but disappeared from the more aggressive tumors with lymph node metastases. The presence of MMP-13 in primary melanomas and lymph node metastases may relate to more aggressive disease. In keratoacanthomas, the expression of MMP-7 and -9 is rare and therefore should raise a suspicion of well-differentiated squamous cell carcinomas. Furthermore, MMP-19 and p16 were observed in benign keratinocyte hyperproliferation of keratoacanthomas, whereas they were generally lost from malignant keratinocytes of SCCs. MMP-26 staining was significantly stronger in squamous cell carcinomas and Bowen s disease samples of organ transplant recipients and it may contribute to the more aggressive nature of squamous cell carcinomas in immunosuppressed patients. In addition, the staining for MMP-9 was significantly stronger in macrophages surrounding the tumors of the immunocompetent group and in neutrophils of those patients on cyclosporin medication. In conclusion, based on our studies, MMP-7 and -19 might serve as biomarkers for more aggressive extramammary Paget's disease and MMP-21 for malignant transformation of melanocytes. MMP -7, -9, and -26, however, could play an important role in the pathobiology of keratinocyte derived malignancies.

Molecular basis for the development of diagnostic methods and specific treatment modalities for idiopathic pulmonary fibrosis

Idiopathic pulmonary fibrosis (IPF) is an interstitial lung disease with unknown aetiology and poor prognosis. IPF is characterized by alveolar epithelial damage that leads tissue remodelling and ultimately to the loss of normal lung architecture and function. Treatment has been focused on anti-inflammatory therapies, but due to their poor efficacy new therapeutic modalities are being sought. There is a need for early diagnosis and also for differential diagnostic markers for IPF and other interstitial lung diseases. The study utilized patient material obtained from bronchoalveolar lavage (BAL), diagnostic biopsies or lung transplantation. Human pulmonary fibroblast cell cultures were propagated and asbestos-induced pulmonary fibrosis in mice was used as an experimental animal model of IPF. The possible markers for IPF were scanned by immunohistochemistry, RT-PCR, ELISA and western blot. Matrix metalloproteinases (MMPs) are proteolytic enzymes that participate in tissue remodelling. Microarray studies have introduced potential markers that could serve as additional tools for the assessment of IPF and one of the most promising was MMP 7. MMP-7 protein levels were measured in the BAL fluid of patients with idiopathic interstitial lung diseases or idiopathic cough. MMP-7 was however similarly elevated in the BAL fluid of all these disorders and thus cannot be used as a differential diagnostic marker for IPF. Activation of transforming growth factor (TGF)-ß is considered to be a key element in the progression of IPF. Bone morphogenetic proteins (BMP) are negative regulators of intracellular TGF-ß signalling and BMP-4 signalling is in turn negatively regulated by gremlin. Gremlin was found to be highly upregulated in the IPF lungs and IPF fibroblasts. Gremlin was detected in the thickened IPF parenchyma and endothelium of small capillaries, whereas in non-specific interstitial pneumonia it localized predominantly in the alveolar epithelium. Parenchymal gremlin immunoreactivity might indicate IPF-type interstitial pneumonia. Gremlin mRNA levels were higher in patients with end-stage fibrosis suggesting that gremlin might be a marker for more advanced disease. Characterization of the fibroblastic foci in the IPF lungs showed that immunoreactivity to platelet-derived growth factor (PDGF) receptor-α and PDGF receptor-β was elevated in IPF parenchyma, but the fibroblastic foci showed only minor immunoreactivity to the PDGF receptors or the antioxidant peroxiredoxin II. Ki67 positive cells were also observed predominantly outside the fibroblastic foci, suggesting that the fibroblastic foci may not be composed of actively proliferating cells. When inhibition of profibrotic PDGF-signalling by imatinib mesylate was assessed, imatinib mesylate reduced asbestos-induced pulmonary fibrosis in mice as well as human pulmonary fibroblast migration in vitro but it had no effect on the lung inflammation.

