Puuttuvien arvojen korvaaminen aliavaruusmenetelmillä

In survey practice as well as in many other data analysis tasks, missing values are a common encounter. In this thesis, the missing value imputation task is studied using three subspace methods, principal component analysis (PCA), the Self-Organizing Map (SOM) and the Generative Topographic Mapping (GTM). The application area of interest is survey imputation, where imputation is conventionally conducted using, e.g., hot deck methods or multiple imputation by chained equations (MICE). Similarities and differences between imputation in survey practice and recommendation systems are discussed, as well. The formalism behind missing value imputation is described together with general mechanisms giving rise to missing data. A detailed review of the aforementioned subspace methods in presence of missing data is given in order to motivate the novelties and new implementations contributed. The contributions of this thesis include (i) a novel way of treating missing data in the SOM algorithm, which is shown to improve properties of the model, (ii) a fine-tuned GTM, where the number of radial basis functions is increased during learning and the initialization is made using the SOM, and (iii) a novel regularization for the GTM for binary data. Experimental comparisons of existing and proposed methods are made using the wine data set and Likert-scale data from two wellbeing-related surveys. The variational Bayesian PCA is shown to be superior in the single imputation task. It also enables automatic relevance determination, i.e., automatic selection of the number of principal components needed. Finally, multiple imputation (MI) using the subspace methods and MICE is demonstrated. It is shown, that with survey data with less than 2 % missing data, all MI methods provide very similar population le vel results.Puuttuvat arvot ovat yleisiä niin kyselyaineistoissa kuin muissakin tilastollisesti analysoitavissa aineistoissa. Tässä opinnäytetyössä tutkitaan puuttuvien arvojen korvaamista käyttäen kolmea aliavaruusmenetelmää, pääkomponenttianalyysiä (PCA), itseorganisoivaa karttaa (SOM) ja generatiivista topografista kuvausta (GTM). Sovellusalueena ovat kyselyaineistot, joiden puuttuvia arvoja korvataan perinteisesti esimerkiksi käyttäen niin sanottuja hot-deck -menetelmiä tai moninkertaista ketjutettua korvaamista (multiple imputation by chained equations, MICE). Opinnäytteessä myös tarkastellaan kyselyaineistojen korvaamisen ja suositusjärjestelmien välisistä eroavaisuuksista ja samankaltaisuuksista menetelmätasolla. Edellä mainitut aliavaruusmenetelmät on esitelty yksityiskohtaisesti motivoiden sekä uusia muutoksia, että niiden käyttöä puuttuvien arvojen korvaamisessa. Työssä esitettyjä kontribuutioita ovat (i) uusi tapa käsitellä puuttuvia arvoja SOM-algoritmissa, minkä näytetään parantavan algoritmin ominaisuuksia, (ii) niin sanottu "fine-tuned GTM", jossa käytettävien kantafunktioiden määrää kasvattamalla voidaan oppia parempia malleja, sekä (iii) uudella tavalla regularisoitu GTM-malli binaariselle aineistolle. Kokeellisessa osuudessa vertaillaan ehdotettuja malleja sekä käyttäen tunnettua viiniaineistoa että kahta Likert-asteikkoista hyvinvointikyselyaineistoa. Variaatioaproksimoitu bayesilainen PCA osoittautuu parhaaksi tehtäessä yksittäisiä puuttuvien arvojen korvauksia. Se tekee myös automaattista mallinvalintaa, jolloin erillistä validointia mallin kompleksisuuden valitsemiseksi ei tarvita. Lopuksi näytetään moninkertaista puuttuvien arvojen korvaamista (MI) käyttäen aliavaruusmenetelmiä sekä MICE-menetelmää. Menetelmät tuottavat hyvin samanlaisia tuloksia kyselyaineistolla, jossa on alle 2 % puuttuvia arvoja

Action recognition from RGB-D data

In recent years, action recognition based on RGB-D data has attracted increasing attention. Different from traditional 2D action recognition, RGB-D data contains extra depth and skeleton modalities. Different modalities have their own characteristics. This thesis presents seven novel methods to take advantages of the three modalities for action recognition. First, effective handcrafted features are designed and frequent pattern mining method is employed to mine the most discriminative, representative and nonredundant features for skeleton-based action recognition. Second, to take advantages of powerful Convolutional Neural Networks (ConvNets), it is proposed to represent spatio-temporal information carried in 3D skeleton sequences in three 2D images by encoding the joint trajectories and their dynamics into color distribution in the images, and ConvNets are adopted to learn the discriminative features for human action recognition. Third, for depth-based action recognition, three strategies of data augmentation are proposed to apply ConvNets to small training datasets. Forth, to take full advantage of the 3D structural information offered in the depth modality and its being insensitive to illumination variations, three simple, compact yet effective images-based representations are proposed and ConvNets are adopted for feature extraction and classification. However, both of previous two methods are sensitive to noise and could not differentiate well fine-grained actions. Fifth, it is proposed to represent a depth map sequence into three pairs of structured dynamic images at body, part and joint levels respectively through bidirectional rank pooling to deal with the issue. The structured dynamic image preserves the spatial-temporal information, enhances the structure information across both body parts/joints and different temporal scales, and takes advantages of ConvNets for action recognition. Sixth, it is proposed to extract and use scene flow for action recognition from RGB and depth data. Last, to exploit the joint information in multi-modal features arising from heterogeneous sources (RGB, depth), it is proposed to cooperatively train a single ConvNet (referred to as c-ConvNet) on both RGB features and depth features, and deeply aggregate the two modalities to achieve robust action recognition