Health Change Detection Using Temporal Transductive Learning

Industrial equipment, devices and patients typically undergo change from a healthy state to an unhealthy state. We develop a novel approach to detect unhealthy entities and also discover the time of change to enable deeper investigation into the cause for change. In the absence of an engineering or medical intervention, health degradation only happens in one direction — healthy to unhealthy. Our transductive learning framework, known as max-margin temporal transduction (MMTT), leverages this chronology of observations for learning a superior model with minimal supervision. Temporal Transduction is achieved by incorporating chronological constraints in the conventional max-margin classifier — Support Vector Machines (SVM). We utilize stochastic gradient descent to solve the resulting optimization problem. We prove that with high probability, an \(\epsilon \)-accurate solution for the proposed model can be achieved in \({\text {O}}\left( \frac{1}{\lambda \epsilon }\right) \) iterations. The runtime is \({\text {O}}\left( \frac{1}{\lambda \epsilon }\right) \) for the linear kernel and \({\text {O}}\left( \frac{n}{\lambda \epsilon }\right) \) for a non-linear Mercer kernel, where n is the number of observations from all entities — labeled and unlabeled. Our experiments on publicly available benchmark datasets demonstrate the effectiveness of our approach in accurately detecting unhealthy entities with less supervision as compared to other strong baselines — conventional and transductive SVM.

1. 1.

   We have ignored the bias b in this work, although it is likely to only further improve the results beyond those presented here. Detailed discussion on the bias term appears in [10].

2. 2.

   Uses: \(\frac{\partial |u|}{\partial v} = \frac{u}{|u|}\frac{\partial u}{\partial v}; u \ne 0\).

3. 3.

   A function \(f(\mathbf {w})\) is called \(\lambda \)-strongly convex if \(f(\mathbf {w}) - \frac{\lambda }{2}\Vert \mathbf {w}\Vert ^2\) is a convex function.

4. 4.

   \(\Vert \phi (\mathbf {x})\Vert ^2 = \langle \phi (x)\phi (x) \rangle = \exp \left( \frac{-|\phi (\mathbf {x}) - \phi (\mathbf {x})\Vert ^2}{2\sigma ^2}\right) = 1\).

5. 5.

   http://svmlight.joachims.org/.

6. 6.

   http://scikit-learn.org.

7. 7.

   https://www.dropbox.com/s/z9kfii51nvc7izq/mmtt.zip?dl=0.

Authors and Affiliations

1. GE Global Research, New York, USA

   Abhay Harpale

Corresponding author

Correspondence to Abhay Harpale .

Editors and Affiliations

1. University of Catania, Catania, Italy

   Giuseppe Nicosia

2. Department of Computer Science, University of Reading, Reading, UK

   Varun Ojha

3. Department of Computer Science, University of Oxford, Oxford, UK

   Emanuele La Malfa

4. Cambridge Judge Business School, University of Cambridge, Cambridge, UK

   Gabriele La Malfa

5. Department of Biochemistry, University of Cambridge, Cambridge, UK

   Giorgio Jansen

6. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

   Panos M. Pardalos

7. University of Catania, Catania, Italy

   Giovanni Giuffrida

8. Department of Informatics, Dana-Farber Cancer Institute, Boston, MA, USA

   Renato Umeton

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