diff --git a/nncf/openvino/graph/nncf_graph_builder.py b/nncf/openvino/graph/nncf_graph_builder.py
index d14b6cd4946..519911d7410 100644
--- a/nncf/openvino/graph/nncf_graph_builder.py
+++ b/nncf/openvino/graph/nncf_graph_builder.py
@@ -98,7 +98,7 @@ def _add_edges_to_nncf_graph(model: ov.Model, graph: NNCFGraph) -> None:
             in_node_id = graph.get_node_by_name(op.get_friendly_name()).node_id
             for output_port_id, out in enumerate(op.outputs()):
                 node_vs_target_inputs = defaultdict(list)
-                for inp in out.get_target_inputs():
+                for inp in sorted(out.get_target_inputs(), key=lambda inp: inp.get_node().get_friendly_name()):
                     node_vs_target_inputs[inp.get_node()].append(inp)
 
                 for out_node, inputs in node_vs_target_inputs.items():
diff --git a/nncf/quantization/algorithms/weight_compression/algorithm.py b/nncf/quantization/algorithms/weight_compression/algorithm.py
index 79363722934..2d126e60474 100644
--- a/nncf/quantization/algorithms/weight_compression/algorithm.py
+++ b/nncf/quantization/algorithms/weight_compression/algorithm.py
@@ -709,19 +709,22 @@ def apply(
         )
         return transformed_model
 
-    def _get_activation_node_and_port(self, node: NNCFNode, nncf_graph: NNCFGraph) -> tuple[NNCFNode, int]:
+    def _get_activation_node_port_and_channel(self, node: NNCFNode, nncf_graph: NNCFGraph) -> tuple[NNCFNode, int]:
         """
-        This method returns the activation layer and corresponding port id for the node.
+        This method returns the activation layer, corresponding port id and channel axis for the given node.
 
         :param node: NNCFGraph node for which the activation is sought.
         :param nncf_graph: NNCFGraph instance with the node.
-        :return: Tuple with the activation node and port id.
+        :return: Tuple with the activation node, port id and channel axis.
         """
         activation_port = self._backend_entity.get_activation_port_id(node, nncf_graph)
         activation_edge = nncf_graph.get_input_edge_by_port_id(node, activation_port)
         activation_node = activation_edge.from_node
         port_id = activation_edge.output_port_id
-        return activation_node, port_id
+        activation_channel_axis = self._backend_entity.get_activation_channel_axis(
+            node, port_id, activation_edge.tensor_shape
+        )
+        return activation_node, port_id, activation_channel_axis
 
     def get_matmul_input_to_output_nodes_map(
         self, matmul_nodes: list[NNCFNode], graph: NNCFGraph
@@ -742,8 +745,8 @@ def get_matmul_input_to_output_nodes_map(
         """
         matmul_input_to_output_nodes_map = defaultdict(list)
         for node in matmul_nodes:
-            act_node, output_port_id = self._get_activation_node_and_port(node, graph)
-            matmul_input_to_output_nodes_map[(act_node, output_port_id)].append(node)
+            act_node, output_port_id, act_channel_axis = self._get_activation_node_port_and_channel(node, graph)
+            matmul_input_to_output_nodes_map[(act_node, output_port_id, act_channel_axis)].append(node)
         return matmul_input_to_output_nodes_map
 
