Scandent Tree: A Random Forest Learning Method for Incomplete Multimodal Datasets
We propose a solution for training random forests on incomplete multimodal datasets where many of the samples are non-randomly missing a large portion of the most discriminative features. For this goal, we present the novel concept of scandent trees. Thes
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University of British Columbia, Vancouver, British Columbia, Canada 2 IBM Almaden Research Center, San Jose, CA, USA [email protected]
Abstract. We propose a solution for training random forests on incomplete multimodal datasets where many of the samples are non-randomly missing a large portion of the most discriminative features. For this goal, we present the novel concept of scandent trees. These are trees trained on the features common to all samples that mimic the feature space division structure of a support decision tree trained on all features. We use the forest resulting from ensembling these trees as a classification model. We evaluate the performance of our method for different multimodal sample sizes and single modal feature set sizes using a publicly available clinical dataset of heart disease patients and a prostate cancer dataset with MRI and gene expression modalities. The results show that the area under ROC curve of the proposed method is less sensitive to the multimodal dataset sample size, and that it outperforms the imputation methods especially when the ratio of multimodal data to all available data is small.
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Introduction
In recent years there has been an interest in multimodality data analysis for disease detection. Ideally, multimodality methods should leverage the strengths of each modality and compensate for weaknesses. Another advantage of multimodality data analysis is discovering novel relations between different modalities. One example is finding the connection between genes related to Alzheimer’s disease and related areas in functional MRI [1]. Acquiring multimodal data is, in general, more costly and time consuming than a single modality. As a result, multimodal datasets usually have valuable features, but small sample sizes. This makes it difficult to build classifiers, with large training data, for highly multimodal protocols. Multomodal data is also often high dimensional and pose difficulties in feature selection and classifier building. Ensemble classifiers such as random forest provide a solution for the large feature space in small datasets using feature bagging. To tackle the issue of incomplete datasets, a variety of data imputation techniques exist. Some of these are non-parametric methods like hot deck imputation, KNN imputation or mean substitution. These methods ignore the possible correlations in data and could add bias. Model-based methods, on the other hand,
Corresponding author.
c Springer International Publishing Switzerland 2015 N. Navab et al. (Eds.): MICCAI 2015, Part I, LNCS 9349, pp. 694–701, 2015. DOI: 10.1007/978-3-319-24553-9_85
Scandent Tree: A Random Forest Learning Method
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assume a certain structure to the missing samples, like missing completely at random (MCAR) or missing not at random (MNAR). Examples of these methods include multiple imputation [2], maximum likelihood, stochastic regression [3], expectation maximization [3] and Bayesian methods [4]. While these methods could result in reduced bias, the assumption of specific pattern in the miss
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