Occupational chronic solvent encephalopathy in Finland 1995 - 2007 : incidence and diagnostic methods

The occurrence of occupational chronic solvent encephalopathy (CSE) seems to decrease, but still every year reveals new cases. To prevent CSE and early retirement of solvent-exposed workers, actions should focus on early CSE detection and diagnosis. Identifying the work tasks and solvent exposure associated with high risk for CSE is crucial. Clinical and exposure data of all the 128 cases diagnosed with CSE as an occupational disease in Finland during 1995-2007 was collected from the patient records at the Finnish Institute of Occupational Health (FIOH) in Helsinki. The data on the number of exposed workers in Finland were gathered from the Finnish Job-exposure Matrix (FINJEM) and the number of employed from the national workforce survey. We analyzed the work tasks and solvent exposure of CSE patients and the findings in brain magnetic resonance imaging (MRI), quantitative electroencephalography (QEEG), and event-related potentials (ERP). The annual number of new cases diminished from 18 to 3, and the incidence of CSE decreased from 8.6 to 1.2 / million employed per year. The highest incidence of CSE was in workers with their main exposure to aromatic hydrocarbons; during 1995-2006 the incidence decreased from 1.2 to 0.3 / 1 000 exposed workers per year. The work tasks with the highest incidence of CSE were floor layers and lacquerers, wooden surface finishers, and industrial, metal, or car painters. Among 71 CSE patients, brain MRI revealed atrophy or white matter hyperintensities or both in 38% of the cases. Atrophy which was associated with duration of exposure was most frequently located in the cerebellum and in the frontal or parietal brain areas. QEEG in a group of 47 patients revealed increased power of the theta band in the frontal brain area. In a group of 86 patients, the P300 amplitude of auditory ERP was decreased, but at individual level, all the amplitude values were classified as normal. In 11 CSE patients and 13 age-matched controls, ERP elicited by a multimodal paradigm including an auditory, a visual detection, and a recognition memory task under single and dual-task conditions corroborated the decrease of auditory P300 amplitude in CSE patients in single-task condition. In dual-task conditions, the auditory P300 component was, more often in patients than in controls, unrecognizable. Due to the paucity and non-specificity of the findings, brain MRI serves mainly for differential diagnostics in CSE. QEEG and auditory P300 are insensitive at individual level and not useful in the clinical diagnostics of CSE. A multimodal ERP paradigm may, however, provide a more sensitive method to diagnose slight cognitive disturbances such as CSE.

Properties of Toeplitz operators on analytic function spaces : from function symbols to distributions

Toeplitz operators are among the most important classes of concrete operators with applications to several branches of pure and applied mathematics. This doctoral thesis deals with Toeplitz operators on analytic Bergman, Bloch and Fock spaces. Usually, a Toeplitz operator is a composition of multiplication by a function and a suitable projection. The present work deals with generalizing the notion to the case where the function is replaced by a distributional symbol. Fredholm theory for Toeplitz operators with matrix-valued symbols is also considered. The subject of this thesis belongs to the areas of complex analysis, functional analysis and operator theory. This work contains five research articles. The articles one, three and four deal with finding suitable distributional classes in Bergman, Fock and Bloch spaces, respectively. In each case the symbol class to be considered turns out to be a certain weighted Sobolev-type space of distributions. The Bergman space setting is the most straightforward. When dealing with Fock spaces, some difficulties arise due to unboundedness of the complex plane and the properties of the Gaussian measure in the definition. In the Bloch-type spaces an additional logarithmic weight must be introduced. Sufficient conditions for boundedness and compactness are derived. The article two contains a portion showing that under additional assumptions, the condition for Bergman spaces is also necessary. The fifth article deals with Fredholm theory for Toeplitz operators having matrix-valued symbols. The essential spectra and index theorems are obtained with the help of Hardy space factorization and the Berezin transform, for instance. The article two also has a part dealing with matrix-valued symbols in a non-reflexive Bergman space, in which case a condition on the oscillation of the symbol (a logarithmic VMO-condition) must be added.