     def get_compression_nodes_info(
@@ -809,15 +812,17 @@ def get_statistic_points(
         statistic_container = StatisticPointsContainer()
         # Statistics for data aware algorithms
         if self._data_aware_compression:
-            for node, output_port_id in nodes_and_port_ids:
+            for node, output_port_id, input_channel_axis in nodes_and_port_ids:
                 statistic_point = self._backend_entity.target_point(
                     TargetType.POST_LAYER_OPERATION, node.node_name, port_id=output_port_id
                 )
-                # Reduce activations across all but the last dimension. The last dimension is assumed to be the hidden
-                # size dimension.
+                # Reduce activations across all but the hidden dimension.
                 n_dims = len(graph.get_output_edges_by_port_id(node, output_port_id)[0].tensor_shape)
+                # negative axis (e.g. -1 for the last axis) is converted into corresponding positive value
+                input_channel_axis = input_channel_axis % n_dims
+                reduction_axes = tuple(i for i in range(n_dims) if i != input_channel_axis)
                 stat_collector = self._backend_entity.mean_statistic_collector(
-                    reduction_axes=tuple(range(n_dims - 1)), subset_size=self._subset_size
+                    reduction_axes=reduction_axes, subset_size=self._subset_size
                 )
                 statistic_container.add_statistic_point(
                     StatisticPoint(
@@ -854,7 +859,7 @@ def _get_statistics_for_weights_compression(
         # Where mean_value is a 1D tensor representing an activation reduced over batch and sequence length dimensions,
         # shape is an original shape of an activation before reduction, n is the size of the dataset (or subset_size).
         statistics = {}
-        for (act_node, output_port_id), matmul_nodes in matmul_input_to_output_nodes_map.items():
+        for (act_node, output_port_id, _), matmul_nodes in matmul_input_to_output_nodes_map.items():
             tensor_collectors = list(
                 statistic_points.get_algo_statistics_for_node(
                     act_node.node_name,
diff --git a/nncf/quantization/algorithms/weight_compression/backend.py b/nncf/quantization/algorithms/weight_compression/backend.py
index 62d0745a0f4..bd24e872b26 100644
--- a/nncf/quantization/algorithms/weight_compression/backend.py
+++ b/nncf/quantization/algorithms/weight_compression/backend.py
@@ -257,6 +257,18 @@ def get_filter_fn_for_statistics(activation_port_id: int, algorithm_key: str) ->
         :return: Backend-specific callable to filter statistic containers according to its statistic point.
         """
 
+    @staticmethod
+    @abstractmethod
+    def get_activation_channel_axis(node: NNCFNode, port_id: int, input_shape: tuple[int]) -> int:
+        """
+        Returns axis number of the activation tensor which correspond to it channel.
+
+        :param node: NNCFNode instance.
+        :param port_id: Port ID for input.
+        :param input_shape: Shape of the input.
+        :return: Channel axis number.
+        """
+
 
 class AWQAlgoBackend(WeightCompressionAlgoBackend):
     @staticmethod
diff --git a/nncf/quantization/algorithms/weight_compression/gptq.py b/nncf/quantization/algorithms/weight_compression/gptq.py
index 76674fd9288..b6f2e27c765 100644
--- a/nncf/quantization/algorithms/weight_compression/gptq.py
+++ b/nncf/quantization/algorithms/weight_compression/gptq.py
@@ -123,8 +123,13 @@ def apply(
             ]:
                 continue
             _, input_tensors = next(iter(inputs.items()))
-            hessian = self._calculate_hessian(node, input_tensors)
-            scale, zero_point = self._quantize_weights(model, graph, wc_params, hessian, input_tensors)
+            input_channel_axis = self._backend_entity.get_activation_channel_axis(
+                node, self._backend_entity.get_activation_port_id(node, graph), input_tensors[0].shape
+            )
+            hessian = self._calculate_hessian(node, input_tensors, input_channel_axis)
+            scale, zero_point = self._quantize_weights(
+                model, graph, wc_params, hessian, input_tensors, input_channel_axis
+            )
             scales[wc_params.weight_name] = scale
             zero_points[wc_params.weight_name] = zero_point
 
@@ -157,7 +162,7 @@ def get_statistic_points(
 
         return self._layerwise_engine.get_statistic_points(model, graph, filtered_nodes)
 
-    def _calculate_hessian(self, node: NNCFNode, inputs: list[Tensor]) -> Tensor:
+    def _calculate_hessian(self, node: NNCFNode, inputs: list[Tensor], input_channel_axis: int) -> Tensor:
         """
         Calculates the Hessian matrix for the given node and inputs.
 
