This paper describes a new approach for detecting objects based on measuring the spatial consistency between different parts of an object. These parts are pre-defined on a set of training images and then located in any arbitrary image. Each part is represented by a group of densely sampled SIFT features. Supervised Locally Linear Embedding is then used to describe the appearance of each part in a low dimensional space. The novelty of this approach is that linear embedding techniques are used to model each object part and the background in the same coordinate space. This permits the detection algorithm to explicitly label test features as belonging to an object part or background. A spatial consistency algorithm is then employed to find object parts that together provide evidence for the location of object(s) in the image. Experiments on the 3D and PASCAL VOC datasets yield results comparable and often superior to those found in the literature.