ANODE ACTIVE MATERIAL FOR LITHIUM SECONDARY BATTERY, METHOD OF PREPARING THE SAME, AND LITHIUM SECONDARY BATTERY INCLUDING THE SAME BACKGROUND OF THE INVENTION 1. Technical Field [0001] The present invention relates to an anode active material for lithium secondary batteries, a preparation method thereof and a lithium secondary battery including the same. More particularly, the present invention relates to an anode active material for lithium secondary batteries, which includes a silicon-containing core provided on the surface thereof with silicon nanoparticles, a preparation method thereof and a lithium secondary battery including the same. 2. Description of the Related Art [0002] Generally, a lithium secondary battery includes: an anode made of a carbon material or a lithium-metal alloy; a cathode made of a lithium-metal oxide; and an electrolyte including an organic solvent and a lithium salt dissolved in the organic solvent. Particularly, as an anode active material constituting an anode of a lithium secondary battery, a lithium metal had initially been used. However, since lithium has a problem of low reversibility and is considered unsafe, currently, a carbon material is being generally used as an anode active material for a lithium secondary battery. Although a carbon material is inferior to a lithium metal in capacity, it has a small volume change and excellent reversibility, and is advantageous in terms of price. [0003] However, with the increase in the usage of lithium secondary batteries, demands for large-capacity lithium secondary battery have gradually increased, and thus a large-capacity 2 anode active material that can replace a carbon material has been required. In order to meet such a requirement, attempts to use a metal (for example, silicon (Si)), having a larger chargedischarge capacity than a carbon material and capable of being electrochemically alloyed together with lithium, as an anode active material have been conducted. [0004] However, such as metal-based anode active material is problematic in that its volume is greatly changed during charging-discharging, and thus an active material layer is cracked. Therefore, a rechargeable battery including this metal-based anode active material is also problematic in that its capacity rapidly decreases during a charge-discharge cycle, and its lifecycle also decreases, and thus it is not commercially available. [0005] However, when a non-carbon material, such as SiO, is used as an anode active material, there are advantages in that high-capacity characteristics can be realized, and volume expansion with respect to Si can be controlled, compared to when a carbon material is used. Thus, research into non-carbon materials has been variously conducted. However, when a noncarbon material is used, there is a disadvantage in that by-products created by the reaction of Li and O cause an irreversible reaction, thus lowering the initial efficiency of a rechargeable battery. [0006] Therefore, in order to overcome the above problems, research into SiOx has been actively conducted. For example, Korean Patent Application Publication No. 2012- 7011002 discloses an anode active material for lithium secondary batteries, wherein SiOx is used as an anode active material. However, this anode active material is problematic in that chargedischarge cycle characteristics cannot be sufficiently improved, and in that the x value of SiOx cannot be easily adjusted by a conventional synthesis method. [Prior art document] [Patent document] (Patent document 1) Korean Patent Application Publication No. 2012-7011002 3 SUMMARY OF THE INVENTION [0007] The present invention has been made to solve the above-mentioned problems, and an object of the present invention is to provide a non-carbon-based anode active material for lithium secondary batteries, wherein the decrease in the initial efficiency of a lithium secondary battery, attributable to the initial irreversible reaction caused by oxygen (O) of a SiO material, can be prevented by the preparation of SiOx(x<1.0), and wherein volume expansion during charging-discharging, which is a disadvantage of silicon (Si), can be overcome by the application of silicon nanoparticles. [0008] In order to accomplish the above object, an aspect of the present invention provides a non-carbon-based anode active material for lithium secondary batteries, including: a core containing silicon (Si); and silicon nanoparticles formed on the surface of the core. [0009] The non-carbon-based anode active material may further include a coating layer formed on the surface of the core and containing carbon (C). [0010] Another aspect of the present invention provides a method of preparing a noncarbon- based anode active material for lithium secondary batteries, including the steps of: preparing a core containing silicon (Si); and mixing silicon nanoparticles with the core to attaching the silicon nanoparticles to the surface of the core. [0011] Still another aspect of the present invention provides a lithium secondary battery, including: an anode including the anode active material; a cathode including a cathode active material; and an electrolyte. [0012] When the non-carbon-based anode active material for lithium secondary batteries according to the present invention is used, an irreversible effect occurring during the initial charging of a lithium secondary battery is reduced to improve the initial efficiency of the 4 lithium secondary battery, and the increase in the volume expansion rate thereof during charging-discharging can be prevented by the application of silicon nanoparticles. Further, when the core containing silicon (Si) and the silicon nanoparticles are carbon-coated, the adhesivity and conductivity between the core and the silicon nanoparticles are enhanced to improve chargedischarge cycle characteristics. BRIEF DESCRIPTION OF THE DRAWINGS [0013] FIG. 1 and FIG. 2 are schematic view showing a process of preparing a noncarbon- based anode active material for lithium secondary batteries. DESCRIPTION OF THE PREFERRED EMBODIMENTS [0014] Hereinafter, preferred embodiment of the present invention will be described in detail. [0015] The non-carbon-based anode active material for lithium secondary batteries according to the present invention includes: a core containing silicon (Si); and silicon nanoparticles formed on the surface of the core. [0016] The core containing silicon (Si) has a particle diameter of 1 to 30 μm, preferably 3 to 20 μm, and more preferably 3 to 10 μm. When the particle diameter of the core is less than 1 μm, the purity of the core is lowered due to the surface oxidation thereof, and the core is bonded with nanosized silicon (Si) to cause agglomeration, and, when the particle diameter thereof is more than 30 μm, volume expansion increases, thus deteriorating cycle characteristics. 5 [0017] The core containing silicon (Si) may include SiOx (0