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Multiple Classifier Systems Incorporating Uncertainty

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Multiple Classifier Systems Incorporating Uncertainty Christian Thiel Multiple Classifier Systems Incorporating Uncertainty The title page and cover show the painting doctors by Michael S. Parker (www.michaelsparker.com), 2003. Used with friendly permission of the artist. Cover layout by Kreativfrosch Grafik + Design (www.kreativfrosch.eu), Wegscheid bei Passau, Germany. Universit¨atUlm | 89069 Ulm | Germany Dissertation zur Erlangung des Doktorgrades Doktor der Naturwissenschaften (Dr. rer. nat.) der Fakult¨at f¨urIngenieurwissenschaften und Informatik der Universit¨at Ulm vorgelegt von Christian Andr´eThiel Angefertigt am Institut f¨urNeuroinformatik Einreichung der Dissertation: Dezember 2009 Tag der Promotion: 10. Juni 2010 Gutachter: Prof. Dr. G¨unther Palm Gutachter: Prof. Dr. Heiko Neumann Gutachter: Prof. Dr. Barbara Hammer Amtierender Dekan der Fakult¨at: Prof. Dr.-Ing. Michael Weber www.ChristianThiel.com Abstract The inclusion of uncertain class information into multi classifier systems (MCS) is the central theme in this thesis. A multi classifier system relies on multiple base classifiers, each of which is trained on a separate view of the problem at hand. Combining their answers will lead to a more accurate final decision. An example would be emotion recognition, with decisions based on observations of the mouth, the eyes or the pitch of the voice. Traditionally in classification one sample is associated with exactly one class, for example anger. But, in practical applications, such a hard distinction is not warranted; instead a sample should have soft class memberships, thus being associated fuzzily with multiple classes at the same time. The inclusion of this uncertain information into various, but isolated building blocks of a MCS has been tackled by a great many researchers. This thesis places these approaches in the greater MCS context and assesses their utility. Remaining problems are identified and in many cases a solution is proposed. Bayesian probability is the most obvious tool for modelling class uncertainty, but perhaps the Dempster-Shafer theory of evidence, fuzzy logic or fuzzy sets, or even a distribution of opinions are much more viable in a classification context. These formal uncertainty theories, as well as some others, are assessed regarding their aptitude to support the core flavours of uncertainty in MCS, as identified in this work: vagueness, imprecision, and certainty. For the very fitting Dempster-Shafer theory, practical applications are reported. Some base classifiers have been extended to be trained on and answer with uncer- tain labels: learning vector quantisation, self-organizing maps, and most notably support vector machines (SVMs). The latter are an already very powerful breed of classifiers, and based on the idea of duplication, the underlying optimisation problem could be altered to accept fuzzy labels. Obtaining soft outputs from the binary SVMs is not trivial, but complete solutions are provided for the One- vs-Rest and One-vs-One multiclass decomposition architectures. Experiments do confirm the effectiveness of the fuzzy trained machines over their hard trained i counterparts, and yield answers as to which variants and parameter settings are to be preferred. Ideas on including certainty weighted information into many classifiers, and a study on the (surprisingly low) impact of label noise complete the classifier chapter. Once all classifiers have provided their answers, the following fusion stage requires an assessment of how certain these opinions are. This can be accomplished by looking at the structure of the answer, for example using the Gini function or an index of fuzziness. A rating of certainty can also be provided by the classifiers themselves. Both approaches are closely related to measuring the fuzzy accuracy of an algorithm, with Binaghi’s fuzzy error matrix being one option. Rejection experiments provide further insight in this regard. Existing fuzzy classifier fusion schemes are presented and categorised, among them those derived from uncertainty theories. For four fusion functions (decision templates, linear associative memory, naive Bayes and pseudoinverse solution) it can be shown that they all share the confusion matrix as the core element. Exper- iments again confirm the superiority of MCS architectures over single classifiers, and give pointers as to which fusion scheme to use in which situations. Numerous experiments were conducted to assess each mentioned aspect. Of the four real-world applications that served as test cases, two are especially note- worthy. The setup for the recognition of emotions in video sequences of facial expressions includes 14 base classifiers, operating on four different areas of the face and utilising PCA, edge orientation, and motion based features. The accu- racy of the system is slightly higher than for the average human, and apparently competitive with approaches described in the literature. Applied to land cover mapping, the fuzzy semi-supervised SOMs provide much smoother soft answers than hitherto proposed techniques, and the award-winning1 fuzzy SVMs produce a rendering of the satellite images that exhibits very compact regions, perfect for easy expert interpretation, and the highest accuracy of all tested classifiers. 