@@ -170,19 +175,18 @@ def _calculate_hessian(self, node: NNCFNode, inputs: list[Tensor]) -> Tensor:
         if node.metatype in self._backend_entity.convolution_metatypes:
             msg = "Convolution metatypes are not supported"
             raise nncf.UnsupportedModelError(msg)
-        if node.layer_attributes.input_attributes["transpose"]:
-            msg = "Transposed input is not supported"
-            raise nncf.UnsupportedModelError(msg)
 
         hessian = fns.zeros(
-            (inputs[0].shape[-1], inputs[0].shape[-1]), backend=inputs[0].backend, dtype=TensorDataType.float32
+            (inputs[0].shape[input_channel_axis], inputs[0].shape[input_channel_axis]),
+            backend=inputs[0].backend,
+            dtype=TensorDataType.float32,
         )
 
         for inp in inputs:
             batch_size = 1 if len(inp.shape) == 2 else inp.shape[0]
             if node.metatype in self._backend_entity.matmul_metatypes:
                 if len(inp.shape) == 3:
-                    inp = inp.reshape((-1, inp.shape[-1]))
+                    inp = inp.reshape((-1, inp.shape[input_channel_axis]))
                 inp = fns.transpose(inp)
             hessian *= nsamples / (nsamples + batch_size)
             nsamples += batch_size
@@ -198,6 +202,7 @@ def _quantize_weights(
         wc_params: WeightCompressionParameters,
         hessian: Tensor,
         inputs: list[Tensor],
+        input_channel_axis: int,
     ):
         """
         Quantizes the weights of the model based on the calculated Hessian matrix.
@@ -210,10 +215,7 @@ def _quantize_weights(
         """
         if wc_params.node_with_weight.metatype in self._backend_entity.convolution_metatypes:
             msg = "Convolution metatypes are not supported"
-            raise RuntimeError(msg)
-        if not wc_params.node_with_weight.layer_attributes.constant_attributes[wc_params.weight_port_id]["transpose"]:
-            msg = "Transpose is not supported"
-            raise RuntimeError(msg)
+            raise nncf.UnsupportedModelError(msg)
 
         weight_tensor = self._backend_entity.get_weight(
             wc_params.node_with_weight, wc_params.weight_port_id, model, graph
@@ -267,8 +269,12 @@ def _quantize_weights(
                         scales.append(scale)
                     else:
                         if self._scale_estimation and block_compression_config.num_bits == 4:
-                            activations = [inp[..., (i1 + i) : (i1 + i + group_size)] for inp in inputs]
-                            wc_statistics = ScaleEstimation.activations_to_wc_statistics(activations)
+                            slicing_along_axis = [slice(None)] * len(inputs[0].shape)
+                            slicing_along_axis[input_channel_axis] = slice(i1 + i, i1 + i + group_size)
+                            activations = [inp[tuple(slicing_along_axis)] for inp in inputs]
+                            wc_statistics = ScaleEstimation.activations_to_wc_statistics(
+                                activations, input_channel_axis
+                            )
                             scale, zero_point = ScaleEstimation.calculate_quantization_params(
                                 wc_statistics,
                                 weight_tensor[:, (i1 + i) : (i1 + i + group_size)],
diff --git a/nncf/quantization/algorithms/weight_compression/mixed_precision.py b/nncf/quantization/algorithms/weight_compression/mixed_precision.py
index 6bb9391d0cb..fa185473965 100644
--- a/nncf/quantization/algorithms/weight_compression/mixed_precision.py
+++ b/nncf/quantization/algorithms/weight_compression/mixed_precision.py
@@ -277,7 +277,7 @@ def get_statistic_points(
         self._set_backend_entity(model)
 
