Matlab object takes up a lot of space in the .mat file

I have an object from some class that I wrote in Matlab. When I use the “whos” command to determine its size, it is approximately 720,000 bytes. When I save it in a .mat file, it takes about 75 MB. What's happening?

Is there an efficient way to save and load an object in Matlab?

EDIT: Here is a list of properties and their size

            CT_COL: 2
            p: 5
            d: 10
            n: 37
            N: 20
          idx: [20x1 double]
           Am: [4-D double]
            X: [4-D double]
            y: [37x1 double]
        KGram: [20x20 double]
       reWave: []
          rpw: 2
         grps: [1x37 double]
        exIDX: [1 4 5 6 13]
          nCV: 100
        prIDX: [100x6 double]
        trIDX: [100x26 double]
            U: [5x100 double]
            V: [10x100 double]
            B: [20x100 double]
         Yhat: [37x100 double]
          Lam: [100x1 double]
    peakRatio: [37x1 double]

Both Am and X are 20x10x5x37 arrays (double)

By the way, the "reWave" property is used to store the method handle of another object. I thought this might not be a good idea (and might be the reason for this), so I removed all mention of this from the class definition. But it somehow appears in a set of properties. (Even after I released "clear classes.")

EDIT2: I use the command save('uvXbMod1.mat','ob') to save only an object. Here comes the riddle: when I use the command whos -file uvXbMod1.mat to see what is stored inside the file, it shows

Name      Size             Bytes   Class        Attributes

ob        1x1              680512  uvXbModel   

( , .) .mat, ?

EDIT3: ... , . , @(X) median(abs(X),2) @median . , , , , (?). , -, , ( ...)