## 4 Experiments
### Classification
Surprisingly, the representations reduced to 3 points per matrix, despite generating over 20% higher autoencoder error, can still be regarded as acceptable for practical applications, as even with so drastically reduced information the classifier is able to recognize the digit correctly in 97.88% of the cases. As the results from Table 6 are denoted as classification accuracies that can be easily compared to each other, we can seek comparison with other MNIST classifiers from the literature as well. However, it must be emphasized that in this paper we treat the image classification just as an analytic tool, and not as the key objective of this paper. Presumably, using the raw MNIST images to train a classifier, without the added difficulty of sparse representation, could only improve the achieved accuracy. The general problem of MNIST classification can be solved with accuracy as great as 99.79% [36]. We do not pursue to beat this result. For broader perspective, we can discuss the relation of our results to the other state-of-art MNIST classifiers that somehow involve sparse representations. Due to the varying objectives and circumstances, such comparisons require analysis that exceeds the straightforward competition for the best accuracy. The results from Table 6 are clearly better than the classification results obtained with the classical approach to sparse representations and dictionary learning. This includes particularly the convolutional sparse coding for classification (CSCC) method presented in [23], which achieved an accuracy of 84.5% on the MNIST data set, outperforming many previous approaches to sparse representations and dictionary learning. It must be emphasized, however, that the problem statement of that paper was not the same as ours. Dictionary-based methods are more computationally complex. Moreover, in [23], only the training subsets of 300 images were used. Thus, while that work may be regarded as an interesting reference for the present study, a direct comparison would be inappropriate. Another remarkable work on sparse representation was based on the idea of maximizing the margin between classes in the sparse representation-based classification (SRC) task [25]. The sparse \begin{table}
\begin{tabular}{c c} \hline \hline
**Model** & **Accuracy** \\ \hline MF4 (3 points) & 93.84\% \\ \hline MF4 (5 points) & 95.59\% \\ \hline MF4 & 95.64\% \\ \hline AF4 (3 points) & 96.86\% \\ \hline AF4 (5 points) & 98.33\% \\ \hline AF4 & **98.67\%** \\ \hline AF5 (3 points) & **97.88\%** \\ \hline AF5 (5 points) & **98.40\%** \\ \hline AF5 & 98.40\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Encodings from Section 4.2 were tested in the image classification task. Each encoding was used both in the original form, obtained as a result of local-maximum filtering, and in the reduced form that guarantees additional sparsity (Section 3.4). For each encoding (MF4, AF4, and AF5) a separate classifier was trained. The results for the additionally thresholded data were generated with the same neural networks that were trained for the original encodings. representations related to this model were strictly related to the classification task. In contrast to that approach, the method presented in this paper does not use any information on object labels when training the encoder. On the other hand, no convolutional neural networks were used in [25], and some solutions used in that paper might be outdated. The best classifier presented there reached a 98.13% accuracy rate. This result is lower than AF5 with 5-point-based reduction, which is already very sparse. The CNN-based architecture ensures that the image features are detected is a translation-invariant manner; translation of a feature would entail translated coding. A similar concept was applied in [22], which proposed another approach to CNN-related sparse coding. The results of MNIST classification were generated for both the unsupervised and the supervised approach to sparse coding, with 97.2% and 98.9% accuracy rates, respectively.