         statistic_container = StatisticPointsContainer()
-        for act_node, output_port_id in nodes_and_port_ids:
+        for act_node, output_port_id, _ in nodes_and_port_ids:
             n_dims = len(graph.get_output_edges_by_port_id(act_node, output_port_id)[0].tensor_shape)
             if n_dims < 2:
                 msg = (
diff --git a/nncf/quantization/algorithms/weight_compression/onnx_backend.py b/nncf/quantization/algorithms/weight_compression/onnx_backend.py
index a962cf163bc..36a7f9e6170 100644
--- a/nncf/quantization/algorithms/weight_compression/onnx_backend.py
+++ b/nncf/quantization/algorithms/weight_compression/onnx_backend.py
@@ -32,6 +32,7 @@
 from nncf.onnx.graph.metatypes.groups import MATMUL_METATYPES
 from nncf.onnx.graph.model_transformer import remove_initializer
 from nncf.onnx.graph.model_transformer import set_initializer
+from nncf.onnx.graph.node_utils import get_act_quantization_axis
 from nncf.onnx.graph.node_utils import get_weight_quantization_axis
 from nncf.onnx.graph.onnx_helper import ONNX_DTYPE_TO_NNCF_DTYPE
 from nncf.onnx.graph.onnx_helper import get_name_to_node_map
@@ -240,6 +241,10 @@ def filter_func(point: StatisticPoint) -> bool:
 
         return filter_func
 
+    @staticmethod
+    def get_activation_channel_axis(node: NNCFNode, port_id: int, input_shape: tuple[int]) -> int:
+        return get_act_quantization_axis(node, port_id)
+
     def insert_adapters(
         self, wc_params: WeightCompressionParameters, lora_A: Tensor, lora_B: Tensor, int8_lora: bool
     ) -> None:
diff --git a/nncf/quantization/algorithms/weight_compression/openvino_backend.py b/nncf/quantization/algorithms/weight_compression/openvino_backend.py
index 7c1838eb8d2..f284073b4f9 100644
--- a/nncf/quantization/algorithms/weight_compression/openvino_backend.py
+++ b/nncf/quantization/algorithms/weight_compression/openvino_backend.py
@@ -33,6 +33,7 @@
 from nncf.openvino.graph.model_transformer import OVModelTransformer
 from nncf.openvino.graph.node_utils import convert_op
 from nncf.openvino.graph.node_utils import create_ov_const_from_tensor
+from nncf.openvino.graph.node_utils import get_activation_channel_axis
 from nncf.openvino.graph.node_utils import get_const_value_as_numpy_tensor
 from nncf.openvino.graph.node_utils import get_const_value_as_ov_tensor
 from nncf.openvino.graph.node_utils import get_weight_channel_axes
@@ -114,9 +115,6 @@ def mean_statistic_collector(
 
     @staticmethod
     def get_activation_port_id(node: NNCFNode, nncf_graph: NNCFGraph) -> int:
-        if node.layer_attributes.input_attributes["transpose"]:
-            msg = "Transposed input is not supported"
-            raise nncf.UnsupportedModelError(msg)
         constant_ports = node.layer_attributes.get_const_port_ids()
         activation_ports = [
             e.input_port_id for e in nncf_graph.get_input_edges(node) if e.input_port_id not in constant_ports
@@ -133,6 +131,9 @@ def get_weight_names_and_port_ids(node: NNCFNode, graph: NNCFGraph) -> list[tupl
         return result
 
     def get_weight(self, node_with_weight: NNCFNode, weight_port_id: int, model: ov.Model, graph: NNCFGraph) -> Tensor:
+        if not node_with_weight.layer_attributes.constant_attributes[weight_port_id]["transpose"]:
+            msg = "Only transposed weights are supported"
+            raise nncf.UnsupportedModelError(msg)
         weight_name = node_with_weight.layer_attributes.constant_attributes[weight_port_id]["name"]
         weight_node = self.name_to_node_mapping[weight_name]
         weight_tensor = get_const_value_as_numpy_tensor(weight_node)
@@ -199,7 +200,12 @@ def insert_adapters(
             A_W = opset.constant(lora_A.data)
             B_W = opset.constant(lora_B.data)
 