1My initial publication on fuzzy-input fuzzy-output support vector machines [260] won the “Best Paper” award at the KES 2007 conference, out of 411 contributions. In collaboration with Ferdinando Giacco, applying the SVMs in a land cover mapping scenario placed us among the winners [156] of the 2008 DFTC Fusion Contest of the IEEE Geoscience and Remote Sensing Society. ii Zusammenfassung Die Berucksichtigung¨ von Unsicherheit in Mehrklassifikatorsystemen (MKS) steht im Zentrum dieser Arbeit. Anwendungen finden sich beispielsweise in der Emo- tionserkennung, wenn die Stimmung einer Person automatisch in eine bestimmte Klasse wie glucklich,¨ wutend¨ oder uberrascht¨ eingeordnet werden soll. Mehre- re Klassifikator-Programme spezialisieren sich dann jeweils auf ein Merkmal der Person, etwa die Augen, den Mund oder die Stimmh¨ohe. Die Entscheidungen der Programme sind mit Unsicherheit behaftet, zum Beispiel weil die Umgebung sehr laut war. Auch soll sich ein Klassifikator nicht auf eine Emotion festlegen; eine Person kann ja wutend¨ und uberrascht¨ zugleich sein. Also wird seine Antwort in einer sogenannten vagen oder weichen Zuordnung bestehen. Um stabilere und genauere Entscheidungen zu bekommen, fasst das MKS die Einzelmeinungen der Programme per Fusion zusammen. Klassifikatoren arbeiten traditionell mit harten Klassen, das heißt, ein Daten- punkt ist genau einer Klasse zugeordnet. Das Beispiel der Emotionserkennung zeigt deutlich, dass dies in einigen Anwendungen eine allzu einschr¨ankende An- nahme ist. Viele Forscher haben deshalb Unsicherheit bereits in zahlreiche, aber isolierte Teilbereiche von MKS integriert. Ihre Ans¨atze und Erkenntnisse wer- den im Gesamtkontext von MKS verortet. Die Arbeit schl¨agt daruber¨ hinaus L¨osungen fur¨ noch bestehende Lucken¨ vor. Es gibt formale Theorien, um Unsicherheit zu repr¨asentieren, unter ihnen die Bayessche Wahrscheinlichkeitstheorie, die Dempster-Shafer Evidenz-Theorie, die Fuzzy Logik sowie Fuzzy Mengen und Meinungsverteilungen. Nachdem mit Vag- heit, Ungenauigkeit und Sicherheit die fur¨ MKS relevanten Arten von Unsicher- heit definiert sind, nimmt sich die Arbeit die Frage vor, inwieweit diese von den jeweiligen Theorien dargestellt und - wichtiger noch - verrechnet werden k¨onnen. Besonders fur¨ die Dempster-Shafer Theorie werden praktische Anwendungen auf- gezeigt. Mit Support-Vektor-Maschinen (SVM), lernender Vektor-Quantisierung und selbst- organisierenden Karten werden einige Basis-Klassifikatoren so erweitert, dass sie iii auch aus unsicheren Klassenzuordnungen lernen k¨onnen und in der Lage sind, unsichere Antworten zu geben. Hervorzuheben ist dabei die Erweiterung der an sich schon m¨achtigen bin¨aren SVM. Sie beruht auf der Verdoppelung der Trai- ningspunkte und erfordert Anderungen¨ am darunterliegenden Optimierungspro- blem. Wie hier vage Antworten errechnet werden k¨onnen, wird fur¨ zwei wichtige Mehrklassenarchitekturen (Eine-gegen-den-Rest und Jede-gegen-Jede) detailliert dargestellt. Experimente best¨atigen, dass die mit unsicheren Zuordnungen trai- nierte Klassifikatoren genauere Antworten geben als die mit harten Zuordnungen trainierten. Eine Untersuchung zum (uberraschend¨ geringen) Einfluss von Klas- senzuordnungsfehlern in den Trainingsdaten rundet die Behandlung der Klassifi- katoren ab. Fur¨ die Klassifikator-Fusion ist es wichtig zu wissen, wie sicher die Antworten der einzelnen Algorithmen sind. Ein Indikator dafur¨ ist die Struktur der vagen Ausga- ben, die etwa mit der Gini-Funktion oder dem Fuzzy-Index charakterisiert werden kann. Eine m¨achtigere Alternative ist, jeden Klassifikator selbst einen Sicherheits- wert ausgeben zu lassen, schließlich kann er absch¨atzen, ob ihm beispielsweise pas- send zur Anfrage Trainingsdaten in ausreichender Menge zur Verfugung¨ stehen. Um den Nutzen von Sicherheitsindikatoren und vagen Klassifikatoren abw¨agen zu k¨onnen, reicht es nicht aus, die Genauigkeit auf Basis der Erkennungsrate zu bestimmen. Abhilfe schaffen hier Maße wie die Fuzzy Fehlermatrix von Binaghi. Durch Zuruckweisungs-Experimente,¨ bei denen das System mit zu großer Unsi- cherheit beurteilte Datenpunkte ablehnt, werden weitere Erkenntnisse gewonnen. Eine sogenannte Fusionsfunktion fasst die Antworten mehrerer Klassifikatoren zusammen. Bestehende Funktionen, die unter anderem auf den verschiedenen Un- sicherheitstheorien
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