Deep neural networks have become a staple in solving intricate problems, proving their mettle in a wide array of applications. However, their training process is often hampered by shifting activation distributions during backpropagation, resulting in unstable gradients. Batch Normalization (BN) addresses this issue by normalizing activations, which allows for the use of higher learning rates. Despite its benefits, BN is not without drawbacks, including its dependence on mini-batch size and the presumption of a uniform distribution of samples. To overcome this, several alternatives have been proposed, such as Layer Normalization, Group Normalization, and Mixture Normalization. These methods may still struggle to adapt to the dynamic distributions of neuron activations during the learning process. To bridge this gap, we introduce Unsupervised Adaptive Normalization (UAN), an innovative algorithm that seamlessly integrates clustering for normalization with deep neural network learning in a singular process. UAN executes clustering using the Gaussian mixture model, determining parameters for each identified cluster, by normalizing neuron activations. These parameters are concurrently updated as weights in the deep neural network, aligning with the specific requirements of the target task during backpropagation. This unified approach of clustering and normalization, underpinned by neuron activation normalization, fosters an adaptive data representation that is specifically tailored to the target task. This adaptive feature of UAN enhances gradient stability, resulting in faster learning and augmented neural network performance. UAN outperforms the classical methods by adapting to the target task and is effective in classification, and domain adaptation.