-        A_MM = opset.matmul(input_node, A_W, transpose_a=False, transpose_b=True)
+        A_MM = opset.matmul(
+            input_node,
+            A_W,
+            transpose_a=wc_params.node_with_weight.layer_attributes.input_attributes["transpose"],
+            transpose_b=True,
+        )
         B_MM = opset.matmul(A_MM, B_W, transpose_a=False, transpose_b=True)
 
         node_output_port = mm_node.output(0)
@@ -367,6 +373,10 @@ def filter_func(point: StatisticPoint) -> bool:
 
         return filter_func
 
+    @staticmethod
+    def get_activation_channel_axis(node: NNCFNode, port_id: int, input_shape: tuple[int]) -> int:
+        return get_activation_channel_axis(node, port_id, input_shape)
+
 
 class OVTensorWeightCompressionAlgoBackend(OVWeightCompressionAlgoBackend):
     """
diff --git a/nncf/quantization/algorithms/weight_compression/scale_estimation.py b/nncf/quantization/algorithms/weight_compression/scale_estimation.py
index 4aea4633ebb..308828e1f2a 100644
--- a/nncf/quantization/algorithms/weight_compression/scale_estimation.py
+++ b/nncf/quantization/algorithms/weight_compression/scale_estimation.py
@@ -371,7 +371,7 @@ def calculate_quantization_params(
         return result_scale, zp
 
     @staticmethod
-    def activations_to_wc_statistics(activations: list[Tensor]) -> WCTensorStatistic:
+    def activations_to_wc_statistics(activations: list[Tensor], input_channel_axis: int) -> WCTensorStatistic:
         """
         Mimic the activation reducing logic from WeightCompression.get_statistic_points.
 
@@ -382,7 +382,9 @@ def activations_to_wc_statistics(activations: list[Tensor]) -> WCTensorStatistic
         shapes = []
         for act in activations:
             shapes.append(act.shape)
-            reduction_shape = tuple(range(act.ndim - 1))
+            # negative axis (e.g. -1 for the last axis) is converted into corresponding positive value
+            input_channel_axis = input_channel_axis % len(act.shape)
+            reduction_shape = tuple(i for i in range(len(act.shape)) if i != input_channel_axis)
             mean_values.append(fns.mean(act, axis=reduction_shape))
         wc_statistics = WCTensorStatistic(mean_values, shapes)
         return wc_statistics
diff --git a/nncf/quantization/algorithms/weight_compression/torch_backend.py b/nncf/quantization/algorithms/weight_compression/torch_backend.py
index 50f765c35c3..c3435d27a3a 100644
--- a/nncf/quantization/algorithms/weight_compression/torch_backend.py
+++ b/nncf/quantization/algorithms/weight_compression/torch_backend.py
@@ -497,6 +497,10 @@ def transform_model(
 
         return transformed_model
 
+    @staticmethod
+    def get_activation_channel_axis(node: NNCFNode, port_id: int, input_shape: tuple[int]) -> int:
+        return node.metatype.output_channel_axis
+
 
 class PTAWQAlgoAlgoBackend(AWQAlgoBackend, PTWeightCompressionAlgoBackend):
     @staticmethod
diff --git a/nncf/quantization/algorithms/weight_compression/torch_fx_backend.py b/nncf/quantization/algorithms/weight_compression/torch_fx_backend.py
index 2650f16600c..590c60ab970 100644
--- a/nncf/quantization/algorithms/weight_compression/torch_fx_backend.py
+++ b/nncf/quantization/algorithms/weight_compression/torch_fx_backend.py
@@ -281,6 +281,10 @@ def transform_model(
 
         return transformed_model
 
+    @staticmethod
+    def get_activation_channel_axis(node: NNCFNode, port_id: int, input_shape: tuple[int]) -> int:
+        return node.metatype.output_channel_axis
+
 
 class FXMixedPrecisionAlgoBackend(MixedPrecisionAlgoBackend, FXWeightCompressionAlgoBackend):
     @staticmethod
diff --git a/tests/openvino/native/quantization/test_gptq.py b/tests/openvino/native/quantization/test_gptq.py
index a141d7c99fe..8d12703a720 100644
--- a/tests/openvino/native/quantization/test_gptq.py
+++ b/tests/openvino/native/quantization/test_gptq.py
@@ -346,7 +346,10 @@ def test_calculate_scale_linear():
 
