Principal polynomial shape analysis: A non-linear tool for statistical shape modeling.

BACKGROUND AND OBJECTIVES: The most widespread statistical modeling technique is based on Principal Component Analysis (PCA). Although this approach has several appealing features, it remains hampered by its linearity. Principal Polynomial Analysis (PPA) can capture non-linearity in a sequential algorithm, while maintaining the interesting properties of PCA. PPA is, however, computationally expensive in handling shape surface data. To this end, we propose Principal Polynomial Shape Analysis (PPSA) as an adjusted approach for non-linear shape analyzes. The aim of this study was to assess PPSA's features, its model boundaries and its general applicability. METHODS: PCA and PPSA-based shape models were investigated on one verification and three model evaluation experiments. In the verification experiment, the estimated mean of the PCA and PPSA model on a data set of synthetic lower limbs of different lengths in different poses were compared to the real mean. Further, the PCA-based and PPSA shape models were tested for three challenging cases namely for shape model creation of gait marker data, for regression analysis on aging faces and for modeling pose variation in full body scans. For the latter, additionally a Fundamental Coordinate Model (FCM) and a PPSA model on Fundamental Coordinate(FC) space was created. The performances were evaluated based on model-based accuracy, generalization, compactness and specificity. RESULTS: In the verification experiment, the scaling error reduced from 75% to below 1% when employing PPSA instead of PCA for a training set with 180° angular variation. For the model evaluation experiments, the PPSA models described the data as accurate and generalized as the PCA-based shape models. The PPSA models were slightly more compact and specific (up to 30%) than the PCA-based models. In regression, PCA and PPSA-based parameterizations explained a similar amount of variation. Lastly, for the full body scans, applying PPSA to parameterizations improved the compactness and accuracy. CONCLUSIONS: PPSA describes the non-linear relationships between principal variations in a parameterized space. Compared to standard PCA-based shape models, capturing the non-linearity reduced the nonsense information in the shape components and improved the description of the data mean.

A hybrid classifier based on nonlinear-PCA and deep belief networks with applications in dysphagia diagnosis.

Traditional dysphagia prescreening diagnostic methods require doctors specialists to give patients a total score based on a water swallow test scale. This method is limited by the high dimensionality of the diagnostic elements in the water swallow test scale with heavy workload (Towards each patient, the scale requires the doctors give score for 18 diagnostic elements respectively) as well as the difficulties of extracting and using the diagnostic scale data's non-linear features and hidden expertise information (Even with the scale scores, specific diagnostic conclusions are still given by expert doctors under the expertise). In this paper, a hybrid classifier model based on Nonlinear-Principal Component Analysis (NPCA) and Deep Belief Networks (DBN) is proposed in order to effectively extract the diagnostic scale data's nonlinear features and hidden information and to provide the key scale elements' locating methods towards the diagnostic results (The key scale elements that affect different diagnostic conclusions are given to improve the efficiency and pertinence of diagnosis and reduce the workload of diagnosis). We demonstrate the effectiveness of the proposed method using the frame of 'information entropy theory'. Real dysphagia diagnosis examples from the China-Japanese Friendship Hospital are used to demonstrate applications of the proposed methods. The examples show satisfactory results compared to the traditional classifier.