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Classification of surface electromyogram (sEMG) signal is important for various applications such as prosthetic control and human computer interface. Surface EMG provides a better insight into the strength of muscle contraction which can be used as control signal for different applications. Due to the various interference between different muscle activities, it is difficult to identify movements using sEMG during low-level flexions. A new set of fractal features - fractal dimension and Maximum fractal length of sEMG has been previously reported by the authors. These features measure the complexity and strength of the muscle contraction during the low-level finger flexions. In order to classify and identify the low-level finger flexions using these features based on the fractal properties, a recently developed machine learning based classifier, Twin Support vector machines (TSVM) has been proposed. TSVM works on basic learning methodology and solves the classification tasks as two SVMs for each classes. This paper reports the novel method on the machine learning based classification of fractal features of sEMG using the Twin Support vector machines. The training and testing was performed using two different kernel functions - Linear and Radial Basis Function (RBF).