     nodes = graph.get_all_nodes()
     wrapped_inputs = [Tensor(inp) for inp in inputs]
-    H = gptq._calculate_hessian(nodes[1], wrapped_inputs)
+    input_channel_axis = gptq._backend_entity.get_activation_channel_axis(
+        nodes[1], gptq._backend_entity.get_activation_port_id(nodes[1], graph), wrapped_inputs[0].shape
+    )
+    H = gptq._calculate_hessian(nodes[1], wrapped_inputs, input_channel_axis)
 
     ref_H = ref_gptq.H.numpy()
     assert np.all(np.isclose(ref_H, H.data))
@@ -356,7 +359,7 @@ def test_calculate_scale_linear():
     )
     wc_params.compression_config = WeightCompressionConfig(mode=CompressWeightsMode.INT4_SYM, group_size=16)
 
-    scale, _ = gptq._quantize_weights(ov_model, graph, wc_params, H, wrapped_inputs)
+    scale, _ = gptq._quantize_weights(ov_model, graph, wc_params, H, wrapped_inputs, input_channel_axis)
     ref_scale = ref_scale.numpy()
     scale = scale.reshape(ref_scale.shape)
     assert np.all(np.isclose(ref_scale, scale.data))
diff --git a/tests/openvino/native/quantization/test_weights_compression.py b/tests/openvino/native/quantization/test_weights_compression.py
index 6122f273114..9ef14cab931 100644
--- a/tests/openvino/native/quantization/test_weights_compression.py
+++ b/tests/openvino/native/quantization/test_weights_compression.py
@@ -11,7 +11,8 @@
 
 import inspect
 import os
-from typing import Callable
+from contextlib import nullcontext
+from typing import Callable, Optional
 from unittest.mock import patch
 
 import numpy as np
@@ -95,7 +96,9 @@ class LMLinearModel(OVReferenceModel):
     HIDDEN_DIM = 16
     INPUT_SHAPE = [1, 24, HIDDEN_DIM]  # [B, SeqLen, HiddenDim]
 
-    def _create_ov_model(self, transpose_b: bool = True, transpose_a=False, input_shape=None):
+    def _create_ov_model(
+        self, transpose_b: bool = True, transpose_a: bool = False, input_shape: Optional[list[int]] = None
+    ):
         self._input_shape = self.INPUT_SHAPE if input_shape is None else input_shape
         hdim_axis = -2 if transpose_a else -1
         self._hidden_dim = self._input_shape[hdim_axis]
@@ -1454,6 +1457,16 @@ def test_compression_with_different_algo_combinations(input_shape, kwargs):
     )
 
 
+@pytest.mark.parametrize(
+    ("transpose_a", "transpose_b", "raises_error"),
+    [
+        (False, True, False),
+        (True, True, False),
+        (False, False, True),
+        (True, False, True),
+    ],
+    ids=["tb_nota", "ta_tb", "nota_notb", "ta_notb"],
+)
 @pytest.mark.parametrize(
     "kwargs",
     [
@@ -1466,14 +1479,19 @@ def test_compression_with_different_algo_combinations(input_shape, kwargs):
             advanced_parameters=CompressionParams(gptq_params=GPTQParams(subset_size=2)),
         ),
     ],
+    ids=["se", "lora", "gptq_se_awq"],
 )
-def test_compression_with_transposed_activations(kwargs):
+def test_compression_with_transpose(transpose_a, transpose_b, raises_error, kwargs):
     dataset_size = 4
-    model = LMLinearModel(transpose_a=True, transpose_b=False).ov_model
+    model = LMLinearModel(transpose_a=transpose_a, transpose_b=transpose_b).ov_model
     input_data = [np.ones(inp.shape) for inp in model.inputs] * dataset_size
     dataset = Dataset(input_data)
 
-    with pytest.raises(nncf.UnsupportedModelError):
+    with (
+        pytest.raises(nncf.UnsupportedModelError)
+        if raises_error and not kwargs.get("lora_correction", False)
+        else nullcontext()
+    ):
         compress_weights(
             model,
             mode=CompressWeightsMode.INT4_SYM,